0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.12/0.34 % Computer : n012.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Aug 9 06:31:31 EDT 2022 0.12/0.34 % CPUTime : 22.80/21.89 ============================== Prover9 =============================== 22.80/21.89 Prover9 (32) version 2009-11A, November 2009. 22.80/21.89 Process 7697 was started by sandbox2 on n012.cluster.edu, 22.80/21.89 Tue Aug 9 06:31:50 2022 22.80/21.89 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_7541_n012.cluster.edu". 22.80/21.89 ============================== end of head =========================== 22.80/21.89 22.80/21.89 ============================== INPUT ================================= 22.80/21.89 22.80/21.89 % Reading from file /tmp/Prover9_7541_n012.cluster.edu 22.80/21.89 22.80/21.89 set(prolog_style_variables). 22.80/21.89 set(auto2). 22.80/21.89 % set(auto2) -> set(auto). 22.80/21.89 % set(auto) -> set(auto_inference). 22.80/21.89 % set(auto) -> set(auto_setup). 22.80/21.89 % set(auto_setup) -> set(predicate_elim). 22.80/21.89 % set(auto_setup) -> assign(eq_defs, unfold). 22.80/21.89 % set(auto) -> set(auto_limits). 22.80/21.89 % set(auto_limits) -> assign(max_weight, "100.000"). 22.80/21.89 % set(auto_limits) -> assign(sos_limit, 20000). 22.80/21.89 % set(auto) -> set(auto_denials). 22.80/21.89 % set(auto) -> set(auto_process). 22.80/21.89 % set(auto2) -> assign(new_constants, 1). 22.80/21.89 % set(auto2) -> assign(fold_denial_max, 3). 22.80/21.89 % set(auto2) -> assign(max_weight, "200.000"). 22.80/21.89 % set(auto2) -> assign(max_hours, 1). 22.80/21.89 % assign(max_hours, 1) -> assign(max_seconds, 3600). 22.80/21.89 % set(auto2) -> assign(max_seconds, 0). 22.80/21.89 % set(auto2) -> assign(max_minutes, 5). 22.80/21.89 % assign(max_minutes, 5) -> assign(max_seconds, 300). 22.80/21.89 % set(auto2) -> set(sort_initial_sos). 22.80/21.89 % set(auto2) -> assign(sos_limit, -1). 22.80/21.89 % set(auto2) -> assign(lrs_ticks, 3000). 22.80/21.89 % set(auto2) -> assign(max_megs, 400). 22.80/21.89 % set(auto2) -> assign(stats, some). 22.80/21.89 % set(auto2) -> clear(echo_input). 22.80/21.89 % set(auto2) -> set(quiet). 22.80/21.89 % set(auto2) -> clear(print_initial_clauses). 22.80/21.89 % set(auto2) -> clear(print_given). 22.80/21.89 assign(lrs_ticks,-1). 22.80/21.89 assign(sos_limit,10000). 22.80/21.89 assign(order,kbo). 22.80/21.89 set(lex_order_vars). 22.80/21.89 clear(print_given). 22.80/21.89 22.80/21.89 % formulas(sos). % not echoed (17292 formulas) 22.80/21.89 22.80/21.89 ============================== end of input ========================== 22.80/21.89 22.80/21.89 % From the command line: assign(max_seconds, 960). 22.80/21.89 22.80/21.89 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 22.80/21.89 22.80/21.89 % Formulas that are not ordinary clauses: 22.80/21.89 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 2 (all A all B (r1_tarski(A,B) <-> (all C (r2_hidden(C,A) -> r2_hidden(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 3 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 4 (all A all B -(r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & r2_hidden(D,C))))))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 5 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 6 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 8 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 9 (all A all B all C (p1_s1_tarski(A,B) & p1_s1_tarski(A,C) -> B = C)) -> (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,f1_s1_tarski) & p1_s1_tarski(C,B))))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 10 (all A all B all C (k2_tarski(A,B) = C <-> (all D (r2_hidden(D,C) <-> D = B | D = A)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 11 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 12 (all A exists B ((all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C -(-r2_hidden(C,B) & -r2_tarski(C,B) & r1_tarski(C,B))) & r2_hidden(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 13 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 14 (all A all B k2_tarski(k2_tarski(A,B),k1_tarski(A)) = k4_tarski(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 15 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 16 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 17 (all A all B (r2_tarski(A,B) <-> (exists C ((all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (E = G <-> F = D))) & (all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D -(r2_hidden(D,A) & (all E -(r2_hidden(k4_tarski(D,E),C) & r2_hidden(E,B))))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 19 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 20 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 21 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 22 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(D,A) & r2_hidden(C,D))))) <-> k3_tarski(A) = B)) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 23 (all A all B ((all C (r2_hidden(C,B) <-> A = C)) <-> B = k1_tarski(A))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 24 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 25 (all A all B (r1_xboole_0(A,B) <-> k3_xboole_0(A,B) = k1_xboole_0)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 26 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 27 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 28 (all A all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(D,A) & -r2_hidden(D,B))) <-> k4_xboole_0(A,B) = C)) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 29 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 30 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 31 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 32 (all A all B (r3_xboole_0(A,B) <-> r1_tarski(B,A) | r1_tarski(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 33 (all A all B all C ((all D (r2_hidden(D,A) & r2_hidden(D,B) <-> r2_hidden(D,C))) <-> C = k3_xboole_0(A,B))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 34 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f1_s2_xboole_0))) & (all A (r2_hidden(A,f2_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]. 22.80/21.89 35 (all A all B ((all C (r2_hidden(C,A) <-> p1_s3_xboole_0(C))) & (all C (r2_hidden(C,B) <-> p1_s3_xboole_0(C))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 36 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,A) | r2_hidden(D,B) <-> r2_hidden(D,C))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 37 (all A all B k5_xboole_0(A,B) = k5_xboole_0(B,A)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 38 (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]. 22.80/21.89 39 (all A all B k3_xboole_0(B,A) = k3_xboole_0(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 40 (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]. 22.80/21.89 41 (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]. 22.80/21.89 42 (all A all B (B = A <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 43 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 44 (all A ((all B -r2_hidden(B,A)) <-> k1_xboole_0 = A)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 45 (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]. 22.80/21.89 46 (all A all B all C -(r2_hidden(C,k2_xboole_0(A,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)) & -(r2_hidden(C,B) & -r2_hidden(C,A)) & r1_xboole_0(A,B))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 47 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 48 (all A all B (-((all C -(r2_hidden(C,B) & r2_hidden(C,A))) & -r1_xboole_0(A,B)) & -((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 49 (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]. 22.80/21.89 50 (all A all B k2_xboole_0(B,A) = k2_xboole_0(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 51 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 52 (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]. 22.80/21.89 53 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> A = k5_xboole_0(B,C))) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 54 (all A all B (-((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)) & -((exists C r2_hidden(C,k3_xboole_0(A,B))) & r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 55 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 56 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 57 (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]. 22.80/21.89 58 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 59 (exists A all B (p1_s1_xboole_0(B) & r2_hidden(B,f1_s1_xboole_0) <-> r2_hidden(B,A))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 60 (all A all B all C (r2_hidden(A,k5_xboole_0(B,C)) <-> -(r2_hidden(A,B) <-> r2_hidden(A,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 61 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 62 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 65 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 66 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 67 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 68 (all A all B -(v1_xboole_0(A) & B != A & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 69 (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]. 22.80/21.89 70 (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]. 22.80/21.89 71 (all A all B all C k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k5_xboole_0(A,C),B)) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 72 (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]. 22.80/21.89 73 (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]. 22.80/21.89 74 (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]. 22.80/21.89 75 (all A all B -(r2_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 76 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,C) & r1_tarski(A,B) -> A = k1_xboole_0)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 77 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 78 (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]. 22.80/21.89 79 (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]. 22.80/21.89 80 (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]. 22.80/21.89 81 (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]. 22.80/21.89 82 (all A all B k4_xboole_0(A,k2_xboole_0(A,B)) = k1_xboole_0) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 83 (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]. 22.80/21.89 84 (all A all B all C -(-r1_xboole_0(A,k3_xboole_0(B,C)) & r1_xboole_0(A,B))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 85 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 86 (all A all B all C k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 87 (all A all B all C -(r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)) & -r1_xboole_0(A,B))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 88 (all A all B all C k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C)))) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 89 (all A all B (r1_tarski(A,B) <-> k4_xboole_0(A,B) = k1_xboole_0)) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 90 (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]. 22.80/21.89 91 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 92 (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]. 22.80/21.89 93 (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]. 22.80/21.89 94 (all A all B -(r2_xboole_0(A,B) & k1_xboole_0 = k4_xboole_0(B,A))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 95 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 96 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 97 (all A all B all C (-v1_xboole_0(C) -> -(r1_tarski(C,A) & r1_tarski(C,B) & r1_xboole_0(A,B)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 98 (all A all B all C all D (k2_xboole_0(A,B) = k2_xboole_0(C,D) & r1_xboole_0(D,B) & r1_xboole_0(C,A) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.89 99 (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]. 22.80/21.90 100 (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]. 22.80/21.90 101 (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]. 22.80/21.90 102 (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]. 22.80/21.90 103 (all A all B (k4_xboole_0(A,B) = k4_xboole_0(B,A) -> B = A)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 104 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 105 (all A all B k3_xboole_0(A,B) = k4_xboole_0(A,k4_xboole_0(A,B))) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 106 (all A all B (A = k4_xboole_0(A,B) <-> r1_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 107 (all A all B (r1_tarski(A,B) -> k3_xboole_0(A,B) = A)) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 108 (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]. 22.80/21.90 109 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 110 (all A all B all C ((all D (r1_tarski(A,D) & r1_tarski(C,D) -> r1_tarski(B,D))) & r1_tarski(C,B) & r1_tarski(A,B) -> k2_xboole_0(A,C) = B)) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 111 (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]. 22.80/21.90 112 (all A (-(k1_xboole_0 = A & -r1_xboole_0(A,A)) & -(r1_xboole_0(A,A) & k1_xboole_0 != A))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 113 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 114 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> A = k1_xboole_0)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 115 (all A all B k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 116 (all A all B all C (r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,k2_xboole_0(B,C)) <-> r1_tarski(A,k5_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 117 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 118 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 119 (all A all B all C (k2_xboole_0(C,B) = k2_xboole_0(A,B) & r1_xboole_0(C,B) & r1_xboole_0(A,B) -> C = A)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 120 (all A all B k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 121 (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]. 22.80/21.90 122 (all A all B all C (r1_tarski(A,B) & (all D (r1_tarski(D,B) & r1_tarski(D,C) -> r1_tarski(D,A))) & r1_tarski(A,C) -> A = k3_xboole_0(B,C))) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 123 (all A all B all C (r1_xboole_0(A,B) -> k4_xboole_0(k2_xboole_0(C,B),A) = k2_xboole_0(k4_xboole_0(C,A),B))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 124 (all A all B (k1_xboole_0 = k2_xboole_0(A,B) -> A = k1_xboole_0)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 125 (all A all B all C k4_xboole_0(A,k3_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 126 (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]. 22.80/21.90 127 (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]. 22.80/21.90 128 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 129 (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]. 22.80/21.90 130 (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]. 22.80/21.90 131 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 132 (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]. 22.80/21.90 133 (all A all B A = k2_xboole_0(A,k3_xboole_0(A,B))) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 134 (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]. 22.80/21.90 135 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 136 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,k4_xboole_0(B,A)) = B)) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 137 (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]. 22.80/21.90 138 (all A all B all C (r1_tarski(A,B) & r1_tarski(B,C) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 139 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D) = k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D))) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 140 (all A all B all C k3_xboole_0(k4_xboole_0(A,C),B) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 141 (all A all B all C (r1_xboole_0(A,C) & r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 142 (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]. 22.80/21.90 143 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 144 (all A all B all C (r1_tarski(A,B) -> k2_xboole_0(A,k3_xboole_0(C,B)) = k3_xboole_0(k2_xboole_0(A,C),B))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 145 (all A all B all C k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C))) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 146 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C)) = k4_xboole_0(A,k5_xboole_0(B,C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 147 (all A all B (-(-r2_xboole_0(A,B) & A != B & -r2_xboole_0(B,A)) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 148 (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]. 22.80/21.90 149 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 150 (all A all B all C all D (r1_xboole_0(A,D) & r1_xboole_0(B,D) & r1_xboole_0(C,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 151 (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]. 22.80/21.90 152 (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]. 22.80/21.90 153 (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]. 22.80/21.90 154 (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]. 22.80/21.90 155 (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]. 22.80/21.90 156 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 157 (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]. 22.80/21.90 158 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 159 (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]. 22.80/21.90 160 (all A all B k4_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 161 (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]. 22.80/21.90 162 (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]. 22.80/21.90 163 (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]. 22.80/21.90 164 (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]. 22.80/21.90 165 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(A,C))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 166 (all A all B all C -(r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,C) & -r1_xboole_0(A,B))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 167 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k4_xboole_0(B,C))) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 168 (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]. 22.80/21.90 169 (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]. 22.80/21.90 170 (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]. 22.80/21.90 171 (all A all B all C k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) = k3_xboole_0(A,k4_xboole_0(B,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 172 (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]. 22.80/21.90 173 (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]. 22.80/21.90 174 (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]. 22.80/21.90 175 (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]. 22.80/21.90 176 (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]. 22.80/21.90 177 (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]. 22.80/21.90 178 (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]. 22.80/21.90 179 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 180 (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]. 22.80/21.90 181 (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,C) & r1_xboole_0(A,B)))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 182 (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]. 22.80/21.90 183 (all A all B all C k1_enumset1(A,B,C) = k6_enumset1(A,A,A,A,A,A,B,C)) # label(t93_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 184 (all A all B all C k1_enumset1(A,B,C) = k4_enumset1(A,A,A,A,B,C)) # label(t84_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 185 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k6_enumset1(A,A,A,A,B,C,D,E)) # label(t86_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 186 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,D,C)) # label(t109_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 187 (all A all B k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B)) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 188 (all A all B all C k2_enumset1(A,A,B,C) = k1_enumset1(A,B,C)) # label(t71_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 189 (all A k3_enumset1(A,A,A,A,A) = k1_tarski(A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 190 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 191 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_enumset1(A,B,C),k2_enumset1(D,E,F,G))) # label(t58_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 192 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 193 (all A all B all C all D all E k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E)) = k3_enumset1(A,B,C,D,E)) # label(t50_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 194 (all A all B all C all D all E all F all G all H k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 195 (all A all B all C all D all E all F k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 196 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H))) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 197 (all A all B all C all D all E all F all G k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t59_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 198 (all A all B all C all D all E k5_enumset1(A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t80_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 199 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H))) # label(t64_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 200 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H))) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 201 (all A all B all C k1_enumset1(B,A,C) = k1_enumset1(A,B,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 202 (all A all B all C all D all E all F all G k6_enumset1(A,A,B,C,D,E,F,G) = k5_enumset1(A,B,C,D,E,F,G)) # label(t75_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 203 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 204 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 205 (all A all B all C all D k2_enumset1(C,D,A,B) = k2_enumset1(A,B,C,D)) # label(t118_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 206 (all A all B all C all D k6_enumset1(A,A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t90_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 207 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 208 (all A all B all C k3_enumset1(A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t78_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 209 (all A all B all C all D all E all F ((all G (r2_hidden(G,F) <-> -(A != G & G != B & D != G & G != E & C != G))) <-> F = k3_enumset1(A,B,C,D,E))) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 210 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 211 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 212 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 213 (all A k1_tarski(A) = k6_enumset1(A,A,A,A,A,A,A,A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 214 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,C,A)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 215 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k5_enumset1(A,A,B,C,D,E,F)) # label(t74_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 216 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 217 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 218 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 219 (all A all B all C all D all E all F k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 220 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 221 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 222 (all A all B all C all D k2_enumset1(C,B,A,D) = k2_enumset1(A,B,C,D)) # label(t116_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 223 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 224 (all A all B all C all D all E all F all G all H all I (I = k6_enumset1(A,B,C,D,E,F,G,H) <-> (all J (r2_hidden(J,I) <-> -(E != J & J != H & J != G & F != J & D != J & C != J & J != B & J != A))))) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 225 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 226 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 227 (all A all B all C all D k2_enumset1(A,C,D,B) = k2_enumset1(A,B,C,D)) # label(t105_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 228 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 229 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D)) # label(t110_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 230 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 231 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 232 (all A all B all C all D k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(A,B,C,D)) # label(t45_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 233 (all A all B k2_tarski(A,B) = k6_enumset1(A,A,A,A,A,A,A,B)) # label(t95_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 234 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 235 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 236 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 237 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 238 (all A all B all C all D ((all E (-(E != A & B != E & C != E) <-> r2_hidden(E,D))) <-> D = k1_enumset1(A,B,C))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 239 (all A k1_tarski(A) = k2_tarski(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 240 (all A all B k2_tarski(A,B) = k5_enumset1(A,A,A,A,A,A,B)) # label(t92_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 241 (all A k1_tarski(A) = k4_enumset1(A,A,A,A,A,A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 242 (all A all B all C k1_enumset1(A,C,B) = k1_enumset1(A,B,C)) # label(t98_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 243 (all A all B k3_enumset1(A,A,A,A,B) = k2_tarski(A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 244 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 245 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H))) # label(t66_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 246 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 247 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 248 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 249 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 250 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,C,D,A)) # label(t111_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 251 (all A all B all C all D all E all F k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) = k4_enumset1(A,B,C,D,E,F)) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 252 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 253 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,B,D,C)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 254 (all A all B all C k1_enumset1(B,C,A) = k1_enumset1(A,B,C)) # label(t100_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 255 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,B,C,A)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 256 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 257 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 258 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 259 (all A all B all C k1_enumset1(A,B,C) = k5_enumset1(A,A,A,A,A,B,C)) # label(t89_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 260 (all A all B all C all D all E all F all G k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t57_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 261 (all A all B k2_tarski(A,B) = k2_enumset1(A,A,A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 262 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H))) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 263 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 264 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 265 (all A all B all C all D k2_enumset1(C,B,D,A) = k2_enumset1(A,B,C,D)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 266 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 267 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,D,C,B)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 268 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 269 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F))) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 270 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 271 (all A all B all C all D all E all F all G k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t56_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 272 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 273 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 274 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,D,A,C)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 275 (all A all B k2_tarski(A,B) = k1_enumset1(A,A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 276 (all A all B all C all D all E k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) = k3_enumset1(A,B,C,D,E)) # label(t49_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 277 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 278 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 279 (all A all B all C all D all E all F k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t53_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 280 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 281 (all A all B all C all D k2_enumset1(A,B,C,D) = k3_enumset1(A,A,B,C,D)) # label(t72_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 282 (all A all B all C all D k2_enumset1(C,D,B,A) = k2_enumset1(A,B,C,D)) # label(t119_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 283 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 284 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 285 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 286 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k6_enumset1(A,A,A,B,C,D,E,F)) # label(t81_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 287 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 288 (all A all B all C all D all E all F all G (k4_enumset1(A,B,C,D,E,F) = G <-> (all H (r2_hidden(H,G) <-> -(H != C & D != H & F != H & E != H & H != B & H != A))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 289 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 290 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C))) # label(t43_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 291 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 292 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D))) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 293 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 294 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G))) # label(t60_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 295 (all A all B all C all D all E ((all F (-(F != A & B != F & F != C & D != F) <-> r2_hidden(F,E))) <-> k2_enumset1(A,B,C,D) = E)) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 296 (all A all B all C all D all E all F all G k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 297 (all A all B k4_enumset1(A,A,A,A,A,B) = k2_tarski(A,B)) # label(t88_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 298 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 299 (all A k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 300 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(B,A,C,D)) # label(t108_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 301 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,C,B,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 302 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 303 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H))) # label(t65_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 304 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 305 (all A all B all C all D all E k4_enumset1(A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t73_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 306 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E))) # label(t47_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 307 (all A k2_enumset1(A,A,A,A) = k1_tarski(A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 308 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E))) # label(t48_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 309 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 310 (all A all B all C all D k5_enumset1(A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t85_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 311 (all A all B all C all D k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D)) = k2_enumset1(A,B,C,D)) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 312 (all A all B all C all D all E all F all G all H ((all I (r2_hidden(I,H) <-> -(I != A & C != I & I != G & F != I & E != I & I != D & I != B))) <-> H = k5_enumset1(A,B,C,D,E,F,G))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 313 (all A all B all C all D k4_enumset1(A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 314 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 315 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 316 (all A all B all C k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C))) # label(t42_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 317 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 318 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(C,B,A)) # label(t102_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 319 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 320 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 321 (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]. 22.80/21.90 322 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 323 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_xboole_0(k2_tarski(A,C),B) = B)) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 324 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> r1_xboole_0(C,D) | C = D)) -> k3_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]. 22.80/21.90 325 (all A all B (r2_hidden(A,B) <-> k4_xboole_0(k1_tarski(A),B) = k1_xboole_0)) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 326 (all A all B all C all D (r2_hidden(A,C) & r2_hidden(B,D) <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 327 (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]. 22.80/21.90 328 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 329 (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]. 22.80/21.90 330 (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]. 22.80/21.90 331 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))) <-> B = D & A = C)) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 332 (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]. 22.80/21.90 333 (all A all B k1_tarski(k4_tarski(A,B)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 334 (all A all B -(k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0 & k1_tarski(B) != A & A != k1_xboole_0)) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 335 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 336 (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]. 22.80/21.90 337 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 338 (all A all B all C -(k2_xboole_0(B,C) = k1_tarski(A) & C != B & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 339 (all A all B all C all D (k4_tarski(A,B) = k4_tarski(C,D) -> C = A & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 340 (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]. 22.80/21.90 341 (all A all B all C (-(k2_tarski(B,C) != A & k1_tarski(C) != A & A != k1_tarski(B) & A != k1_xboole_0) <-> k1_xboole_0 = k4_xboole_0(A,k2_tarski(B,C)))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 342 (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]. 22.80/21.90 343 (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]. 22.80/21.90 344 (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]. 22.80/21.90 345 (all A all B all C all D -(k2_tarski(C,D) = k2_tarski(A,B) & A != C & D != A)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 346 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 347 (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]. 22.80/21.90 348 (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]. 22.80/21.90 349 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 350 (all A all B (k1_xboole_0 = k2_zfmisc_1(A,B) <-> A = k1_xboole_0 | k1_xboole_0 = B)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 351 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 352 (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]. 22.80/21.90 353 (all A all B all C all D -(r1_tarski(A,k2_zfmisc_1(B,C)) & r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & D = k4_tarski(E,F) & r2_hidden(F,C))))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 354 (all A all B all C (r2_hidden(A,k4_xboole_0(B,k1_tarski(C))) <-> C != A & r2_hidden(A,B))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 355 (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]. 22.80/21.90 356 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 357 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k3_xboole_0(k2_tarski(A,C),B) = k2_tarski(A,C))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 358 (all A all B all C -(A != k1_xboole_0 & (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))) & -r1_tarski(B,C))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 359 (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]. 22.80/21.90 360 (all A all B k1_tarski(A) = k3_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 361 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 362 (all A all B k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B)) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 363 (all A all B (r2_hidden(A,B) -> k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 364 (all A all B (A = k1_tarski(B) | A = k1_xboole_0 <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 365 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 366 (all A all B k1_xboole_0 = k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 367 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 368 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 369 (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]. 22.80/21.90 370 (all A all B (r1_tarski(A,k2_zfmisc_1(A,B)) | r1_tarski(A,k2_zfmisc_1(B,A)) -> A = k1_xboole_0)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 371 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 372 (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]. 22.80/21.90 373 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 374 (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]. 22.80/21.90 375 (all A all B all C -(k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) & r2_hidden(B,C) & B != A)) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 376 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 377 (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]. 22.80/21.90 378 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 379 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 380 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 381 (all A all B all C (r2_hidden(B,C) & r2_hidden(A,C) <-> k1_xboole_0 = k4_xboole_0(k2_tarski(A,B),C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 382 (all A all B (A != B -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 383 (all A all B all C (-r2_hidden(A,C) & -r2_hidden(B,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 384 (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]. 22.80/21.90 385 (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]. 22.80/21.90 386 (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]. 22.80/21.90 387 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),B) | k4_xboole_0(k1_tarski(A),B) = k1_tarski(A))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 388 (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]. 22.80/21.90 389 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 390 (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]. 22.80/21.90 391 (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]. 22.80/21.90 392 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 393 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> B = A)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 394 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 395 (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]. 22.80/21.90 396 (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]. 22.80/21.90 397 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 398 (all A all B all C all D (r2_hidden(A,C) & D = B <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))))) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 399 (all A all B -(r1_xboole_0(k1_tarski(A),k1_tarski(B)) & A = B)) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 400 (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]. 22.80/21.90 401 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 402 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 403 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 404 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 405 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 406 (all A all B all C all D all E -(r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))) & (all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 407 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 408 (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]. 22.80/21.90 409 (all A all B -(A != k1_tarski(B) & (all C -(r2_hidden(C,A) & C != B)) & k1_xboole_0 != A)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 410 (all A exists B (r2_hidden(A,B) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & (all C -(-r2_hidden(C,B) & -r2_tarski(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 411 (all A all B all C all D (r1_xboole_0(C,D) | r1_xboole_0(A,B) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 412 (all A all B all C all D -(r1_tarski(k2_tarski(A,B),k2_tarski(C,D)) & A != C & A != D)) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 413 (all A all B all C -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D all E k4_tarski(D,E) != A))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 414 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 415 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 416 (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]. 22.80/21.90 417 (all A all B (B = k1_zfmisc_1(A) <-> (all C (r1_tarski(C,A) <-> r2_hidden(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 418 (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]. 22.80/21.90 419 (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]. 22.80/21.90 420 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 421 (all A all B all C (k2_zfmisc_1(k4_xboole_0(A,B),C) = k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k4_xboole_0(A,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 422 (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]. 22.80/21.90 423 (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]. 22.80/21.90 424 (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]. 22.80/21.90 425 (all A all B all C (k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k2_xboole_0(A,B)) & k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 426 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.90 427 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k1_tarski(B) & k1_tarski(C) != A & A != k2_tarski(B,C) & k1_xboole_0 != A))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 428 (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]. 22.80/21.91 429 (all A all B ((all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E C != k4_tarski(D,E)))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 430 (all A all B all C all D k2_zfmisc_1(k3_zfmisc_1(A,B,C),D) = k4_zfmisc_1(A,B,C,D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 431 (all A all B all C (C = k2_zfmisc_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E exists F (D = k4_tarski(E,F) & r2_hidden(F,B) & r2_hidden(E,A))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 432 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 433 (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]. 22.80/21.91 434 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 435 (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]. 22.80/21.91 436 (all A all B (k3_xboole_0(A,k1_tarski(B)) = k1_tarski(B) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 437 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 438 (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]. 22.80/21.91 439 (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]. 22.80/21.91 440 (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]. 22.80/21.91 441 (all A all B (k1_zfmisc_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 442 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 443 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 444 (all A all B all C -(B != A & C != A & r1_tarski(k1_tarski(A),k2_tarski(B,C)))) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 445 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 446 (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]. 22.80/21.91 447 (all A all B all C (r2_hidden(A,B) -> k3_xboole_0(k2_tarski(A,C),B) = k1_tarski(A) | A != C & r2_hidden(C,B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 448 (all A all B all C (-r2_hidden(A,C) & (B = A | r2_hidden(B,C)) <-> k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 449 (all A all B all C all D all E all F ((all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> A = D)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 450 (all A all B all C k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 451 (all A all B all C k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 452 (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_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)) = k2_zfmisc_1(k2_tarski(A,B),C))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 453 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> k1_xboole_0 = B | C = A & B = D | A = k1_xboole_0)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 454 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 455 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = A)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 456 (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]. 22.80/21.91 457 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> k1_xboole_0 = A | A = B | k1_xboole_0 = B)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 458 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 459 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 460 (all A all B k2_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k2_tarski(A,B)) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 461 (all A all B all C -(-r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B) & -r2_hidden(A,B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 462 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & -(k1_tarski(A) = C & B = k1_tarski(A)) & -(k1_tarski(A) = C & B = k1_xboole_0) & -(B = k1_tarski(A) & C = k1_xboole_0))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 463 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),B) | r1_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 464 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 465 (all A all B all C (k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k3_xboole_0(A,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 466 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)) & k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0)) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 467 (all A all B all C (r1_tarski(k2_tarski(A,B),C) <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 468 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 469 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 470 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 471 (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) = k3_xboole_0(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 472 (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]. 22.80/21.91 473 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 474 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 475 (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]. 22.80/21.91 476 (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]. 22.80/21.91 477 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 478 (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]. 22.80/21.91 479 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k4_subset_1(A,B,C)) = k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 480 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 481 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,C) | r2_hidden(E,D)))) -> k4_subset_1(A,C,D) = B))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 482 (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]. 22.80/21.91 483 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 484 (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]. 22.80/21.91 485 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k2_xboole_0(B,C) = k4_subset_1(A,B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 486 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 487 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 488 (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]. 22.80/21.91 489 (all A all B (m1_subset_1(B,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 490 (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]. 22.80/21.91 491 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (A != k1_xboole_0 -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 492 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 493 (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]. 22.80/21.91 494 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k5_subset_1(A,B,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 495 (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]. 22.80/21.91 496 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 498 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 499 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k3_subset_1(A,k3_subset_1(A,B)))) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 500 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 501 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 502 (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]. 22.80/21.91 503 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 504 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 505 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 506 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> A = B))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 507 (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]. 22.80/21.91 508 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 509 (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]. 22.80/21.91 510 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) <-> r1_tarski(B,k3_subset_1(A,C))))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 511 (all A all B ((-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))) & (v1_xboole_0(A) -> (v1_xboole_0(B) <-> m1_subset_1(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 512 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 513 (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]. 22.80/21.91 514 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k6_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),C))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 515 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,B)) <-> B = k1_subset_1(A)))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 516 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 517 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 518 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f2_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) -> f2_s4_subset_1 = f3_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 519 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 520 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 521 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_xboole_0(B,k3_subset_1(A,C))))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 522 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 523 (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]. 22.80/21.91 524 (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]. 22.80/21.91 525 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k2_subset_1(A) = k4_subset_1(A,B,k3_subset_1(A,B)))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 526 (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]. 22.80/21.91 527 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 528 (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)))) -> k5_subset_1(A,C,D) = B))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 529 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -r2_hidden(E,D) & r2_hidden(E,C)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 530 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> B = k2_subset_1(A)))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 531 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(B) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 532 (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]. 22.80/21.91 533 (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]. 22.80/21.91 534 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 535 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 536 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 537 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 538 (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]. 22.80/21.91 539 (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]. 22.80/21.91 540 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_xboole_0(D,C) & r1_tarski(B,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 541 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 542 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 543 (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]. 22.80/21.91 544 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 545 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 546 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & B != k1_xboole_0))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 547 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 548 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 549 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 550 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 551 (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]. 22.80/21.91 552 (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]. 22.80/21.91 553 (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]. 22.80/21.91 554 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 555 (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]. 22.80/21.91 556 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 557 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 558 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 559 (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]. 22.80/21.91 560 (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]. 22.80/21.91 561 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 562 (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]. 22.80/21.91 563 (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]. 22.80/21.91 564 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 565 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 566 (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]. 22.80/21.91 567 (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]. 22.80/21.91 568 (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]. 22.80/21.91 569 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 570 (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]. 22.80/21.91 571 (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)) -> B = k3_subset_1(A,C)))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 572 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (-(r2_hidden(E,D) <-> r2_hidden(E,C)) <-> r2_hidden(E,B)))) -> k7_subset_1(A,C,D) = B))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 573 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 574 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 575 (all A (m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) & v1_xboole_0(k1_subset_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 576 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 577 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 578 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,k7_setfam_1(A,C)) <-> r1_tarski(k7_setfam_1(A,B),C)))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 579 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> ((all D (r2_hidden(D,C) -> r2_hidden(B,D))) <-> r2_hidden(B,k8_setfam_1(A,C)))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 580 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_tarski(A) = B -> k1_tarski(k1_xboole_0) = k7_setfam_1(A,B)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 581 (exists A (v1_setfam_1(A) & -v1_xboole_0(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 582 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 583 (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]. 22.80/21.91 584 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(-r1_tarski(D,B) & -r1_tarski(D,A) & r2_hidden(D,C))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 585 (all A all B (B != k1_xboole_0 -> k4_xboole_0(A,k3_tarski(B)) = k1_setfam_1(k4_setfam_1(k1_tarski(A),B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 586 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 587 (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]. 22.80/21.91 588 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 589 (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]. 22.80/21.91 590 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 591 (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]. 22.80/21.91 592 (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]. 22.80/21.91 593 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 594 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 595 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 596 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 597 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 598 (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]. 22.80/21.91 599 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 600 (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]. 22.80/21.91 601 (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]. 22.80/21.91 602 (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]. 22.80/21.91 603 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 604 (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]. 22.80/21.91 605 (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]. 22.80/21.91 606 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 607 (all A all B ((k1_xboole_0 != A -> ((all C (r2_hidden(C,B) <-> (all D (r2_hidden(D,A) -> r2_hidden(C,D))))) <-> B = k1_setfam_1(A))) & (A = k1_xboole_0 -> (B = k1_setfam_1(A) <-> B = k1_xboole_0)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 608 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = B -> k8_setfam_1(A,B) = A) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 609 (all A all B all C (r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) & (all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 610 (all A all B (r1_tarski(A,B) -> k1_xboole_0 = A | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 611 (all A all B (r2_setfam_1(B,A) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 612 (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]. 22.80/21.91 613 (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]. 22.80/21.91 614 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 615 (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]. 22.80/21.91 616 (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]. 22.80/21.91 617 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D ((exists E exists F (r2_hidden(E,A) & D = k3_xboole_0(E,F) & r2_hidden(F,B))) <-> r2_hidden(D,C))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 618 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 619 (all A (v1_setfam_1(A) <-> -r2_hidden(k1_xboole_0,A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 620 (all A all B k3_xboole_0(A,B) = k1_setfam_1(k2_tarski(A,B))) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 621 (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]. 22.80/21.91 622 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k2_xboole_0(E,F) = D & r2_hidden(F,B))))) <-> k2_setfam_1(A,B) = C)) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 623 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 624 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 625 (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]. 22.80/21.91 626 (all A all B (v1_setfam_1(A) & v1_setfam_1(B) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 627 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 628 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_xboole_0(B) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 629 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 630 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k4_xboole_0(E,F))))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 631 (all A all B (r2_setfam_1(A,B) <-> (all C -((all D -(r1_tarski(D,C) & r2_hidden(D,A))) & r2_hidden(C,B))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 632 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 633 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 634 (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]. 22.80/21.91 635 (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]. 22.80/21.91 636 (all A (r1_setfam_1(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 637 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 638 (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]. 22.80/21.91 639 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,B) = k7_setfam_1(A,C) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 640 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (C = k7_setfam_1(A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(k3_subset_1(A,D),B) <-> r2_hidden(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 641 (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]. 22.80/21.91 642 (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]. 22.80/21.91 643 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 644 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 645 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 646 (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]. 22.80/21.91 647 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 648 (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]. 22.80/21.91 649 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 650 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 651 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> k1_xboole_0 = A | r1_tarski(B,k1_setfam_1(A)))) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 652 (all A all B -(k1_xboole_0 != B & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != A)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 653 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 654 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 655 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k7_setfam_1(A,B) = k1_xboole_0 & B != k1_xboole_0))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 656 (all A all B k2_setfam_1(B,A) = k2_setfam_1(A,B)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 657 (all A all B ((all C -((all D -(r1_tarski(C,D) & r2_hidden(D,B))) & r2_hidden(C,A))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 658 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 659 (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]. 22.80/21.91 660 (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]. 22.80/21.91 661 (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]. 22.80/21.91 662 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 663 (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]. 22.80/21.91 664 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 665 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 666 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 667 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k1_setfam_1(B) = k6_setfam_1(A,B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 668 (all A (v1_setfam_1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 669 (all A all B (B != k1_xboole_0 -> 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]. 22.80/21.91 670 (all A all B (B != k1_xboole_0 -> k1_setfam_1(k2_setfam_1(k1_tarski(A),B)) = k2_xboole_0(A,k1_setfam_1(B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 671 (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]. 22.80/21.91 672 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 673 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 674 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 675 (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]. 22.80/21.91 676 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k7_relat_1(B,A) <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 677 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 678 (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]. 22.80/21.91 679 (all A (v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k1_relat_1(k4_relat_1(A)))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 680 (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]. 22.80/21.91 681 (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]. 22.80/21.91 682 (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]. 22.80/21.91 683 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))) # label(t14_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 684 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 = k9_relat_1(B,A)))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 685 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 686 (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]. 22.80/21.91 687 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 688 (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]. 22.80/21.91 689 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 690 (all A (v1_relat_1(A) -> k8_relat_1(k2_relat_1(A),A) = A)) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 691 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k8_relat_1(A,C),B) = k8_relat_1(A,k7_relat_1(C,B)))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 692 (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]. 22.80/21.91 693 (exists A ((all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C) & r2_hidden(B,f1_s1_relat_1))) & v1_relat_1(A))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 694 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k9_relat_1(B,k2_relat_1(A)) = k2_relat_1(k5_relat_1(A,B)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 695 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 696 (all A (v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))) <-> r2_hidden(D,C))) <-> k9_relat_1(A,B) = C)))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 697 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 698 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 699 (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]. 22.80/21.91 700 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 701 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 702 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 703 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> (C = k7_relat_1(A,B) <-> (all D all E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 704 (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]. 22.80/21.91 705 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_relat_1(A),k1_relat_1(B)) & r1_tarski(k2_relat_1(A),k2_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 706 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 707 (all A all B (v1_relat_1(B) -> k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) = k10_relat_1(B,A))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 708 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k3_xboole_0(A,B)) = k7_relat_1(k7_relat_1(C,A),B))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 709 (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]. 22.80/21.91 710 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.91 711 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 712 (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]. 22.80/21.92 713 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,B) = k1_xboole_0))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 714 (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]. 22.80/21.92 715 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 716 (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]. 22.80/21.92 717 (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]. 22.80/21.92 718 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 719 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 720 (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))) <-> B = A))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 721 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 722 (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]. 22.80/21.92 723 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 | k1_relat_1(A) = k1_xboole_0 -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 724 (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]. 22.80/21.92 725 (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]. 22.80/21.92 726 (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]. 22.80/21.92 727 (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]. 22.80/21.92 728 (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]. 22.80/21.92 729 (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]. 22.80/21.92 730 (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]. 22.80/21.92 731 (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]. 22.80/21.92 732 (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]. 22.80/21.92 733 (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]. 22.80/21.92 734 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 735 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 736 (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]. 22.80/21.92 737 (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]. 22.80/21.92 738 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 739 (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]. 22.80/21.92 740 (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]. 22.80/21.92 741 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 742 (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]. 22.80/21.92 743 (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]. 22.80/21.92 744 (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]. 22.80/21.92 745 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 746 (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]. 22.80/21.92 747 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 748 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 749 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(A,k2_relat_1(k8_relat_1(B,C)))))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 750 (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]. 22.80/21.92 751 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,B) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 752 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0 & k1_xboole_0 != A))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 753 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(D,C),A))) <-> B = k4_relat_1(A)))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 754 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 755 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 756 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 757 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 758 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 759 (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]. 22.80/21.92 760 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 761 (all A (v1_relat_1(A) -> k4_relat_1(k4_relat_1(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 762 (all A k6_relat_1(A) = k4_relat_1(k6_relat_1(A))) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 763 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 764 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 765 (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]. 22.80/21.92 766 (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]. 22.80/21.92 767 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 768 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 769 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C) <-> r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C)))))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 770 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) = k5_relat_1(A,k2_xboole_0(B,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 771 (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]. 22.80/21.92 772 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = k1_tarski(A)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 773 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 774 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 775 (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]. 22.80/21.92 776 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 777 (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]. 22.80/21.92 778 (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]. 22.80/21.92 779 (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]. 22.80/21.92 780 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 781 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 782 (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]. 22.80/21.92 783 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_relat_1(C)) & r2_hidden(A,k1_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 784 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 785 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 786 (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]. 22.80/21.92 787 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 788 (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]. 22.80/21.92 789 (exists A (v1_relat_1(A) & v1_xboole_0(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 790 (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]. 22.80/21.92 791 (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]. 22.80/21.92 792 (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(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 793 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (r1_tarski(C,D) & k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 794 (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]. 22.80/21.92 795 (all A all B (v1_relat_1(B) -> (B = k6_relat_1(A) <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & C = D))))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 796 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k5_relat_1(B,k6_relat_1(A))))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 797 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 798 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 799 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 800 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k9_relat_1(B,A) <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 801 (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]. 22.80/21.92 802 (all A (v1_relat_1(A) -> k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))) = A)) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 803 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(A,D),C))) <-> r2_hidden(A,k10_relat_1(C,B))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 804 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 805 (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]. 22.80/21.92 806 (all A all B (v1_relat_1(B) -> k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 807 (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]. 22.80/21.92 808 (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]. 22.80/21.92 809 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 810 (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]. 22.80/21.92 811 (all A all B (v1_relat_1(B) -> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 812 (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]. 22.80/21.92 813 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k2_xboole_0(A,B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 814 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 815 (all A all B (v1_relat_1(B) -> -(v3_relat_1(B) & -v3_relat_1(k7_relat_1(B,A))))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 816 (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]. 22.80/21.92 817 (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]. 22.80/21.92 818 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k6_relat_1(k1_relat_1(D)) = k5_relat_1(C,B) & k6_relat_1(A) = k5_relat_1(B,D) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(B) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 819 (all A (v1_xboole_0(A) -> v1_relat_1(k4_relat_1(A)) & v1_xboole_0(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 820 (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]. 22.80/21.92 821 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 822 (all A all B all C all D all E (v1_relat_1(E) -> (k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = E -> k2_tarski(B,D) = k2_relat_1(E) & k2_tarski(A,C) = k1_relat_1(E)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 823 (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]. 22.80/21.92 824 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 825 (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]. 22.80/21.92 826 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k1_relat_1(B)) & (all C -r2_hidden(C,k2_relat_1(B)))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 827 (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]. 22.80/21.92 828 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 829 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 830 (all A all B (v1_relat_1(B) -> k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)) = k8_relat_1(A,B))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 831 (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]. 22.80/21.92 832 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 833 (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]. 22.80/21.92 834 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 835 (all A (v1_relat_1(A) -> (r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0)) <-> v3_relat_1(A)))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 836 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> k2_relat_1(A) = B)))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 837 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 838 (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]. 22.80/21.92 839 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 840 (all A (v1_xboole_0(A) -> v1_relat_1(k2_relat_1(A)) & v1_xboole_0(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 841 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 842 (all A (v1_relat_1(A) -> (all B all C (C = k10_relat_1(A,B) <-> (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]. 22.80/21.92 843 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v3_relat_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 844 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 845 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 846 (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]. 22.80/21.92 847 (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]. 22.80/21.92 848 (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]. 22.80/21.92 849 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k2_tarski(A,B) = k3_relat_1(C)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 850 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 851 (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]. 22.80/21.92 852 (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]. 22.80/21.92 853 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 854 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 855 (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]. 22.80/21.92 856 (all A (v1_relat_1(A) -> k1_xboole_0 = k9_relat_1(A,k1_xboole_0))) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 857 (all A (v1_relat_1(A) -> k1_xboole_0 = k5_relat_1(k1_xboole_0,A) & k5_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 858 (all A (v1_relat_1(A) -> ((all B (r2_hidden(B,k2_relat_1(A)) -> B = k1_xboole_0)) <-> v3_relat_1(A)))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 859 (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]. 22.80/21.92 860 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 861 (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]. 22.80/21.92 862 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,k5_relat_1(B,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 863 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 864 (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]. 22.80/21.92 865 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 866 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 867 (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]. 22.80/21.92 868 (all A (v1_relat_1(A) <-> (all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 869 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> 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]. 22.80/21.92 870 (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]. 22.80/21.92 871 (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]. 22.80/21.92 872 (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]. 22.80/21.92 873 (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]. 22.80/21.92 874 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 875 (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]. 22.80/21.92 876 (all A (v1_relat_1(A) -> k1_xboole_0 = k10_relat_1(A,k1_xboole_0))) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 877 (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]. 22.80/21.92 878 (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]. 22.80/21.92 879 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 880 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 881 (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]. 22.80/21.92 882 (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]. 22.80/21.92 883 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 884 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 885 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k2_relat_1(k8_relat_1(A,B)) = A))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 886 (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]. 22.80/21.92 887 (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]. 22.80/21.92 888 (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]. 22.80/21.92 889 (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]. 22.80/21.92 890 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 891 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B))) <-> C = k8_relat_1(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 892 (all A (v1_relat_1(A) -> k1_xboole_0 = k8_relat_1(k1_xboole_0,A))) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 893 (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]. 22.80/21.92 894 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C))) <-> k5_relat_1(A,B) = C))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 895 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k1_xboole_0 = k7_relat_1(A,B))))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 896 (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]. 22.80/21.92 897 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 898 (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]. 22.80/21.92 899 (all A (v1_relat_1(A) -> (all B ((all C ((exists D r2_hidden(k4_tarski(C,D),A)) <-> r2_hidden(C,B))) <-> B = k1_relat_1(A))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 900 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k7_relat_1(B,A),C) = k7_relat_1(k5_relat_1(B,C),A))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 901 (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]. 22.80/21.92 902 (all A all B (v1_relat_1(B) -> k2_relat_1(k8_relat_1(A,B)) = k3_xboole_0(k2_relat_1(B),A))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 903 (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]. 22.80/21.92 904 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 905 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A)))) <-> r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A)))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 906 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 907 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 908 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & (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) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 909 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 910 (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 B != k4_tarski(C,D)) & r2_hidden(B,A))) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 911 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 912 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(B,A) = k9_relat_1(k2_funct_1(B),A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 913 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 914 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 915 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 916 (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))) -> k1_funct_1(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 917 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 918 (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]. 22.80/21.92 919 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 920 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 921 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_tarski(A) = k1_relat_1(B) -> k2_relat_1(B) = k1_tarski(k1_funct_1(B,A))))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 922 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 923 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 924 (all A all B -(-(k1_xboole_0 != B & k1_xboole_0 = A) & (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]. 22.80/21.92 925 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 926 (exists A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 927 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 928 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 929 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 930 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 931 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 932 (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(B) = k1_relat_1(A) -> A = B))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 933 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 934 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k9_relat_1(k6_relat_1(A),B))) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 935 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(A) & v2_funct_1(B)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 936 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 937 (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]. 22.80/21.92 938 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 939 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A)))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 940 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 941 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 942 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(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]. 22.80/21.92 943 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 944 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 945 (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) & k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 946 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (v1_funct_1(B) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 947 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 948 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 949 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 950 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 951 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_relat_1(k5_relat_1(k6_relat_1(A),B)) = k3_xboole_0(k1_relat_1(B),A))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 952 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 953 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 954 (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]. 22.80/21.92 955 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 956 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(D) & k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(C) = A & k2_relat_1(B) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 957 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 958 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> C = k1_funct_1(A,B))) & (r2_hidden(B,k1_relat_1(A)) -> (k1_funct_1(A,B) = C <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 959 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 960 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 961 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & k1_relat_1(B) = k1_relat_1(C) & k5_relat_1(B,A) = k5_relat_1(C,A) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> C = B))))) <-> v2_funct_1(A)))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 962 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 963 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k6_relat_1(A) = B <-> k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 964 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 965 (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)) & k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) = A))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 966 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 967 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 968 (all A all B (v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & k10_relat_1(B,k1_tarski(C)) = k1_xboole_0)) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 969 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_funct_1(A) <-> (all C all D ((C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> r2_hidden(C,k2_relat_1(A)) & D = k1_funct_1(B,C)) & (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))) & k1_relat_1(B) = k2_relat_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 970 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.92 971 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B -((all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))) & r2_hidden(B,k2_relat_1(A))))))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 972 (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))) & f1_s3_funct_1 = k1_relat_1(A) & v1_funct_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 973 (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]. 22.80/21.93 974 (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(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A))))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 975 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 976 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 977 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),B) = k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 978 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 979 (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) & (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) -> (exists A (v1_relat_1(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))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 980 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 981 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k1_relat_1(B) = k2_relat_1(A) -> k2_funct_1(A) = B))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 982 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 983 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(C,k1_relat_1(A)) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 984 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,B) = k10_relat_1(C,A) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 985 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 986 (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]. 22.80/21.93 987 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 988 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 989 (all A (v1_relat_1(A) & v1_funct_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]. 22.80/21.93 990 (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]. 22.80/21.93 991 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 992 (all A (v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 993 (all A (v1_relat_1(A) & v1_funct_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]. 22.80/21.93 994 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 995 (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]. 22.80/21.93 996 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 997 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 998 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (C = k10_relat_1(A,B) <-> (all D (r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,C))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 999 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1000 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,k1_funct_1(B,A)) = k1_funct_1(k5_relat_1(B,C),A)))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1001 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1002 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1003 (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) -> (k1_relat_1(C) = A & k5_relat_1(B,D) = k5_relat_1(B,C) & A = k1_relat_1(D) -> C = D))))) -> k2_relat_1(B) = A))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1004 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1005 (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]. 22.80/21.93 1006 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D ((exists E (r2_hidden(E,B) & D = k1_funct_1(A,E) & r2_hidden(E,k1_relat_1(A)))) <-> r2_hidden(D,C))) <-> C = k9_relat_1(A,B))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1007 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A)) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1008 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1009 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_relat_1(A) <-> (all B -(r2_hidden(B,k1_relat_1(A)) & v1_xboole_0(k1_funct_1(A,B))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1010 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> k2_funct_1(k5_relat_1(A,B)) = k5_relat_1(k2_funct_1(B),k2_funct_1(A))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1011 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(k1_funct_1(B,D) = C & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1012 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1013 (all A (v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1014 (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]. 22.80/21.93 1015 (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(C) & A = k1_relat_1(B) -> B = C))))) -> A = k1_xboole_0)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1016 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1017 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1018 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1019 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1020 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1021 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1022 (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(C)) & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1023 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1024 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> k9_relat_1(C,k2_tarski(A,B)) = k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1025 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 22.80/21.93 1026 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1027 (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,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]. 22.80/21.93 1028 (all A (k1_xboole_0 != A -> (all B exists C (k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1029 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1030 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1031 (all A all B k6_relat_1(k3_xboole_0(A,B)) = k5_relat_1(k6_relat_1(B),k6_relat_1(A))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1032 (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]. 22.80/21.93 1033 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1034 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1035 (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]. 22.80/21.93 1036 (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(B) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(C) & k1_relat_1(C) = k1_relat_1(B) -> C = B))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1037 (all A (v1_relat_1(A) & v1_funct_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]. 22.80/21.93 1038 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1039 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1040 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1041 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_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]. 22.80/21.93 1042 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1043 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k2_funct_1(A)) = k1_relat_1(A) & k1_relat_1(k2_funct_1(A)) = k2_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1044 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1045 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(B) & k5_relat_1(C,B) = B & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(C) & A = k1_relat_1(B) -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1046 (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]. 22.80/21.93 1047 (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]. 22.80/21.93 1048 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1049 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k1_funct_1(A,D)) = k1_funct_1(C,D))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1050 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1051 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1052 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1053 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1054 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1055 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1056 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) & r2_hidden(B,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1057 (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]. 22.80/21.93 1058 (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]. 22.80/21.93 1059 (all A all B all C (p1_s1_funct_1(A,B) & p1_s1_funct_1(A,C) -> C = B)) -> (exists A (v1_relat_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> p1_s1_funct_1(B,C) & r2_hidden(B,f1_s1_funct_1))) & v1_funct_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1060 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1061 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k8_relat_1(A,C) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1062 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1063 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1064 (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))) <-> r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1065 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1066 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A)))))) <-> k2_relat_1(A) = B)))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1067 (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]. 22.80/21.93 1068 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1069 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1070 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1071 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (B = k1_funct_1(C,A) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1072 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k9_relat_1(B,k10_relat_1(B,A)) = k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1073 (all A all B (v1_relat_1(B) -> (k10_relat_1(B,k1_tarski(A)) != k1_xboole_0 <-> r2_hidden(A,k2_relat_1(B))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1074 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1075 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1076 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & 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]. 22.80/21.93 1077 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1078 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1079 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1080 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1081 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1082 (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]. 22.80/21.93 1083 (exists A (v1_relat_1(A) & k1_relat_1(A) = f1_s4_funct_1 & (all B (m1_subset_1(B,f1_s4_funct_1) -> f2_s4_funct_1(B) = k1_funct_1(A,B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1084 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1085 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k5_relat_1(A,k2_funct_1(A)) = k6_relat_1(k1_relat_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]. 22.80/21.93 1086 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_funct_1(A) = k4_relat_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1087 (all A (v1_relat_1(A) & v1_funct_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1088 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1089 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1090 (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]. 22.80/21.93 1091 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & k5_relat_1(A,B) = A -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1092 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1093 (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]. 22.80/21.93 1094 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k4_xboole_0(A,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1095 (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]. 22.80/21.93 1096 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1097 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1098 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k3_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1099 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1100 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1101 (all A (v1_relat_1(A) -> (all B (r6_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) & D != C)))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1102 (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]. 22.80/21.93 1103 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1104 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r4_relat_2(A,k3_relat_1(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1105 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1106 (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]. 22.80/21.93 1107 (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]. 22.80/21.93 1108 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1109 (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]. 22.80/21.93 1110 (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]. 22.80/21.93 1111 (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]. 22.80/21.93 1112 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r2_relat_2(A,k3_relat_1(A))))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1113 (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]. 22.80/21.93 1114 (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]. 22.80/21.93 1115 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A)))))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1116 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1117 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1118 (all A (v1_relat_1(A) -> (v3_relat_2(A) <-> r3_relat_2(A,k3_relat_1(A))))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1119 (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]. 22.80/21.93 1120 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k1_relat_1(A) = k1_relat_1(k4_relat_1(A)) & k2_relat_1(A) = k2_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1121 (all A (v1_relat_1(A) -> (v1_relat_2(A) <-> r1_tarski(k6_relat_1(k3_relat_1(A)),A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1122 (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]. 22.80/21.93 1123 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(C,B) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1124 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) & 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]. 22.80/21.93 1125 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1126 (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]. 22.80/21.93 1127 (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(E,B) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1128 (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]. 22.80/21.93 1129 (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]. 22.80/21.93 1130 (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]. 22.80/21.93 1131 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1132 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1133 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1134 (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]. 22.80/21.93 1135 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v1_relat_2(A) & v6_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1136 (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]. 22.80/21.93 1137 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r1_xboole_0(k6_relat_1(k3_relat_1(A)),A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1138 (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]. 22.80/21.93 1139 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(B) & v8_relat_2(A) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1140 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1141 (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]. 22.80/21.93 1142 (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]. 22.80/21.93 1143 (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]. 22.80/21.93 1144 (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]. 22.80/21.93 1145 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1146 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1147 (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]. 22.80/21.93 1148 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1149 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(B) & v3_relat_2(A) -> v3_relat_2(k4_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k2_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1150 (all A (v1_relat_1(A) -> (all B (r5_relat_2(A,B) <-> (all C all D -(r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1151 (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]. 22.80/21.93 1152 (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]. 22.80/21.93 1153 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A))) <-> r7_relat_2(A,B))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1154 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(B) & v5_relat_2(A) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1155 (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]. 22.80/21.93 1156 (all A (v1_relat_1(A) -> (v1_relat_2(A) <-> r1_relat_2(A,k3_relat_1(A))))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1157 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1158 (all A (v1_relat_1(A) -> (r8_relat_2(A,k3_relat_1(A)) <-> v8_relat_2(A)))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1159 (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]. 22.80/21.93 1160 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1161 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1162 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1163 (all A (v1_relat_1(A) -> (r7_relat_2(A,k3_relat_1(A)) <-> v7_relat_2(A)))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1164 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1165 (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]. 22.80/21.93 1166 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1167 (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]. 22.80/21.93 1168 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1169 (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]. 22.80/21.93 1170 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1171 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1172 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1173 (all A (v3_ordinal1(A) -> -(v4_ordinal1(A) & (exists B (A = k1_ordinal1(B) & v3_ordinal1(B)))) & -((all B (v3_ordinal1(B) -> k1_ordinal1(B) != A)) & -v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1174 (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]. 22.80/21.93 1175 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1176 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1177 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1178 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1179 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1180 (all A all B (v3_ordinal1(B) -> -(A != k1_xboole_0 & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & r1_tarski(A,B)))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1181 (all A all B all C all D -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,A) & r2_hidden(C,D))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1182 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1183 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(A,B) & r2_hidden(C,A) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1184 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r2_hidden(A,k1_ordinal1(B))))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1185 (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]. 22.80/21.93 1186 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1187 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1188 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1189 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1190 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1191 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1192 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> r2_hidden(A,B) | A = B)) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1193 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1194 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1195 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1196 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1197 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r1_tarski(A,B) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1198 (all A ((all B all C -(r2_hidden(C,A) & -r2_hidden(C,B) & B != C & -r2_hidden(B,C) & r2_hidden(B,A))) <-> v2_ordinal1(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1199 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1200 (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]. 22.80/21.93 1201 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1202 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1203 (all A all B all C all D all E all F -(r2_hidden(A,B) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(D,E) & r2_hidden(C,D) & r2_hidden(B,C))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1204 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v1_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1205 (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]. 22.80/21.93 1206 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r2_hidden(B,A) | r1_ordinal1(A,B))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1207 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1208 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> (r1_tarski(A,B) <-> r1_ordinal1(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1209 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(k1_ordinal1(A),B) <-> r2_hidden(A,B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1210 (exists A (v1_relat_1(A) & f1_s4_ordinal1 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) -> (C = k2_ordinal1(A,B) & r2_hidden(B,f1_s4_ordinal1) -> k1_funct_1(A,B) = f2_s4_ordinal1(C)))))) & v5_ordinal1(A) & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1211 (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]. 22.80/21.93 1212 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1213 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1214 (all A exists B (v3_ordinal1(B) & -r2_hidden(B,A) & (all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1215 (all A all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1216 (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]. 22.80/21.93 1217 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1218 (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]. 22.80/21.93 1219 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(B,A) & A != B & -r2_xboole_0(A,B)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1220 k1_relat_1(f3_s3_ordinal1) = f1_s3_ordinal1 & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> k1_funct_1(f4_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f3_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f3_s3_ordinal1,A)))))) -> f3_s3_ordinal1 = f4_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1221 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1222 (all A k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A))) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1223 (all A (v4_ordinal1(A) <-> k3_tarski(A) = A)) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1224 (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]. 22.80/21.93 1225 (all A (v3_ordinal1(A) -> v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1226 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1227 (all A all B all C all D all E -(r2_hidden(C,D) & r2_hidden(E,A) & r2_hidden(D,E) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.93 1228 (all A (v1_xboole_0(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1229 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A ((all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A) & v3_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1230 (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]. 22.80/21.94 1231 (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]. 22.80/21.94 1232 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1233 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1234 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1235 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1236 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1237 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(B,A) & A != B & -r2_hidden(A,B)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1238 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1239 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f3_s5_ordinal1(C) = B & v1_relat_1(C))) <-> f2_s5_ordinal1(A) = B)))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_s5_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1240 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1241 (all A (v6_ordinal1(A) & (all B (r2_hidden(B,A) -> v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B))) -> v1_funct_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_relat_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1242 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1243 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1244 (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]. 22.80/21.94 1245 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1246 (all A (v1_relat_1(A) -> -((all B -(r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A))))) & k3_relat_1(A) != k1_xboole_0 & v2_wellord1(A)))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1247 (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]. 22.80/21.94 1248 (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]. 22.80/21.94 1249 (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]. 22.80/21.94 1250 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1251 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,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]. 22.80/21.94 1252 (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]. 22.80/21.94 1253 (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]. 22.80/21.94 1254 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r3_wellord1(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]. 22.80/21.94 1255 (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]. 22.80/21.94 1256 (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]. 22.80/21.94 1257 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r1_wellord1(A,B) & r6_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B) <-> r2_wellord1(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1258 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r2_hidden(B,k3_relat_1(A)) & r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B)))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1259 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1260 (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]. 22.80/21.94 1261 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) <-> (exists C (v1_relat_1(C) & r3_wellord1(A,B,C) & v1_funct_1(C)))))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1262 (all A (v1_relat_1(A) -> (r1_wellord1(A,k3_relat_1(A)) <-> v1_wellord1(A)))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1263 (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]. 22.80/21.94 1264 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> k1_xboole_0 = k3_relat_1(A) | (all B -((exists C (-r2_hidden(k4_tarski(C,B),A) & r2_hidden(C,k3_relat_1(A)))) & (all C -(r2_hidden(k4_tarski(B,C),A) & (all D -(r2_hidden(k4_tarski(B,D),A) & D != B & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,k3_relat_1(A)))) & r2_hidden(C,k3_relat_1(A)))) & r2_hidden(B,k3_relat_1(A))))))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1265 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1266 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (v1_relat_2(A) -> v1_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v8_relat_2(A) -> v8_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1267 (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]. 22.80/21.94 1268 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1269 (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) -> C = D)))))))))) # label(t55_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1270 (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]. 22.80/21.94 1271 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) & v2_wellord1(A) -> (all D -((all E -(r2_hidden(E,k3_relat_1(B)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t61_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1272 (all A all B all C (v1_relat_1(C) -> -(v2_wellord1(C) & r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & B != A & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C))))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1273 (all A all B (v1_relat_1(B) -> k1_xboole_0 = k1_wellord1(B,A) | r2_hidden(A,k3_relat_1(B)))) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1274 (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]. 22.80/21.94 1275 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> ((all C (r2_hidden(C,A) -> (all D (r2_hidden(k4_tarski(D,C),B) -> r2_hidden(D,A))))) <-> -((all C -(r2_hidden(C,k3_relat_1(B)) & A = k1_wellord1(B,C))) & k3_relat_1(B) != A))))) # label(t36_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1276 (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]. 22.80/21.94 1277 (all A all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k2_wellord1(B,A)),k3_relat_1(B)) & r1_tarski(k3_relat_1(k2_wellord1(B,A)),A))) # label(t20_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1278 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_wellord1(C,B)) <-> r2_hidden(A,k2_zfmisc_1(B,B)) & r2_hidden(A,C)))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1279 (all A all B (v1_relat_1(B) -> -(-r4_wellord1(B,k2_wellord1(B,A)) & (all C -(r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)) & r2_hidden(C,k3_relat_1(B)))) & v2_wellord1(B) & r1_tarski(A,k3_relat_1(B))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1280 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) & (all D all E (r2_hidden(E,k3_relat_1(A)) & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(D,E),A))) & k3_relat_1(B) = k2_relat_1(C) & k1_relat_1(C) = k3_relat_1(A) <-> r3_wellord1(A,B,C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1281 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) & v2_wellord1(A) -> (all D -((all E -(k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E) & r2_hidden(E,k3_relat_1(B)))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1282 (all A (v1_relat_1(A) -> (all B (v1_relat_1(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))) & -r4_wellord1(A,B) & v2_wellord1(B) & v2_wellord1(A)))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1283 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k1_wellord1(B,A) = k3_relat_1(k2_wellord1(B,k1_wellord1(B,A)))))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1284 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(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]. 22.80/21.94 1285 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1286 (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]. 22.80/21.94 1287 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (v2_wellord1(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)) & r2_hidden(A,k3_relat_1(D)) & v2_wellord1(E) -> r1_tarski(k1_wellord1(E,C),k1_wellord1(E,B)) & r2_hidden(k4_tarski(C,B),E)))))) # label(t62_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1288 (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(k2_wellord1(C,k1_wellord1(C,A)),B) = k1_wellord1(C,B)))) # label(t35_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1289 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r1_tarski(B,k3_relat_1(A)) & (all C -((all D (r2_hidden(D,B) -> r2_hidden(k4_tarski(C,D),A))) & r2_hidden(C,B))) & B != k1_xboole_0))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1290 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1291 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1292 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> v1_relat_2(A) & v8_relat_2(A) & v1_wellord1(A) & v6_relat_2(A) & v4_relat_2(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1293 (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]. 22.80/21.94 1294 (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]. 22.80/21.94 1295 (all A (v1_relat_1(A) -> (v1_wellord1(A) <-> (all B -(B != k1_xboole_0 & (all C -(r1_xboole_0(k1_wellord1(A,C),B) & r2_hidden(C,B))) & r1_tarski(B,k3_relat_1(A))))))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1296 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & k1_xboole_0 != C & (all D -(r1_xboole_0(k1_wellord1(A,D),C) & r2_hidden(D,C))))) <-> r1_wellord1(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1297 (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]. 22.80/21.94 1298 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1299 (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]. 22.80/21.94 1300 (all A (v1_relat_1(A) -> (all B all C ((all D (B != D & r2_hidden(k4_tarski(D,B),A) <-> r2_hidden(D,C))) <-> k1_wellord1(A,B) = C)))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1301 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> B != D & r2_hidden(k4_tarski(D,B),C))) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1302 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1303 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1304 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (all D all E (r2_hidden(k4_tarski(D,E),A) -> r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & k1_funct_1(C,D) != k1_funct_1(C,E) | D = E))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1305 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1306 (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]. 22.80/21.94 1307 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(C,A)))) # label(t29_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1308 (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]. 22.80/21.94 1309 (all A all B all C (v1_relat_1(C) -> k2_wellord1(C,k3_xboole_0(A,B)) = k2_wellord1(k2_wellord1(C,A),B))) # label(t26_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1310 (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]. 22.80/21.94 1311 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -(C != k1_xboole_0 & (all D -(r2_hidden(D,C) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))))) & r1_tarski(C,A)))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1312 (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]. 22.80/21.94 1313 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> A = k3_relat_1(k2_wellord1(B,A))))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1314 (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]. 22.80/21.94 1315 (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]. 22.80/21.94 1316 (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) -> C = D | r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A) & k1_funct_1(B,D) != k1_funct_1(B,C))) & 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]. 22.80/21.94 1317 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) & r4_wellord1(A,B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_wellord1(A,B) = C <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1318 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1319 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1320 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1321 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> r2_wellord1(A,k3_relat_1(A))))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1322 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,D,C) = k2_relset_1(A,B,C,D))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1323 (all A all B all C (m2_relset_1(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C)))) <-> k5_relset_1(A,B,C) = B))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1324 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> ((exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1325 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(r2_hidden(E,A) & r2_hidden(F,B) & k4_tarski(E,F) = C)) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1326 (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]. 22.80/21.94 1327 (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]. 22.80/21.94 1328 (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]. 22.80/21.94 1329 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1330 (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]. 22.80/21.94 1331 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & k5_relat_1(B,k6_relat_1(A)) = B)) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1332 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1333 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1334 (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]. 22.80/21.94 1335 (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]. 22.80/21.94 1336 (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,D) = k1_relset_1(A,B,D,C))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1337 (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]. 22.80/21.94 1338 (all A all B all C (m2_relset_1(C,B,A) -> k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) & k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1339 (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]. 22.80/21.94 1340 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1341 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1342 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> D = k8_relset_1(B,A,D,C)))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1343 (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]. 22.80/21.94 1344 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1345 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1346 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> k1_xboole_0 = C))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1347 (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]. 22.80/21.94 1348 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> C = k2_relset_1(A,B,C,C))) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1349 (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]. 22.80/21.94 1350 (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]. 22.80/21.94 1351 (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]. 22.80/21.94 1352 (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]. 22.80/21.94 1353 (all A all B all C (m1_relset_1(C,A,B) -> k2_relat_1(C) = k5_relset_1(A,B,C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1354 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> 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]. 22.80/21.94 1355 (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]. 22.80/21.94 1356 (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]. 22.80/21.94 1357 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1358 (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]. 22.80/21.94 1359 (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]. 22.80/21.94 1360 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1361 (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]. 22.80/21.94 1362 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1363 (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]. 22.80/21.94 1364 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k10_relset_1(C,A,D,B)) <-> (exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D) & m1_subset_1(F,C)))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1365 (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]. 22.80/21.94 1366 (all A all B all C all D (m1_relset_1(D,A,B) -> k9_relset_1(A,B,C,D) = k8_relat_1(C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1367 (exists A ((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))) & m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1368 (all A all B all C (m2_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)) & k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1369 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> B = k5_relset_1(A,B,C) & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1370 (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]. 22.80/21.94 1371 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1372 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1373 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1374 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> (r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E)) <-> (exists H (r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E) & m1_subset_1(H,B)))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1375 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1376 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C)) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1377 (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]. 22.80/21.94 1378 (all A all B all C (m1_relset_1(C,A,B) -> k1_relat_1(C) = k4_relset_1(A,B,C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1379 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k4_relset_1(A,B,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C))))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1380 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1381 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1382 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k3_relset_1(A,B,C,D) = k4_xboole_0(C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1383 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> B = k4_relset_1(B,A,C) & r1_tarski(B,k5_relset_1(B,A,C))))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1384 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1385 (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]. 22.80/21.94 1386 (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]. 22.80/21.94 1387 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1388 (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]. 22.80/21.94 1389 (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]. 22.80/21.94 1390 (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]. 22.80/21.94 1391 (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)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(E,D),C)))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1392 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1393 (exists A ((all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (r2_hidden(k4_tarski(B,C),A) <-> p1_s2_relset_1(B,C)))))) & m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1394 (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]. 22.80/21.94 1395 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1396 (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]. 22.80/21.94 1397 (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 (r2_hidden(k4_tarski(E,F),D) & r2_hidden(F,B) & m1_subset_1(F,C))) <-> r2_hidden(E,k11_relset_1(A,C,D,B))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1398 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1399 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1400 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1401 (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]. 22.80/21.94 1402 (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]. 22.80/21.94 1403 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1404 (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]. 22.80/21.94 1405 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> C = k1_relset_1(A,B,C,C))) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1406 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,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]. 22.80/21.94 1407 (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]. 22.80/21.94 1408 (all A all B all C all D (m1_relset_1(C,A,B) -> k8_relset_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1409 (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]. 22.80/21.94 1410 (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]. 22.80/21.94 1411 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1412 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),C) = k4_relset_1(A,k1_tarski(B),D) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1413 (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]. 22.80/21.94 1414 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1415 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1416 (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) -> v1_funct_1(C) & m2_relset_1(C,A,B)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1417 (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]. 22.80/21.94 1418 (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]. 22.80/21.94 1419 (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]. 22.80/21.94 1420 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1421 (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)) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) <-> r1_partfun1(A,B))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1422 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k5_partfun1(A,B,C) = k1_tarski(C) <-> v1_partfun1(C,A,B)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1423 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1424 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1425 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1426 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1427 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,C) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 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]. 22.80/21.94 1429 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1430 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) & v1_funct_1(E) -> k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1431 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) & (all C (v1_funct_1(C) & v1_relat_1(C) -> k2_xboole_0(A,B) != C))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1432 (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]. 22.80/21.94 1433 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1434 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(k1_xboole_0,A,B))) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1435 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> (all D (m2_relset_1(D,B,k1_xboole_0) & v1_funct_1(D) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1436 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (k4_relset_1(k2_zfmisc_1(A,B),C,E) = k4_relset_1(k2_zfmisc_1(A,B),C,D) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1437 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1438 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1439 (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_partfun1(C,D) & v1_partfun1(D,A,B) & v1_partfun1(C,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1440 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1441 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1442 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1443 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1444 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1445 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1446 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1447 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1448 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1449 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1450 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (A != k1_xboole_0 -> k5_partfun1(A,k1_xboole_0,B) = k1_xboole_0))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1451 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1452 (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]. 22.80/21.94 1453 (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]. 22.80/21.94 1454 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.94 1455 (all A all B all C all D all E all F (v1_funct_1(F) & m1_relset_1(F,C,D) & m1_relset_1(E,A,B) & v1_funct_1(E) -> v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1456 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1457 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & r1_partfun1(A,B) -> A = B))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1458 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A ((all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) <-> r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & v1_funct_1(A))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1459 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1460 (all A all B (v1_funct_1(B) & v1_relat_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]. 22.80/21.95 1461 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1462 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1463 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1464 (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]. 22.80/21.95 1465 (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]. 22.80/21.95 1466 (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]. 22.80/21.95 1467 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1468 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1469 (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) & (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) -> C = B)) -> (exists A (m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) <-> (exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1))) & v1_funct_1(A))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1470 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1471 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1472 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1473 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k2_relat_1(C) = k9_relat_1(C,A))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1474 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1475 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1476 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> B = k1_xboole_0)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1477 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1478 (all A k4_partfun1(A,k1_xboole_0) = k1_tarski(k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1479 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1480 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1481 (all A k1_tarski(k1_xboole_0) = k4_partfun1(k1_xboole_0,A)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1482 (all A all B all C ((all D ((exists E (v1_relat_1(E) & E = D & r1_tarski(k1_relat_1(E),A) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E))) <-> r2_hidden(D,C))) <-> C = k4_partfun1(A,B))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1483 (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]. 22.80/21.95 1484 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1485 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_tarski(A,C) & r1_tarski(B,D) -> v1_funct_1(E) & m2_relset_1(E,C,D)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1486 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1487 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1488 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,D) = k1_funct_1(B,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1489 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1490 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1491 (all A all B exists C (m1_relset_1(C,A,B) & v1_funct_1(C) & v1_relat_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1492 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1493 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1494 (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]. 22.80/21.95 1495 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> C = k3_partfun1(C,A,B)))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1496 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1497 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1498 (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]. 22.80/21.95 1499 (all A (v1_relat_1(A) & v8_relat_2(A) & v3_relat_2(A) -> v1_relat_1(A) & v1_relat_2(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1500 (all A all B all C (r2_hidden(A,f1_s4_partfun1) & r2_hidden(B,f2_s4_partfun1) & p1_s4_partfun1(A,B,C) -> 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) -> D = C)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) <-> (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(C,f2_s4_partfun1) & r2_hidden(B,f1_s4_partfun1))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1501 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1502 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1503 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1504 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1505 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1506 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1507 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1508 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1509 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1510 (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(A,C) & r1_tarski(B,C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1511 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1512 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,E) = k1_funct_1(C,D) -> D = E))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1513 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1514 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_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]. 22.80/21.95 1515 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1516 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1517 (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 (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1518 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1519 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1520 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1521 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) & k1_xboole_0 = B -> k1_xboole_0 = A))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1522 (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]. 22.80/21.95 1523 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1524 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1525 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1526 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(C,k6_relat_1(B)))) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1527 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1528 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1529 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1530 (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]. 22.80/21.95 1531 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1532 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1533 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1534 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((all E (m1_subset_1(E,A) -> -(C = k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,D))))) & r2_hidden(C,k2_relat_1(D))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1535 (all A exists B (v1_relat_1(B) & v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1536 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1537 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1538 (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]. 22.80/21.95 1539 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k2_funct_1(k3_partfun1(C,A,B)) = k3_partfun1(k2_funct_1(C),B,A)))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1540 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1541 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (D = k5_partfun1(A,B,C) <-> (all E (r2_hidden(E,D) <-> (exists F (m2_relset_1(F,A,B) & v1_partfun1(F,A,B) & r1_partfun1(C,F) & F = E & v1_funct_1(F))))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1542 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1543 (all A (v1_funct_1(A) & v1_relat_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]. 22.80/21.95 1544 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1545 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1546 (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]. 22.80/21.95 1547 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),A,B))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1548 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(k1_funct_1(D,E) = C & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1549 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1550 (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) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1551 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> B = k1_xboole_0)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1552 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1553 (all A (v1_relat_1(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1554 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1555 (all A all B (v1_funct_1(k1_xboole_0) & m2_relset_1(k1_xboole_0,A,B))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1556 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1557 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m2_relset_1(k2_partfun1(A,B,C,D),A,B) & v1_funct_1(k2_partfun1(A,B,C,D)))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1558 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1559 (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]. 22.80/21.95 1560 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1561 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1562 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_relat_1(C) = k1_xboole_0 -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1563 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1564 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1565 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> (exists C (v1_relat_1(C) & C = k2_xboole_0(A,B) & v1_funct_1(C)))))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1566 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)) = k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1567 (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]. 22.80/21.95 1568 (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]. 22.80/21.95 1569 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1570 (all A (v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1571 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1572 (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]. 22.80/21.95 1573 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1574 (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]. 22.80/21.95 1575 (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]. 22.80/21.95 1576 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1577 (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) -> v1_funct_1(D) & m2_relset_1(D,B,C)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1578 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1579 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1580 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1581 (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) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> -(v1_partfun1(E,A,B) & r1_partfun1(C,E) & r1_partfun1(D,E))))))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1582 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1583 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1584 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(k6_relat_1(A),C) = C)) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1585 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1586 (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]. 22.80/21.95 1587 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1588 (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_1(D) & m2_relset_1(D,A,B))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1589 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1590 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1591 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1592 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1593 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1594 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> f3_s3_partfun1(B) = k1_funct_1(A,B))) & (all B (r2_hidden(B,f1_s3_partfun1) & p1_s3_partfun1(B) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1595 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1596 (exists A (v1_relat_1(A) & f1_s1_partfun1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> k1_funct_1(A,B) = f3_s1_partfun1(B)) & (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1597 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k10_relat_1(C,B))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1598 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1599 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B) & k1_xboole_0 = k2_relat_1(B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1600 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1601 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1602 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1603 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1604 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1605 (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]. 22.80/21.95 1606 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(D,C) & r1_partfun1(C,E) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1607 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & r1_partfun1(C,D) & (k1_xboole_0 = B -> k1_xboole_0 = A)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1608 (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]. 22.80/21.95 1609 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1610 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1611 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1612 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1613 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1614 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1615 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1616 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1617 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1618 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k3_partfun1(D,k3_xboole_0(A,C),B) = k2_partfun1(A,B,k3_partfun1(D,A,B),C))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1619 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)) & m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1620 (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]. 22.80/21.95 1621 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1622 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) & r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1623 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1624 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1625 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) = E)) & k1_xboole_0 != D & k1_xboole_0 != C & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1626 (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]. 22.80/21.95 1627 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k10_mcart_1(A,B,C,D,I),G) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k8_mcart_1(A,B,C,D,I),E)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1628 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> r2_hidden(k1_mcart_1(A),B) & k2_mcart_1(A) = C)) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1629 (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]. 22.80/21.95 1630 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1631 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> D = A & E = B & F = C)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1632 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(A,E) & -r1_xboole_0(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(B,F))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1633 (all A all B all C -(k1_xboole_0 != A & k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k6_mcart_1(A,B,C,D) != D & k7_mcart_1(A,B,C,D) != D & D != k5_mcart_1(A,B,C,D))) & C != k1_xboole_0)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1634 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1635 (all A -((all B -(r2_hidden(B,A) & (all C all D all E all F -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_mcart_1(C,D,E,F) = B)))) & k1_xboole_0 != A)) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1636 (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]. 22.80/21.95 1637 (all A -((all B -((all C all D -((r2_hidden(C,A) | r2_hidden(D,A)) & k4_tarski(C,D) = B)) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1638 (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]. 22.80/21.95 1639 (all A all B all C all D -(B != k1_xboole_0 & C != 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) & k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k9_mcart_1(A,B,C,D,E) & k2_mcart_1(E) = k11_mcart_1(A,B,C,D,E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E))) & D != k1_xboole_0 & A != k1_xboole_0)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1640 (all A all B all C -(A != k1_xboole_0 & B != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != C)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1641 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1642 (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]. 22.80/21.95 1643 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> F = D))))))) -> C = k1_xboole_0 | k5_mcart_1(A,B,C,E) = D | B = k1_xboole_0 | A = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1644 (all A all B all C all D k4_tarski(k3_mcart_1(A,B,C),D) = k4_mcart_1(A,B,C,D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1645 (all A all B all C all D all E all F (r2_hidden(C,F) & r2_hidden(B,E) & r2_hidden(A,D) <-> r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1646 (all A all B all C all D k1_tarski(k4_mcart_1(A,B,C,D)) = k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1647 (all A all B all C all D all E all F all G all H -(k1_xboole_0 != C & D != k1_xboole_0 & (exists I ((exists J (-(k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I) & k11_mcart_1(A,B,C,D,I) = k11_mcart_1(E,F,G,H,J) & k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k9_mcart_1(E,F,G,H,J) = k9_mcart_1(A,B,C,D,I)) & I = J & 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 != H & k1_xboole_0 != G & k1_xboole_0 != F & E != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1648 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k8_mcart_1(A,B,C,D,E),A))) # label(dt_k8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1649 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1650 (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]. 22.80/21.95 1651 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> k4_zfmisc_1(A,B,C,D) = k1_xboole_0 | A = E & F = B & G = C & D = H)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1652 (all A all B all C all D k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1653 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(A != k1_xboole_0 & k1_xboole_0 != D & (exists F exists G exists H exists I (-(F = k8_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 & k9_mcart_1(A,B,C,D,E) = G) & E = k4_mcart_1(F,G,H,I))) & k1_xboole_0 != C & k1_xboole_0 != B))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1654 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1655 (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]. 22.80/21.95 1656 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k1_mcart_1(C) & k2_mcart_1(C) != C)))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1657 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,B) -> r1_xboole_0(C,A))))))) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1658 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1659 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> (k2_mcart_1(A) = D | k2_mcart_1(A) = C) & r2_hidden(k1_mcart_1(A),B))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1660 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1661 (all A all B -(k1_xboole_0 != B & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) = C)) & k1_xboole_0 != A)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1662 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> k3_zfmisc_1(A,B,C) = k1_xboole_0 | C = F & E = B & A = D)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1663 (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]. 22.80/21.95 1664 (all A all B all C all D all E ((all F ((exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(H,C) & r2_hidden(I,D) & r2_hidden(J,E) & F = k4_mcart_1(G,H,I,J))) <-> r2_hidden(F,A))) -> k4_zfmisc_1(B,C,D,E) = A)) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.95 1665 (all A all B all C all D (A != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != B <-> k1_xboole_0 != k4_zfmisc_1(A,B,C,D))) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1666 (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]. 22.80/21.96 1667 (all A all B all C all D all E all F all G all H (m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1668 (all A all B all C all D all E all F (m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(D,k1_zfmisc_1(A)) -> k3_zfmisc_1(D,E,F) = k13_mcart_1(A,B,C,D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1669 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> k1_xboole_0 != C & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1670 (all A all B all C all D all E all F all G all H (r2_hidden(D,H) & r2_hidden(C,G) & r2_hidden(B,F) & r2_hidden(A,E) <-> r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1671 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1672 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> k1_mcart_1(A) = B & C = k2_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1673 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1674 (all A all B all C (r2_hidden(k2_mcart_1(A),C) & r2_hidden(k1_mcart_1(A),B) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E A != k4_tarski(D,E)))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1675 (all A all B all C all D -(k1_xboole_0 != C & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k8_mcart_1(A,B,C,D,E) != E & E != k10_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) != E & E != k9_mcart_1(A,B,C,D,E))) & k1_xboole_0 != B & A != k1_xboole_0)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1676 (all A all B all C all D k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D)) = k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1677 (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 = G))))))))) -> k1_xboole_0 = A | k8_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | C = k1_xboole_0 | k1_xboole_0 = B))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1678 (all A all B all C -(-(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k5_mcart_1(A,B,C,D) = k1_mcart_1(k1_mcart_1(D)) & k2_mcart_1(D) = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k2_mcart_1(k1_mcart_1(D)))) & C != k1_xboole_0 & B != k1_xboole_0 & k1_xboole_0 != A)) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1679 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k16_mcart_1(A) <-> k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k2_mcart_1(k1_funct_1(A,C))))))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1680 (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]. 22.80/21.96 1681 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (A = k4_tarski(C,D) -> B = D)) <-> B = k2_mcart_1(A))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1682 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(B) = k1_relat_1(A) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1683 (all A all B all C -(B != k1_xboole_0 & -(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 & A != k1_xboole_0)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1684 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k11_mcart_1(A,B,C,D,E),D))) # label(dt_k11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1685 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != D & (exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (-(F = k8_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) = G & I = k11_mcart_1(A,B,C,D,E) & k10_mcart_1(A,B,C,D,E) = H) & E = k4_mcart_1(F,G,H,I))))) & C != k1_xboole_0 & B != k1_xboole_0)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1686 (all A ((exists B exists C k4_tarski(B,C) = A) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1687 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (A = k4_tarski(C,D) -> C = B)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1688 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = I))))))))) -> B = k1_xboole_0 | k1_xboole_0 = C | k1_xboole_0 = D | k10_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = A))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1689 (all A all B all C all D all E all F (k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) = A & B = k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D & E = k20_mcart_1(k4_tarski(F,k4_tarski(D,E))))) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1690 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1691 (all A all B all C all D all E all F all G all H (r1_tarski(C,D) & r1_tarski(E,F) & r1_tarski(G,H) & 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]. 22.80/21.96 1692 (all A k2_mcart_1(k2_mcart_1(A)) = k20_mcart_1(A)) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1693 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k16_mcart_1(A)) & v1_relat_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1694 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(F,B) & r2_hidden(H,D) & k4_mcart_1(F,G,H,I) = A & r2_hidden(I,E) & r2_hidden(G,C))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1695 (all A all B -(k1_xboole_0 != A & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) != C & k1_mcart_1(C) != C)) & k1_xboole_0 != B)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1696 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1697 (all A all B all C -(k1_xboole_0 != B & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> ((all F all G all H (k3_mcart_1(F,G,H) = D -> G = E)) <-> E = k6_mcart_1(A,B,C,D)))))) & k1_xboole_0 != A)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1698 (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]. 22.80/21.96 1699 (all A all B all C all D k4_tarski(k4_tarski(k4_tarski(A,B),C),D) = k4_mcart_1(A,B,C,D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1700 (all A all B (k1_mcart_1(k4_tarski(A,B)) = A & B = k2_mcart_1(k4_tarski(A,B)))) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1701 (all A ((exists B exists C k4_tarski(B,C) = A) -> k2_mcart_1(A) != A & A != k1_mcart_1(A))) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1702 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1703 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1704 (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) -> H = D))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k7_mcart_1(A,B,C,E) = D | A = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1705 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D all E all F all G (r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(G,B) & r2_hidden(F,G) -> r1_xboole_0(C,A))))))) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1706 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D all E all F (r2_hidden(C,D) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(D,E) -> r1_xboole_0(C,A))))))) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1707 (all A all B all C all D -((all E all F all G -(r2_hidden(G,D) & A = k3_mcart_1(E,F,G) & r2_hidden(F,C) & r2_hidden(E,B))) & r2_hidden(A,k3_zfmisc_1(B,C,D)))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1708 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> r2_hidden(k2_mcart_1(A),D) & (k1_mcart_1(A) = C | k1_mcart_1(A) = B))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1709 (all A all B all C -((exists D ((exists E exists F exists G (-(G = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = F & k5_mcart_1(A,B,C,D) = E) & D = k3_mcart_1(E,F,G))) & m1_subset_1(D,k3_zfmisc_1(A,B,C)))) & k1_xboole_0 != C & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1710 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k3_zfmisc_1(k2_zfmisc_1(A,B),C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1711 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1712 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1713 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> k1_xboole_0 = A | E = B & C = F & A = D | k1_xboole_0 = C | B = k1_xboole_0)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1714 (all A k19_mcart_1(A) = k1_mcart_1(k2_mcart_1(A))) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1715 (all A all B all C all D k4_mcart_1(A,B,C,D) = k3_mcart_1(k4_tarski(A,B),C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1716 (all A all B all C -(k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> ((all F all G all H (D = k3_mcart_1(F,G,H) -> E = H)) <-> k7_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1717 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))))) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1718 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> B = k1_mcart_1(A) & (k2_mcart_1(A) = C | D = k2_mcart_1(A)))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1719 (all A all B all C all D all E all F all G all H (k4_mcart_1(A,B,C,D) = k4_mcart_1(E,F,G,H) -> F = B & C = G & H = D & E = A)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1720 (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]. 22.80/21.96 1721 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(A,D) & -r1_xboole_0(B,E) & -r1_xboole_0(C,F))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1722 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> k1_xboole_0 = A | k1_xboole_0 = D | B = F & C = G & H = D & E = A | C = k1_xboole_0 | k1_xboole_0 = B)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1723 (all A all B all C all D ((all E (r2_hidden(E,A) <-> (exists F exists G exists H (r2_hidden(G,C) & r2_hidden(H,D) & E = k3_mcart_1(F,G,H) & r2_hidden(F,B))))) -> k3_zfmisc_1(B,C,D) = A)) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1724 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1725 (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]. 22.80/21.96 1726 (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]. 22.80/21.96 1727 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> k2_mcart_1(A) = D & (B = k1_mcart_1(A) | k1_mcart_1(A) = C))) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1728 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1729 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(k1_xboole_0 != A & k1_xboole_0 != C & (exists E exists F exists G (-(k7_mcart_1(A,B,C,D) = G & F = k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = E) & k3_mcart_1(E,F,G) = D)) & B != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1730 (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]. 22.80/21.96 1731 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1732 (all A all B all C all D all E all F -(B != k1_xboole_0 & k1_xboole_0 != E & (exists G ((exists H (m1_subset_1(H,k3_zfmisc_1(D,E,F)) & H = G & -(k7_mcart_1(D,E,F,H) = k7_mcart_1(A,B,C,G) & k6_mcart_1(A,B,C,G) = k6_mcart_1(D,E,F,H) & k5_mcart_1(A,B,C,G) = k5_mcart_1(D,E,F,H)))) & m1_subset_1(G,k3_zfmisc_1(A,B,C)))) & F != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & k1_xboole_0 != A)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1733 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (C = k1_mcart_1(A) | k1_mcart_1(A) = B) & (k2_mcart_1(A) = D | E = k2_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1734 (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)) -> (all F (m1_subset_1(F,C) -> (F = k10_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = I))))))) & k1_xboole_0 != D & C != k1_xboole_0 & B != k1_xboole_0)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1735 (all A all B all C all D all E all F k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F)) = k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1736 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A))) -> A = k1_xboole_0)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1737 (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,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 & k1_xboole_0 != C & k1_xboole_0 != B & A != k1_xboole_0)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1738 (all A all B all C k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C)) = k1_tarski(k3_mcart_1(A,B,C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1739 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k1_mcart_1(A) != A & k2_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1740 (all A -((all B -(r1_xboole_0(B,A) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1741 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> H = E))))))))) -> k1_xboole_0 = B | D = k1_xboole_0 | E = k9_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1742 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1743 (all A -(k1_xboole_0 != A & (all B -((all C all D all E -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k3_mcart_1(C,D,E))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1744 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1745 (all A all B all C all D -(C != k1_xboole_0 & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = G)) <-> F = k8_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1746 (all A all B (k4_zfmisc_1(B,B,B,B) = k4_zfmisc_1(A,A,A,A) -> B = A)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1747 (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 -> G = D))))))) -> A = k1_xboole_0 | D = k6_mcart_1(A,B,C,E) | C = k1_xboole_0 | B = k1_xboole_0))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1748 (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]. 22.80/21.96 1749 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))))) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1750 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = J))))))))) -> C = k1_xboole_0 | k11_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | B = k1_xboole_0 | A = k1_xboole_0))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1751 (all A all B all C all D -(k1_xboole_0 != A & B != k1_xboole_0 & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> (F = k11_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> J = F))))))) & k1_xboole_0 != C)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1752 (all A all B all C all D all E k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E)) = k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1753 (all A all B all C all D all E all F all G all H (m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1754 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1755 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1756 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1757 (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]. 22.80/21.96 1758 (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]. 22.80/21.96 1759 (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]. 22.80/21.96 1760 (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]. 22.80/21.96 1761 (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]. 22.80/21.96 1762 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1763 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1764 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1765 (all A (-v1_xboole_0(A) -> -((all B -(r2_hidden(B,A) & B = k1_xboole_0)) & (all B exists C (r2_hidden(C,A) & (all D k1_tarski(D) != k3_xboole_0(B,C)))) & (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r1_xboole_0(B,C) | B = C))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1766 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> v2_wellord1(k2_wellord1(B,A)) & k3_relat_1(k2_wellord1(B,A)) = A))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1767 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1768 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1769 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & (all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B))))))) # label(t14_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1770 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> A = k1_wellord1(k1_wellord2(B),A)))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1771 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1772 (all A -((all B -(r2_hidden(B,f2_s1_wellord2) & p1_s1_wellord2(A,B))) & r2_hidden(A,f1_s1_wellord2))) -> (exists A (v1_relat_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_funct_1(A))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1773 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1774 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1775 (all A -((all B all C -(r2_hidden(C,f3_s2_wellord2) & p1_s2_wellord2(A,B,C) & r2_hidden(B,f2_s2_wellord2))) & r2_hidden(A,f1_s2_wellord2))) -> (exists A (v1_relat_1(A) & (exists B (v1_relat_1(B) & k1_relat_1(A) = f1_s2_wellord2 & f1_s2_wellord2 = k1_relat_1(B) & (all C (r2_hidden(C,f1_s2_wellord2) -> p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)))) & v1_funct_1(B))) & v1_funct_1(A))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1776 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1777 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1778 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1779 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1780 (all A (-v1_xboole_0(A) -> -((all B -(r2_hidden(B,A) & k1_xboole_0 = B)) & (all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))) & A = k1_relat_1(B))))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1781 (all A all B (v1_relat_1(B) -> (k1_wellord2(A) = B <-> (all C all D (r2_hidden(C,A) & r2_hidden(D,A) -> (r2_hidden(k4_tarski(C,D),B) <-> r1_tarski(C,D)))) & A = k3_relat_1(B)))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1782 (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]. 22.80/21.96 1783 (all A exists B (v1_relat_1(B) & r2_wellord1(B,A))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1784 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1785 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1786 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(B)) & r4_wellord1(A,k1_wellord2(C)) -> B = C))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1787 (all A all B all C (r2_wellord2(A,B) & r2_wellord2(B,C) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1788 (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]. 22.80/21.96 1789 (all A all B ((exists C (k1_relat_1(C) = A & k2_relat_1(C) = B & v2_funct_1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1790 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1791 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1792 (all A all B (r2_tarski(A,B) <-> r2_wellord2(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1793 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(B,C) -> v1_funct_2(D,A,C) & m2_relset_1(D,A,C) & v1_funct_1(D) | k1_xboole_0 = B & A != k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1794 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> D = k9_funct_2(A,B,C))) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1795 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> A != k1_xboole_0 & k1_xboole_0 = B | C = D))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1796 (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 <-> v2_funct_2(C,A,B)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1797 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1798 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (k2_relat_1(C) = B <-> (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]. 22.80/21.96 1799 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) & v2_funct_1(D) -> k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) = C | k1_xboole_0 = B))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1800 (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) -> k8_funct_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1801 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (B = k2_relat_1(D) & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) & v2_funct_1(E) | k1_xboole_0 = C & k1_xboole_0 != B))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1802 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1803 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & B = k2_relat_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A)))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1804 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1805 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1806 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (p1_s14_funct_2(A,B) & m1_subset_1(B,f2_s14_funct_2))))) -> (exists A (m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1807 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A ((all B (m1_subset_1(B,f1_s11_funct_2) -> -(f3_s11_funct_2 != B & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & B != f4_s11_funct_2))) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2 & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & v1_funct_1(A))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1808 (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(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1809 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) -> (k6_partfun1(A) = k5_funct_2(A,B,C) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1810 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) -> (all C all D (k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(D,A) & r2_hidden(C,A) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1811 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1812 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1813 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_partfun1(C,D) -> 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]. 22.80/21.96 1814 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1815 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1816 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k2_relat_1(C) = B & v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> B = k1_xboole_0 | k2_funct_1(C) = D | k1_xboole_0 = A))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1817 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1818 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1819 (all A all B all C (v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (r1_tarski(B,A) -> k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1820 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) | A != k1_xboole_0 & k1_xboole_0 = B))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1821 (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 ((all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1822 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1823 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1824 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1825 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> -(k1_xboole_0 != A & -(v2_funct_1(C) <-> (all D all E (m2_relset_1(E,D,A) & v1_funct_2(E,D,A) & v1_funct_1(E) -> (all F (v1_funct_2(F,D,A) & m2_relset_1(F,D,A) & v1_funct_1(F) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> F = E)))))) & k1_xboole_0 != B))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1826 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (C = k5_funct_2(A,B,C) -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1827 (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) -> (-(C != k1_xboole_0 & A != k1_xboole_0 & k1_xboole_0 = B) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1828 (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 = k2_funct_2(k1_xboole_0,A,C,B))) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1829 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1830 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1831 (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) -> (v2_funct_1(B) & k4_funct_2(A,C,B) = B -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1832 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k4_funct_2(A,B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1833 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1834 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) & k2_relat_1(B) = A -> v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1835 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1836 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1837 (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(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1838 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1839 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E k1_tarski(E) != B) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1840 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (B != k1_xboole_0 -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1841 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1842 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1843 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1844 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1845 (all A all B -(r2_hidden(A,f1_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))) & r2_hidden(B,f2_s5_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s5_funct_2) & r2_hidden(C,f2_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1846 (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) -> k6_partfun1(A) = k5_funct_2(A,k6_funct_2(A,B),B) & k5_funct_2(A,B,k6_funct_2(A,B)) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1847 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.96 1848 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_2(C,A,B) & v1_funct_2(C,A,B) & v2_funct_1(C) -> v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1849 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (k1_xboole_0 != B -> (all E (r2_hidden(E,k10_relat_1(D,C)) <-> r2_hidden(k1_funct_1(D,E),C) & r2_hidden(E,A)))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1850 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1851 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1852 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1853 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & 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) -> f3_s9_funct_2(B) = k1_funct_1(A,B)) & (-p1_s9_funct_2(B) -> f4_s9_funct_2(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1854 (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 (v1_funct_1(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))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1855 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1856 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & 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))))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1857 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1858 (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 & -v2_funct_1(C) & (exists D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A)))))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1859 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> ((all C all D (r2_hidden(C,A) & r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1860 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (B = k2_relat_1(C) & (all E all F ((r2_hidden(E,B) & k1_funct_1(D,E) = F -> r2_hidden(F,A) & k1_funct_1(C,F) = E) & (r2_hidden(F,A) & k1_funct_1(C,F) = E -> k1_funct_1(D,E) = F & r2_hidden(E,B)))) & v2_funct_1(C) -> k1_xboole_0 = A | B = k1_xboole_0 | D = k2_funct_1(C)))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1861 (all A all B all C all D all E (v1_funct_1(D) & m1_relset_1(D,A,B) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & v1_funct_2(D,A,B) & -v1_xboole_0(B) -> v1_funct_1(k7_funct_2(A,B,C,D,E)) & 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))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1862 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1863 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1864 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1865 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1866 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (exists E (k1_funct_1(C,E) != k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,C)))))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1867 (all A all B all C all D all E all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (r2_hidden(E,B) & r2_hidden(D,A) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1868 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1869 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1870 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> B = k1_xboole_0 | v2_funct_1(C) & A = k2_relat_1(D)))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1871 (all A all B all C (m2_relset_1(C,A,B) -> k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C & C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)))) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1872 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(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]. 22.80/21.97 1873 (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) -> k2_relat_1(C) = k2_funct_2(A,B,C,A)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1874 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> k1_xboole_0 = B | r2_hidden(k1_funct_1(D,C),B)))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1875 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> v1_funct_2(B,k1_xboole_0,A) & m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1876 (all A (k1_xboole_0 != A -> k1_funct_2(A,k1_xboole_0) = k1_xboole_0)) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1877 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1878 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1879 (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]. 22.80/21.97 1880 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1881 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1882 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1883 (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 -> B = k1_xboole_0 | k5_relat_1(k2_funct_1(C),C) = k6_partfun1(B) & k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C))))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1884 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1885 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1886 (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) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1887 (all A all B all C (k1_funct_2(A,B) = C <-> (all D ((exists E (v1_funct_1(E) & r1_tarski(k2_relat_1(E),B) & k1_relat_1(E) = A & D = E & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1888 (all A exists B (v2_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) & v1_relat_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1889 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1890 (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]. 22.80/21.97 1891 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1892 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((all D -((all E -(r2_hidden(E,A) & D = k1_funct_1(C,E))) & r2_hidden(D,B))) -> B = k1_xboole_0 | B = k2_relat_1(C)))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1893 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,C) & m2_relset_1(F,B,C) & v1_funct_1(F) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) & (C = k1_xboole_0 -> B = k1_xboole_0)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1894 (all A all B k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B)) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1895 (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]. 22.80/21.97 1896 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1897 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((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(D,E) = k1_funct_1(C,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1898 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1899 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (exists C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & r1_partfun1(B,C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1900 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1901 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1902 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1903 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1904 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -r1_partfun1(C,D))) & (k1_xboole_0 = B -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1905 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v3_funct_2(C,A,B) <-> v2_funct_1(C) & v2_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1906 (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))) & (k1_xboole_0 = B -> A = k1_xboole_0 | (v1_funct_2(C,A,B) <-> C = k1_xboole_0)))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1907 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1908 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1909 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> B != k1_xboole_0 & C = k1_xboole_0 | B = k1_xboole_0 & A != k1_xboole_0 | v2_funct_1(D)))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1910 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1911 (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]. 22.80/21.97 1912 (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]. 22.80/21.97 1913 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1914 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1915 (all A all B all C (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_1(B) -> v1_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v3_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]. 22.80/21.97 1916 (all A all B all C (v1_funct_1(C) & 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) -> k5_partfun1(A,k1_tarski(B),C) = k1_tarski(D))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1917 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(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]. 22.80/21.97 1918 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1919 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> B = k2_relat_1(C)))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1920 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(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]. 22.80/21.97 1921 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1922 (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_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> A != k1_xboole_0 & B = k1_xboole_0 | r1_partfun1(C,D)))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1923 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1924 (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_relat_1(E) -> (r2_hidden(C,A) -> k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C) | B = k1_xboole_0))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1925 (exists A (v1_funct_1(A) & k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2 & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> 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))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1926 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1927 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1928 (exists A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1929 (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) -> (r2_hidden(k1_funct_1(E,C),D) & r2_hidden(C,A) -> k1_funct_1(E,C) = k1_funct_1(k9_relset_1(A,B,D,E),C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1930 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1931 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,B,C) & A = k2_relat_1(B) -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1932 (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 -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(D,E) & r1_partfun1(C,E))))))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1933 (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(A,C) -> k2_partfun1(A,B,D,C) = D))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1934 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1935 (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 -> k2_relat_1(C) = k1_tarski(k1_funct_1(C,A))))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1936 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1937 (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 | v1_funct_1(k2_partfun1(A,B,D,C)) & m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_2(k2_partfun1(A,B,D,C),C,B)))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1938 (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]. 22.80/21.97 1939 (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) -> (A = k2_relat_1(B) & A = k2_relat_1(C) -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1940 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_1(A))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1941 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1942 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1943 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(E) & C = k2_relat_1(k1_partfun1(A,B,B,C,D,E)) -> k2_relat_1(D) = B | k1_xboole_0 = C))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1944 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1945 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1946 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k3_funct_2(A,B,C,k2_funct_2(A,B,C,A)) = A))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1947 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | k1_xboole_0 = B))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1948 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1949 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1950 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1951 (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) & v1_funct_2(B,k1_relat_1(B),A)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1952 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1953 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1954 (all A all B all C (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(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]. 22.80/21.97 1955 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(E) = C & k2_relat_1(D) = B -> B = k1_xboole_0 | C = k1_xboole_0 | C = k2_relat_1(k1_partfun1(A,B,B,C,D,E))))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1956 (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) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1957 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1958 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1959 (all A -(r2_hidden(A,f1_s1_funct_2) & (all B -(p1_s1_funct_2(A,B) & r2_hidden(B,f2_s1_funct_2))))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & (all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1960 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_partfun1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1961 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1962 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1963 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) -> k6_funct_2(A,B) = k2_funct_1(B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1964 (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 B != k1_tarski(E)) & k5_partfun1(A,B,C) = k5_partfun1(A,B,D) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1965 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1966 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1967 (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]. 22.80/21.97 1968 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1969 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1970 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(C,A) -> r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) | B = k1_xboole_0 & A != k1_xboole_0))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1971 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(C,D) = k1_funct_1(B,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1972 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> C = D))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1973 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1974 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1975 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(D) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1976 (all A all B (r2_hidden(B,f2_s6_funct_2) & r2_hidden(A,f1_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(C,f2_s6_funct_2) & r2_hidden(B,f1_s6_funct_2) -> f4_s6_funct_2(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1977 (all A all B all C (v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> D = C)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1978 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & -v1_xboole_0(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1979 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s4_funct_2) -> f3_s4_funct_2(B) = k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B))) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1980 (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_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1981 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(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 | v1_partfun1(C,A,B)))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.80/21.97 1982 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(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]. 22.80/21.97 1983 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (k1_xboole_0 != B -> (all E ((exists F (k1_funct_1(D,F) = E & r2_hidden(F,C) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1984 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(C) & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1985 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1986 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> -(k2_relat_1(D) = B & (all E -(k1_funct_1(D,E) = C & r2_hidden(E,A))) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1987 (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]. 22.90/21.97 1988 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) & v1_funct_1(B) -> v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v2_funct_1(B) & v1_funct_1(B)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1989 (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) -> (v2_funct_1(C) <-> (all D all E (r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(D,A) -> D = E)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1990 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1991 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B & B = k7_relset_1(A,A,A,A,k6_partfun1(A),B))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1992 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1993 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1994 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1995 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1996 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1997 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1998 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_2(C,A,B) & v1_funct_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 1999 (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 -> (B = k2_relat_1(C) <-> (all D (D != k1_xboole_0 -> (all E (m2_relset_1(E,B,D) & v1_funct_2(E,B,D) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,E) = k1_partfun1(A,B,B,D,C,F) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2000 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(A,A,k3_partfun1(B,A,A)))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2001 (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 -((all F -(r2_hidden(F,A) & k1_funct_1(D,F) = E & r2_hidden(F,C))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2002 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2003 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) -> 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]. 22.90/21.97 2004 (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) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2005 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2006 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2007 (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]. 22.90/21.97 2008 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> (all F (v1_funct_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]. 22.90/21.97 2009 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,C) & v1_funct_2(F,A,C) -> (all G (m2_relset_1(G,A,C) & v1_funct_2(G,A,C) & v1_funct_1(G) -> (k13_funct_3(E,G) = k13_funct_3(D,F) -> k1_xboole_0 = B & k1_xboole_0 != A | E = D & G = F | k1_xboole_0 = C & k1_xboole_0 != A))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2010 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2011 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> 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]. 22.90/21.97 2012 (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) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (k1_xboole_0 = C -> 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)))))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2013 (all A all B all C all D all E (-v1_xboole_0(C) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_2(D,A,B) & v1_funct_1(D) & -v1_xboole_0(B) -> k14_funct_3(A,B,C,D,E) = k13_funct_3(D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2014 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2015 (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]. 22.90/21.97 2016 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(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]. 22.90/21.97 2017 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k3_funct_3(A) <-> k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k2_relat_1(A)) -> k1_funct_1(B,C) = k10_relat_1(A,C)))))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2018 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2019 (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]. 22.90/21.97 2020 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (B = k1_relat_1(C) & B = k1_relat_1(D) & r2_hidden(A,B) -> 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]. 22.90/21.97 2021 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> r1_tarski(k2_relat_1(k13_funct_3(D,E)),k2_zfmisc_1(B,C)))))) # label(t80_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2022 (all A all B all C (r2_hidden(A,k4_xboole_0(B,C)) -> k1_funct_1(k4_funct_3(C,B),A) = np__0)) # label(t43_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2023 (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]. 22.90/21.97 2024 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,C,D) & v1_funct_2(F,C,D) -> (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]. 22.90/21.97 2025 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2026 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2027 (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]. 22.90/21.97 2028 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2029 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2030 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2031 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2032 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k1_funct_3(B))) -> k9_relat_1(B,A) = k1_funct_1(k1_funct_3(B),A)))) # label(t8_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2033 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & k4_funct_3(C,B) = k4_funct_3(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2034 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) -> (r1_tarski(B,k1_zfmisc_1(A)) -> k2_funct_2(A,C,D,k3_tarski(B)) = k3_tarski(k9_relat_1(k1_funct_3(D),B))))))) # label(t17_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2035 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k1_funct_3(A)) & v1_funct_1(k1_funct_3(A)))) # label(dt_k1_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2036 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k3_xboole_0(k1_relat_1(B),k1_relat_1(C))) -> k4_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k1_funct_1(k13_funct_3(B,C),A)))))) # label(t68_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.97 2037 (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]. 22.90/21.97 2038 (all A (v1_relat_1(A) & v1_funct_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) = k1_relat_1(A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2039 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(D) & -v1_xboole_0(C) -> v1_funct_1(k14_funct_3(A,B,C,D,E)) & m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2040 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2041 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t27_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2042 (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]. 22.90/21.98 2043 (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]. 22.90/21.98 2044 (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]. 22.90/21.98 2045 (all A all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> 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]. 22.90/21.98 2046 (all A all B (v1_funct_1(k10_funct_3(A,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))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2047 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 22.90/21.98 2048 (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]. 22.90/21.98 2049 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> k5_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)) = k13_funct_3(D,E))))) # label(t99_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2050 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> ((all E all F (r2_hidden(F,B) & r2_hidden(E,A) -> k1_funct_1(C,k4_tarski(E,F)) = k1_funct_1(D,k4_tarski(E,F)))) & k2_zfmisc_1(A,B) = k1_relat_1(D) & k1_relat_1(C) = k2_zfmisc_1(A,B) -> D = C))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2051 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2052 (all A all B (k1_xboole_0 != A -> B = k2_relat_1(k7_funct_3(B,A)))) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2053 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k1_funct_3(B),A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2054 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,k2_tarski(np__0,np__1)) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) -> k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A) = B)) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2055 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2056 (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) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> -(k16_funct_3(A,C,B,D,E,F) != k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F)) & (k1_xboole_0 = D -> C = k1_xboole_0) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2057 (all A all B (v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2058 (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s2_funct_3) & r2_hidden(C,f2_s2_funct_3) -> f3_s2_funct_3(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) = k1_relat_1(A) & v1_relat_1(A))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2059 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k11_funct_3(A) = B <-> k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k4_tarski(C,C)))))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2060 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k3_funct_3(A)) & m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2061 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2062 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(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]. 22.90/21.98 2063 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2064 (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]. 22.90/21.98 2065 (all A all B (v1_funct_1(k5_funct_3(A,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)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2066 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k3_tarski(k9_relat_1(k3_funct_3(B),A)) = k10_relat_1(B,k3_tarski(A))))) # label(t30_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2067 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) -> r1_tarski(k10_relat_1(k1_funct_3(D),B),k1_zfmisc_1(A)))))) # label(t14_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2068 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k13_funct_3(A,B)) & v1_funct_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2069 (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_2(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_1(k1_funct_3(C))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2070 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funct_3(A)) & v1_relat_1(k3_funct_3(A)))) # label(dt_k3_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2071 (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]. 22.90/21.98 2072 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2073 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2074 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2075 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_zfmisc_1(k1_relat_1(A)) & (all C (r1_tarski(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k9_relat_1(A,C))) <-> B = k1_funct_3(A)))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2076 (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]. 22.90/21.98 2077 (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]. 22.90/21.98 2078 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2079 (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) -> (k13_funct_3(A,B) = C <-> (all D (r2_hidden(D,k1_relat_1(C)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C)))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2080 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D all E (r2_hidden(E,k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)) = k1_funct_1(C,k4_tarski(D,E)))) & k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) <-> C = k15_funct_3(A,B)))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2081 (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]. 22.90/21.98 2082 (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]. 22.90/21.98 2083 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2084 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> k4_tarski(k8_funct_2(A,B,D,F),k8_funct_2(A,C,E,F)) = k8_funct_2(A,k2_zfmisc_1(B,C),k14_funct_3(A,B,C,D,E),F))))))))))))) # label(t79_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2085 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2086 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> 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]. 22.90/21.98 2087 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k7_funct_3(A,B) <-> k2_zfmisc_1(A,B) = k1_relat_1(C) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = D))))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2088 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 22.90/21.98 2089 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k3_funct_3(B),A) = k10_relat_1(k1_funct_3(B),A)))) # label(t34_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2090 (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]. 22.90/21.98 2091 (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]. 22.90/21.98 2092 (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))) -> k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)) = k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2093 (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]. 22.90/21.98 2094 (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]. 22.90/21.98 2095 (all A (v1_funct_1(k12_funct_3(A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2096 (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(B) = A & A = k1_relat_1(C) -> 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]. 22.90/21.98 2097 (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]. 22.90/21.98 2098 (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]. 22.90/21.98 2099 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & r1_tarski(k2_relat_1(D),B) & r1_tarski(k2_relat_1(C),A) -> k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C & D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B))))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2100 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_funct_1(k6_funct_3(A,B)) & m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2101 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v2_funct_1(A) -> r1_tarski(k9_relat_1(k1_funct_3(A),B),k10_relat_1(k3_funct_3(A),B)))))) # label(t36_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2102 (all A all B -(r2_hidden(A,f1_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(B,f2_s1_funct_3))) & (all A all B all C all D (r2_hidden(A,f1_s1_funct_3) & p1_s1_funct_3(A,B,D) & p1_s1_funct_3(A,B,C) & r2_hidden(B,f2_s1_funct_3) -> C = D)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(C,f2_s1_funct_3) & r2_hidden(B,f1_s1_funct_3) -> p1_s1_funct_3(B,C,k1_funct_1(A,k4_tarski(B,C))))) & k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) = k1_relat_1(A) & v1_relat_1(A))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2103 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k15_funct_3(A,B)) & v1_funct_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2104 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k2_zfmisc_1(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]. 22.90/21.98 2105 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> k1_funct_3(C) = k2_funct_3(A,B,C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2106 (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]. 22.90/21.98 2107 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D all E (r2_hidden(E,B) & r2_hidden(D,A) -> k1_funct_1(C,k4_tarski(D,E)) = E)) & k1_relat_1(C) = k2_zfmisc_1(A,B) <-> C = k8_funct_3(A,B)))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2108 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2109 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k10_relat_1(B,A) = k1_funct_1(k3_funct_3(B),A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2110 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2111 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> E = k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)) & D = k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)))))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2112 (all A k11_funct_3(A) = k12_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2113 (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]. 22.90/21.98 2114 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2115 (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]. 22.90/21.98 2116 (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]. 22.90/21.98 2117 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2118 (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) -> -(-(E = k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) & D = k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C))) & (C = k1_xboole_0 -> A = k1_xboole_0) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2119 (all A all B (A != k1_xboole_0 -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2120 (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]. 22.90/21.98 2121 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k10_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t28_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2122 (all A all B all C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> v1_funct_1(k2_funct_3(A,B,C)) & m2_relset_1(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_2(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2123 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k1_funct_3(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t10_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2124 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(B) = k1_relat_1(A) & k13_funct_3(D,C) = k13_funct_3(A,B) & k1_relat_1(C) = k1_relat_1(D) -> B = C & A = D))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2125 (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]. 22.90/21.98 2126 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(k1_funct_3(A),k1_funct_3(B)) = k1_funct_3(k5_relat_1(A,B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2127 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_1(F) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_2(E,A,C) -> v1_funct_1(k16_funct_3(A,B,C,D,E,F)) & m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2128 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m2_relset_1(F,A,C) & v1_funct_2(F,A,C) & v1_funct_1(F) -> (all G (m2_relset_1(G,A,C) & v1_funct_2(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 & F = G))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2129 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k13_funct_3(B,C),A),k2_zfmisc_1(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t76_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2130 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> k1_relat_1(k13_funct_3(B,C)) = A))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2131 (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]. 22.90/21.98 2132 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2133 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k10_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t13_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2134 (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) -> 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]. 22.90/21.98 2135 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)) = k5_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2136 (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]. 22.90/21.98 2137 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k3_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t29_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2138 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2139 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_1(k1_funct_3(A),k1_xboole_0) = k1_xboole_0)) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2140 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,B) -> (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D)) & (r2_hidden(D,A) -> k1_funct_1(C,D) = np__1))) & B = k1_relat_1(C) <-> C = k4_funct_3(A,B)))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2141 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2142 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> ((exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & p1_s3_domain_1(E,F,G) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2143 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> k13_mcart_1(A,B,C,D,E,F) = a_6_0_domain_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2144 (all A all B all C all D all E all F all G all H (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k5_enumset1(B,C,D,E,F,G,H) = k12_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2145 (all A all B all C all D all E (-v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists F exists G exists H exists I (m1_subset_1(G,C) & A = k5_domain_1(B,C,D,E,F,G,H,I) & p1_s4_domain_1(F,G,H,I) & m1_subset_1(I,E) & m1_subset_1(H,D) & m1_subset_1(F,B))) <-> r2_hidden(A,a_4_2_domain_1(B,C,D,E))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2146 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> H = A))))))) <-> k7_mcart_1(B,C,D,E) = A))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2147 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (k6_mcart_1(B,C,D,E) = A <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = G)))))))))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2148 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (-(r2_hidden(E,C) <-> r2_hidden(E,D)) & A = E & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2149 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2150 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2151 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_5_domain_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2152 (all A (r2_hidden(A,a_0_3_domain_1) <-> (exists B (p2_s10_domain_1(B) & p1_s10_domain_1(B) & A = B & m1_subset_1(B,f1_s10_domain_1))))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2153 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2154 (all A (-v1_xboole_0(A) -> a_1_1_domain_1(A) = k1_subset_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2155 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2156 (all A all B all C all D all E all F all G (m1_subset_1(C,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_enumset1(B,C,D,E,F,G) = k11_domain_1(A,B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2157 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & -v1_xboole_0(C) -> ((exists F exists G exists H exists I (m1_subset_1(G,C) & m1_subset_1(H,D) & k5_domain_1(B,C,D,E,F,G,H,I) = A & m1_subset_1(I,E) & m1_subset_1(F,B))) <-> r2_hidden(A,a_4_0_domain_1(B,C,D,E))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2158 (all A all B all C all D all E all F all G all H (m1_subset_1(E,A) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(F,B) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2159 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = a_3_3_domain_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2160 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2161 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,B) & m1_subset_1(C,A) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2162 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2163 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2164 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = F))))))) <-> k5_mcart_1(B,C,D,E) = A))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2165 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k3_domain_1(A,B,C) = k2_mcart_1(C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2166 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2167 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(C) & -v1_xboole_0(E) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(I,k1_zfmisc_1(E)) & -v1_xboole_0(D) & -v1_xboole_0(B) -> ((exists J exists K exists L exists M (m1_subset_1(J,B) & m1_subset_1(K,C) & m1_subset_1(M,E) & A = k5_domain_1(B,C,D,E,J,K,L,M) & r2_hidden(J,F) & r2_hidden(L,H) & r2_hidden(M,I) & r2_hidden(K,G) & m1_subset_1(L,D))) <-> r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2168 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2169 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_2_domain_1(B,C,D)) <-> (exists E (E = A & (r2_hidden(E,C) | r2_hidden(E,D)) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2170 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2171 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (m1_subset_1(B,f1_s7_domain_1) & B = A & p1_s7_domain_1(B))))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2172 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k6_domain_1(A,B) = k1_tarski(B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2173 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = a_8_0_domain_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2174 (all A all B all C all D all E all F all G all H (m1_subset_1(B,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2175 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2176 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k2_mcart_1(D) = k2_mcart_1(C) & k1_mcart_1(C) = k1_mcart_1(D) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2177 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2178 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_domain_1(B)) <-> (exists C (A = C & -$T & m1_subset_1(C,B)))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2179 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> k3_zfmisc_1(A,B,C) = a_3_0_domain_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2180 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k7_domain_1(A,B,C) = k7_domain_1(A,C,B))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2181 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))))))) # label(s2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2182 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2183 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_7_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2184 (all A all B all C all D all E all F all G all H all I (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(G,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k13_domain_1(A,B,C,D,E,F,G,H,I) = k6_enumset1(B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2185 (all A (-v1_xboole_0(A) -> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)))) # label(s1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2186 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(G,D))) <-> r2_hidden(A,a_3_0_domain_1(B,C,D))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2187 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2188 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_6_domain_1(B)) <-> (exists C (A = C & p2_s6_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2189 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k9_mcart_1(A,B,C,D,E) = k9_mcart_1(A,B,C,D,F) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,F) = k10_mcart_1(A,B,C,D,E) & k8_mcart_1(A,B,C,D,F) = k8_mcart_1(A,B,C,D,E) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2190 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2191 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2192 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2193 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E ((-r2_hidden(E,C) & r2_hidden(E,D) | r2_hidden(E,C) & -r2_hidden(E,D)) & E = A & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_4_domain_1(B,C,D))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2194 (all A (r2_hidden(A,a_0_4_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & B = A)))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2195 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(C)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_1_domain_1(B,C,D,E)) <-> (exists F exists G (A = k1_domain_1(B,C,F,G) & r2_hidden(G,E) & r2_hidden(F,D) & m1_subset_1(G,C) & m1_subset_1(F,B)))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2196 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))))))))) # label(s4_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2197 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G ((exists H (m1_subset_1(H,C) & (exists I ((exists J (F = k4_mcart_1(G,H,I,J) & m1_subset_1(J,E))) & m1_subset_1(I,D))))) & m1_subset_1(G,B))))) -> A = k4_zfmisc_1(B,C,D,E)))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2198 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = a_2_2_domain_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2199 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2200 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F ((exists G ((exists H (E = k3_mcart_1(F,G,H) & m1_subset_1(H,D))) & m1_subset_1(G,C))) & m1_subset_1(F,B))) <-> r2_hidden(E,A))) -> k3_zfmisc_1(B,C,D) = A))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2201 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2202 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2203 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_5_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & p1_s6_domain_1(C) & A = C))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2204 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k16_domain_1(A,B,C,D),B))) # label(dt_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2205 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E) & k6_mcart_1(A,B,C,E) = k6_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = k7_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2206 (all A all B all C all D all E all F all G (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2207 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2208 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k9_domain_1(A,B,C,D,E) = k2_enumset1(B,C,D,E))) # label(redefinition_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.98 2209 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & C = A))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2210 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (A = C & p1_s1_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2211 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2212 (all A ((exists B exists C (f4_s9_domain_1(B,C) = A & p1_s9_domain_1(B,C) & m1_subset_1(C,f2_s9_domain_1) & m1_subset_1(B,f1_s9_domain_1))) <-> r2_hidden(A,a_0_2_domain_1))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2213 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2214 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists D (m1_subset_1(D,B) & D = A & r2_hidden(D,C))) <-> r2_hidden(A,a_2_1_domain_1(B,C))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2215 (all A ((exists B (f3_s8_domain_1(B) = A & p1_s8_domain_1(B) & m1_subset_1(B,f1_s8_domain_1))) <-> r2_hidden(A,a_0_1_domain_1))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2216 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_1_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(E,D) & r2_hidden(E,C) & A = E))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2217 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_4_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2218 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2219 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2220 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2221 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))))))) # label(s3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2222 (all A all B all C all D (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_enumset1(B,C,D) = k8_domain_1(A,B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2223 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2224 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) -> k1_domain_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2225 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & p1_s5_domain_1(C) & C = A))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2226 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_3_domain_1(B,C)) <-> (exists D exists E (m1_subset_1(E,C) & p1_s2_domain_1(D,E) & A = k1_domain_1(B,C,D,E) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2227 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_1_domain_1(A,B,C) = k5_subset_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2228 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2229 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.90/21.99 2230 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2231 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E (m1_subset_1(E,B) & E = A & (r2_hidden(E,C) <-> -r2_hidden(E,D)))) <-> r2_hidden(A,a_3_6_domain_1(B,C,D))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2232 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) -> ((exists D (m1_subset_1(D,B) & -r2_hidden(D,C) & A = D)) <-> r2_hidden(A,a_2_2_domain_1(B,C))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2233 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> k4_tarski(D,E) != A))))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2234 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) -> k17_mcart_1(D) = k14_domain_1(A,B,C,D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2235 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_2_domain_1(A,B,C) = k4_subset_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2236 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> k4_zfmisc_1(A,B,C,D) = a_4_0_domain_1(A,B,C,D))))))))) # label(t51_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2237 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k7_domain_1(A,B,C) = k2_tarski(B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2238 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2239 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> a_2_0_domain_1(A,B) = k2_zfmisc_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2240 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2241 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (k4_zfmisc_1(B,C,D,E) = A <-> (all F (r2_hidden(F,A) <-> (exists G (m1_subset_1(G,B) & (exists H ((exists I ((exists J (k4_mcart_1(G,H,I,J) = F & m1_subset_1(J,E))) & m1_subset_1(I,D))) & m1_subset_1(H,C)))))))))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2242 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_0_domain_1(B,C)) <-> (exists D exists E (m1_subset_1(E,C) & A = k1_domain_1(B,C,D,E) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2243 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k18_mcart_1(D) = k15_domain_1(A,B,C,D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2244 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> J = A)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2245 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> A = G))))))))) <-> k8_mcart_1(B,C,D,E,F) = A))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2246 (all A all B all C all D (m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2247 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2248 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E ((r2_hidden(E,D) <-> -r2_hidden(E,C)) & E = A & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_5_domain_1(B,C,D))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2249 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2250 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2251 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2252 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_4_domain_1(B)) <-> (exists C (A = C & p2_s5_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2253 (all A all B all C all D all E all F (-v1_xboole_0(C) & m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(D,A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k3_mcart_1(D,E,F) = k4_domain_1(A,B,C,D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2254 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (r2_hidden(A,k4_zfmisc_1(B,C,D,E)) <-> (exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H ((exists I (A = k4_mcart_1(F,G,H,I) & m1_subset_1(I,E))) & m1_subset_1(H,D)))))))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2255 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(D) & m1_subset_1(F,B) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(E,A) & -v1_xboole_0(C) -> k4_mcart_1(E,F,G,H) = k5_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2256 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2257 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2258 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2259 (all A all B all C all D all E all F all G (-v1_xboole_0(C) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & m1_subset_1(E,k1_zfmisc_1(B)) & -v1_xboole_0(D) & -v1_xboole_0(B) -> ((exists H exists I exists J (m1_subset_1(I,C) & m1_subset_1(J,D) & k4_domain_1(B,C,D,H,I,J) = A & r2_hidden(J,G) & r2_hidden(I,F) & r2_hidden(H,E) & m1_subset_1(H,B))) <-> r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2260 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = a_2_1_domain_1(A,B))))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2261 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> I = A))))))))) <-> A = k10_mcart_1(B,C,D,E,F)))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2262 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_domain_1(A,B,C),A))) # label(dt_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2263 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k9_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> A = H)))))))))))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2264 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,B) & E = A & r2_hidden(E,C) & -r2_hidden(E,D))) <-> r2_hidden(A,a_3_3_domain_1(B,C,D))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2265 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) -> k3_enumset1(B,C,D,E,F) = k10_domain_1(A,B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2266 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2267 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2268 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s6_domain_1(B) <-> p2_s6_domain_1(B)))) -> a_1_6_domain_1(A) = a_1_5_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2269 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(F,C) & m1_subset_1(E,B) & m1_subset_1(D,A) & -v1_xboole_0(B) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2270 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F (m1_subset_1(F,B) & (exists G ((exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))) & m1_subset_1(G,C))))) <-> r2_hidden(E,A))) <-> k3_zfmisc_1(B,C,D) = A))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2271 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2272 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B) & A = B)))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2273 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2274 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2275 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((exists E ((exists F ((exists G (A = k3_mcart_1(E,F,G) & m1_subset_1(G,D))) & m1_subset_1(F,C))) & m1_subset_1(E,B))) <-> r2_hidden(A,k3_zfmisc_1(B,C,D))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2276 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_6_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2277 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> a_4_1_domain_1(A,B,C,D) = k12_mcart_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2278 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2279 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,B,D) = D)) <-> r1_binop_1(A,B,C)))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2280 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k1_funct_1(A,k4_tarski(B,C)) = k1_binop_1(A,B,C)))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2281 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(C,B,D)))))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2282 (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) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)) = k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)))))))))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2283 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(D) & m1_subset_1(E,A) & m1_subset_1(F,B) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> k1_binop_1(D,E,F) = k2_binop_1(A,B,C,D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2284 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2285 (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) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,k1_binop_1(B,C,D),E) = k1_binop_1(B,C,k1_binop_1(B,D,E)))))))) <-> v2_binop_1(B,A)))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2286 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2287 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2288 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,C,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]. 22.92/21.99 2289 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2290 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2291 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2292 (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) -> (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]. 22.92/21.99 2293 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r2_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2294 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2295 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> 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(B,k1_binop_1(C,D,E),F) = k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)))))))) <-> r6_binop_1(A,B,C)))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2296 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2297 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2298 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (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]. 22.92/21.99 2299 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r7_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> 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))))))))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2300 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,D,C) = k1_binop_1(B,C,D))))) <-> v1_binop_1(B,A)))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2301 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = C))))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2302 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r2_binop_1(A,C,B) <-> r3_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2303 (exists A ((all B (m1_subset_1(B,f1_s2_binop_1) -> (all C (m1_subset_1(C,f1_s2_binop_1) -> k2_binop_1(f1_s2_binop_1,f1_s2_binop_1,f1_s2_binop_1,A,B,C) = f2_s2_binop_1(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & v1_funct_1(A))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2304 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D) & D = k1_binop_1(B,D,C))) <-> r3_binop_1(A,C,B)))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2305 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> ((exists C (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]. 22.92/21.99 2306 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r2_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k1_binop_1(C,D,B)))))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2307 (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,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) -> k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E)) = k1_funct_1(B,k1_binop_1(C,D,E)))))) <-> r7_binop_1(A,B,C)))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2308 (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 (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]. 22.92/21.99 2309 (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,D,C))))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2310 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,B,C,D,F,G) = k2_binop_1(A,B,C,E,F,G))))) -> D = E))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2311 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2312 (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_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)))))))) <-> r4_binop_1(A,B,C)))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2313 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,F)) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F))))))))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2314 (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) -> k1_binop_1(B,C,C) = C)) <-> v3_binop_1(B,A)))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2315 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (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]. 22.92/21.99 2316 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> v1_xboole_0(A) & v1_binop_1(A,k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2317 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2318 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2319 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F)) = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F))))))))))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2320 (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) -> (r4_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2321 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2322 (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) <-> r1_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2323 (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) -> (r2_binop_1(A,B,C) & r1_binop_1(A,B,C) <-> r3_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2324 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2325 (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_1(A) & (all B (m1_subset_1(B,f1_s1_binop_1) -> (all C (m1_subset_1(C,f1_s1_binop_1) -> p1_s1_binop_1(B,C,k2_binop_1(f1_s1_binop_1,f1_s1_binop_1,f1_s1_binop_1,A,B,C)))))) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & v1_funct_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2326 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> 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]. 22.92/21.99 2327 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2328 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & -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]. 22.92/21.99 2329 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F)))))))) <-> r5_binop_1(A,B,C)))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2330 (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]. 22.92/21.99 2331 (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]. 22.92/21.99 2332 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r5_binop_1(A,C,B) <-> r6_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2333 (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_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]. 22.92/21.99 2334 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k5_relat_1(k2_funcop_1(B,C),A) = k2_funcop_1(B,k1_funct_1(A,C)))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2335 (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 (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2336 (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(k7_relat_1(A,C),B) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2337 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(k4_funcop_1(D,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2338 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2339 (all A (v1_relat_1(A) -> (all B all C (A = k2_zfmisc_1(B,C) -> k1_xboole_0 = B | C = k1_xboole_0 | B = k1_relat_1(A) & k2_relat_1(A) = C)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2340 (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) -> 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]. 22.92/21.99 2341 (all A (k1_xboole_0 = k2_relat_1(k2_funcop_1(k1_xboole_0,A)) & k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2342 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2343 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k4_funcop_1(C,D,E),A,B) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & v1_funct_1(k4_funcop_1(C,D,E)))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2344 (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) -> 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]. 22.92/21.99 2345 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2346 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k4_tarski(E,D) = k1_funct_1(B,C))) & -(k1_funct_1(A,C) != k1_funct_1(B,C) & (all D all E k1_funct_1(A,C) != k4_tarski(D,E))))) & k1_relat_1(A) = k1_relat_1(B) <-> B = k1_funcop_1(A)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/21.99 2347 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2348 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2349 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2350 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> k6_funcop_1(B,A,C,D,D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2351 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2352 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2353 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2354 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2355 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_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) & v1_funct_1(C) & -v1_xboole_0(A) -> k6_funcop_1(A,B,C,D,E) = k3_funcop_1(C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2356 (all A (v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2357 (all A all B all C all D (v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(B) & -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]. 22.92/22.00 2358 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (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]. 22.92/22.00 2359 (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 (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,B),D) = k7_relat_1(k3_funcop_1(E,C,A),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2360 (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) -> (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]. 22.92/22.00 2361 (all A all B all C (v1_relat_1(A) & v1_funct_1(C) & v1_relat_1(C) & v1_funct_1(A) -> v1_relat_1(k5_funcop_1(A,B,C)) & v1_funct_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2362 (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(k4_funcop_1(B,A,D))) -> k1_binop_1(B,k1_funct_1(A,C),D) = k1_funct_1(k4_funcop_1(B,A,D),C))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2363 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2364 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> 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]. 22.92/22.00 2365 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F))) -> D = k7_funcop_1(A,B,C,E,F)))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2366 (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 (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,B) & m2_relset_1(F,A,B) -> ((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]. 22.92/22.00 2367 (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(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]. 22.92/22.00 2368 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C))))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2369 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_funct_1(k5_funcop_1(B,D,A),C) = k1_binop_1(B,D,k1_funct_1(A,C)))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2370 (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]. 22.92/22.00 2371 (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,k7_funcop_1(B,B,C,k6_partfun1(B),E)) = k7_funcop_1(B,A,C,D,E))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2372 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> 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]. 22.92/22.00 2373 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2374 (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]. 22.92/22.00 2375 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2376 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_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]. 22.92/22.00 2377 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2378 (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) -> (v3_binop_1(C,B) -> D = k6_funcop_1(B,A,C,D,D)))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2379 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (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]. 22.92/22.00 2380 (exists A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2381 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> 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]. 22.92/22.00 2382 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2383 (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]. 22.92/22.00 2384 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(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) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -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]. 22.92/22.00 2385 (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]. 22.92/22.00 2386 (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 k4_funcop_1(C,k5_relat_1(B,A),D) = k5_relat_1(B,k4_funcop_1(C,A,D))))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2387 (all A k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A))) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2388 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2389 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) -> k10_funcop_1(A,B,C,D) = k1_funcop_1(D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2390 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2391 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,B) & m2_relset_1(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]. 22.92/22.00 2392 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)) = D)) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2393 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k5_funcop_1(C,E,D)) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & m2_relset_1(k5_funcop_1(C,E,D),A,B))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2394 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2395 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k4_funcop_1(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]. 22.92/22.00 2396 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k4_funcop_1(C,k7_relat_1(A,B),D) = k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D))))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2397 (all A all B all C (-r2_hidden(B,C) -> k1_xboole_0 = k10_relat_1(k2_funcop_1(A,B),C))) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2398 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_funcop_1(C,D,k5_relat_1(B,A)) = k5_relat_1(B,k5_funcop_1(C,D,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2399 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> B = k1_funct_1(A,C))) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2400 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k1_funcop_1(k13_funct_3(B,A)) = k13_funct_3(A,B))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2401 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(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]. 22.92/22.00 2402 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2403 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2404 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,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]. 22.92/22.00 2405 (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]. 22.92/22.00 2406 (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) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2407 (all A all B all C all D all E (v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_funcop_1(C,D,E) = k7_funcop_1(A,B,C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2408 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2409 (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]. 22.92/22.00 2410 (all A all B all C k2_funcop_1(A,k4_tarski(C,B)) = k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C)))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2411 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) -> m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & v1_funct_1(k10_funcop_1(A,B,C,D)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2412 (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]. 22.92/22.00 2413 (all A all B (-v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2414 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> ((all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)))) & k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2415 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2416 (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,k7_funcop_1(A,A,B,k6_partfun1(A),C),C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2417 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2418 (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_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)) = k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2419 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) -> 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]. 22.92/22.00 2420 (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]. 22.92/22.00 2421 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(A) = k1_relat_1(B) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2422 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(A) & k1_relat_1(B) = k1_xboole_0 -> A = B))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2423 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2424 (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(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]. 22.92/22.00 2425 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F)) = k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F)))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2426 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2427 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2428 (all A all B (v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_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]. 22.92/22.00 2429 (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(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]. 22.92/22.00 2430 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2431 (all A all B (k1_xboole_0 != A -> k2_relat_1(k2_funcop_1(A,B)) = k1_tarski(B))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2432 (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_xboole_0 = k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)))))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2433 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (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]. 22.92/22.00 2434 (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 k4_funcop_1(k5_relat_1(C,A),B,D) = k5_relat_1(k4_funcop_1(C,B,D),A)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2435 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (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]. 22.92/22.00 2436 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2437 (all A all B all C (r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = A)) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2438 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2439 (all A all B A = k10_relat_1(k2_funcop_1(A,B),k1_tarski(B))) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2440 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k4_funcop_1(A,B,C)) & v1_funct_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2441 (all A all B all C (r2_hidden(C,B) -> v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2442 (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) -> (all E (m1_subset_1(E,A) -> k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))) = k1_funct_1(k1_funcop_1(D),E))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2443 (all A all B (k1_relat_1(k2_funcop_1(A,B)) = A & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2444 (all A all B (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2445 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(C) -> 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]. 22.92/22.00 2446 (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),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]. 22.92/22.00 2447 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k2_funcop_1(k10_relat_1(A,B),C) = k5_relat_1(A,k2_funcop_1(B,C))))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2448 (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]. 22.92/22.00 2449 (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]. 22.92/22.00 2450 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = k2_funct_4(k2_funct_4(C))))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2451 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(C) = k2_relat_1(k2_funct_4(C))))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2452 (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]. 22.92/22.00 2453 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k3_funct_4(A,B) <-> (all D (r2_hidden(D,k1_relat_1(C)) <-> (exists E exists F exists G exists H (r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)) & D = k4_tarski(k4_tarski(E,G),k4_tarski(F,H)))))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),k1_relat_1(B)) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)) -> k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G))) = k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G)))))))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2454 (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]. 22.92/22.00 2455 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> k1_funct_4(A,B) = B & k1_funct_4(B,A) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2456 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> v1_funct_1(k2_funct_4(D)) & 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))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2457 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_funct_4(A,B)) <-> r1_partfun1(A,B)))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2458 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & k4_tarski(E,D) = C)))) & (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)))) <-> k2_funct_4(A) = B))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2459 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(B,C) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2460 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (C != k1_xboole_0 -> D = k2_funct_4(k2_funct_4(D))))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2461 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2462 (all A (v1_funct_1(A) & v1_relat_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]. 22.92/22.00 2463 (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(A,k1_funct_4(B,C)) = k1_funct_4(k1_funct_4(A,B),C))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2464 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (k1_relat_1(F) = k2_zfmisc_1(C,D) & k1_relat_1(E) = k2_zfmisc_1(A,B) -> k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) = k1_relat_1(k3_funct_4(E,F))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2465 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2466 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2467 (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(C)) | r2_hidden(A,k1_relat_1(B)) <-> r2_hidden(A,k1_relat_1(k1_funct_4(B,C)))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2468 (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)) -> k1_funct_4(A,B) = B))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2469 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_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]. 22.92/22.00 2470 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2471 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (r2_hidden(k4_tarski(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]. 22.92/22.00 2472 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2473 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k1_funct_4(k1_xboole_0,A))) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2474 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> k1_funct_4(A,A) = A)) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2475 (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]. 22.92/22.00 2476 (all A all B all C all D (C != A -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2477 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_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]. 22.92/22.00 2478 (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 -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D))))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2479 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2480 (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) -> k1_funct_4(B,C) = C)))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2481 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> D = k1_funct_4(C,D)))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2482 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2483 (all A all 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) -> D = k2_funct_4(k2_funct_4(D)))))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2484 (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]. 22.92/22.00 2485 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k1_funct_4(A,k1_xboole_0))) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2486 (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]. 22.92/22.00 2487 (all A (v1_funct_1(A) & v1_relat_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]. 22.92/22.00 2488 (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) -> E = k4_funct_4(A,B,C,D)))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2489 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2490 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2491 (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(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2492 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2493 (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) -> (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]. 22.92/22.00 2494 (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))) -> k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2495 (all A all B all C all D (B != A -> D = k1_funct_1(k4_funct_4(A,B,C,D),B) & C = k1_funct_1(k4_funct_4(A,B,C,D),A))) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2496 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2497 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.00 2498 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(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]. 22.92/22.01 2499 (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]. 22.92/22.01 2500 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k1_relat_1(k2_funct_4(C)) = k2_zfmisc_1(B,A)))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2501 (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]. 22.92/22.01 2502 (all A all B all C all D all E all F all G (v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (v1_funct_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 & -(m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H))) & k1_xboole_0 != F))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2503 (all A all B all C all D all E all F (k4_funct_4(A,B,C,D) = k4_funct_4(A,B,E,F) -> F = D & E = C | A = B)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2504 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) = k7_relat_1(k1_funct_4(A,B),C)))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2505 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2506 (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]. 22.92/22.01 2507 (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]. 22.92/22.01 2508 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_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]. 22.92/22.01 2509 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> v1_funct_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) & v1_funct_1(k5_funct_4(A,B,C,D,E)))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2510 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> k2_xboole_0(A,B) = k1_funct_4(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2511 (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_tarski(k1_relat_1(B),D) & r1_xboole_0(C,D) -> A = k7_relat_1(k1_funct_4(A,B),C) & B = k7_relat_1(k1_funct_4(A,B),D))))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2512 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_2(G,k2_zfmisc_1(A,B),E) & m2_relset_1(G,k2_zfmisc_1(A,B),E) & v1_funct_1(G) -> (all H (v1_funct_2(H,k2_zfmisc_1(C,D),F) & m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> v1_funct_1(k3_funct_4(G,H)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & 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)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2513 (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]. 22.92/22.01 2514 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_relat_1(A),k1_relat_1(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]. 22.92/22.01 2515 (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(k2_funct_4(C),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(B,A))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2516 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(A,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2517 (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]. 22.92/22.01 2518 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2519 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_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]. 22.92/22.01 2520 (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]. 22.92/22.01 2521 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(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]. 22.92/22.01 2522 (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]. 22.92/22.01 2523 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2524 (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) -> (C = k1_funct_4(A,B) <-> (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)) & (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(A,D)))) & k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2525 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_partfun1(A,B) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2526 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(B,A) = k1_funct_4(A,B)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2527 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> 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]. 22.92/22.01 2528 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> D = B | k1_xboole_0 = A)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2529 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_relat_1(k3_funct_4(A,B)) & v1_funct_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2530 (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) -> 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]. 22.92/22.01 2531 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2532 (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(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2533 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2534 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2535 (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]. 22.92/22.01 2536 (all A all B all C all D k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D)) = k4_funct_4(A,B,C,D)) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2537 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2538 (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(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]. 22.92/22.01 2539 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(B,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2540 (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]. 22.92/22.01 2541 (all A -((all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2542 (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]. 22.92/22.01 2543 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))) = k5_relat_1(B,A))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2544 (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) = k2_xboole_0(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 22.92/22.01 2545 (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]. 22.92/22.01 2546 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (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))))) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> B = k1_xboole_0 | f4_s11_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & f1_s11_ordinal2 = k1_relat_1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2547 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2548 (exists A (v1_funct_1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s5_ordinal2) -> k1_xboole_0 = B | f4_s5_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s5_ordinal2(B,k1_funct_1(A,B))))) & v5_ordinal1(A) & v1_relat_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2549 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2550 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2551 (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]. 23.03/22.14 2552 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2553 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2554 (exists A (v1_relat_1(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) -> f2_s2_ordinal2(B) = k1_funct_1(A,B)))))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2555 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2556 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2557 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2558 (all A (v3_ordinal1(A) -> A = k3_tarski(k1_ordinal1(A)))) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2559 (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]. 23.03/22.14 2560 (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & B = k1_ordinal2(C) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | f6_s6_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_relat_1(C) = k1_ordinal1(A) & v1_relat_1(C))))))) & (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(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) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & f3_s6_ordinal2 = k1_relat_1(f1_s6_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> f2_s6_ordinal2(A) = k1_funct_1(f1_s6_ordinal2,A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2561 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2562 (all A all B (v3_ordinal1(B) -> v1_ordinal2(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2563 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2564 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2565 (all A all B (v3_ordinal1(B) -> (k7_ordinal2(A) = B <-> r1_tarski(k2_ordinal2(A),B) & (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C))))))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2566 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2567 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2568 (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]. 23.03/22.14 2569 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2570 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_ordinal1(A) -> k1_ordinal2(B) = k1_funct_1(B,A)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2571 (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]. 23.03/22.14 2572 (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]. 23.03/22.14 2573 (all A all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) & v3_ordinal1(A) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2574 (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]. 23.03/22.14 2575 (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]. 23.03/22.14 2576 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> k1_xboole_0 = 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) = k14_ordinal2(B,D)))) -> k14_ordinal2(B,A) = k8_ordinal2(C))))))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2577 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2578 (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]. 23.03/22.14 2579 (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]. 23.03/22.14 2580 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(A,k16_ordinal2(A,B)) = k16_ordinal2(A,k1_ordinal1(B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2581 (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]. 23.03/22.14 2582 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2583 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2584 (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]. 23.03/22.14 2585 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.14 2586 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f4_s15_ordinal2(A) = B <-> (exists C (v1_relat_1(C) & k1_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f3_s15_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s15_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & 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]. 23.03/22.15 2587 (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]. 23.03/22.15 2588 (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]. 23.03/22.15 2589 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2590 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> (v2_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C)))))))))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2591 (all A (v3_ordinal1(A) -> (all B -(r2_hidden(A,k7_ordinal2(B)) & (all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2592 (exists A ((exists B (v1_funct_1(B) & v1_ordinal2(B) & k1_relat_1(B) = k1_ordinal1(f1_s13_ordinal2) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> f4_s13_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C) | k1_xboole_0 = C))) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & k1_ordinal2(B) = A & v5_ordinal1(B) & v1_relat_1(B))) & v3_ordinal1(A))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2593 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(A != B & (exists C (v5_ordinal1(C) & k1_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C))) & (exists C (v5_ordinal1(C) & v1_ordinal2(C) & k1_ordinal2(C) = A & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) -> 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)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & v1_funct_1(C) & v1_relat_1(C)))))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2594 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2595 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2596 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2597 (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]. 23.03/22.15 2598 (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]. 23.03/22.15 2599 (all A all B (v1_funct_1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_relat_1(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2600 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2601 (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]. 23.03/22.15 2602 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2603 (exists A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2604 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) & v4_ordinal1(A) -> p1_s1_ordinal2(A) | A = k1_xboole_0))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2605 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(k1_ordinal1(A),B) = k14_ordinal2(k15_ordinal2(A,B),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2606 (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]. 23.03/22.15 2607 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2608 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v5_ordinal1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k1_funct_1(D,k1_ordinal1(E)) = k14_ordinal2(k1_funct_1(D,E),B)))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(A)) & v4_ordinal1(E) -> k1_xboole_0 = E | k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E)))))) & k1_xboole_0 = k1_funct_1(D,k1_xboole_0) & k1_relat_1(D) = k1_ordinal1(A) & C = k1_ordinal2(D) & v1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D))) <-> k15_ordinal2(A,B) = C))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2609 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v5_ordinal1(C) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (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)) -> f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f2_s14_ordinal2 & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C))) <-> B = f1_s14_ordinal2(A)))))) -> f2_s14_ordinal2 = f1_s14_ordinal2(k1_xboole_0) # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2610 (all A (v3_ordinal1(A) -> (exists B (v3_ordinal1(B) & (exists C (v3_ordinal1(C) & v4_ordinal1(B) & v4_ordinal2(C) & A = k14_ordinal2(B,C))))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2611 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2612 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> ((exists B (r1_ordinal2(B,A) & v3_ordinal1(B))) -> (all B (v3_ordinal1(B) -> (r1_ordinal2(B,A) <-> k12_ordinal2(A) = B)))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2613 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.03/22.15 2614 (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]. 23.11/22.22 2615 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2616 (all A (v3_ordinal1(A) -> (exists B (v3_ordinal1(B) & v4_ordinal1(B) & r2_hidden(A,B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2617 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2618 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2619 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k16_ordinal2(A,B) <-> (exists D (v1_relat_1(D) & v1_funct_1(D) & v1_ordinal2(D) & k1_ordinal1(B) = k1_relat_1(D) & (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) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_funct_1(D,E) = k12_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & C = k1_ordinal2(D) & v5_ordinal1(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2620 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2621 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2622 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2623 (all A all B (B = k2_ordinal2(A) <-> (all C (r2_hidden(C,A) & v3_ordinal1(C) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2624 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)) & k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2625 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2626 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_ordinal2(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]. 23.11/22.22 2627 k1_relat_1(f1_s12_ordinal2) = f3_s12_ordinal2 & (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(A,f3_s12_ordinal2) & v4_ordinal1(A) -> k1_xboole_0 = A | k1_funct_1(f1_s12_ordinal2,A) = f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v1_ordinal2(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & f4_s12_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & v5_ordinal1(C) & v1_relat_1(C))) <-> B = f2_s12_ordinal2(A)))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> k1_funct_1(f1_s12_ordinal2,A) = f2_s12_ordinal2(A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2628 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2629 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2630 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.22 2631 (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]. 23.11/22.24 2632 (all A all B ((all C ((exists D (v4_ordinal1(D) & D = C & v3_ordinal1(D))) & r2_hidden(C,A) <-> r2_hidden(C,B))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2633 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) & A = k1_relat_1(C) -> k12_ordinal2(C) = k16_ordinal2(B,A)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2634 (all A all B (v1_funct_1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(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]. 23.11/22.24 2635 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2636 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2637 (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]. 23.11/22.24 2638 (all A (v3_ordinal1(A) -> k16_ordinal2(k4_ordinal2,A) = k4_ordinal2 & k16_ordinal2(A,k4_ordinal2) = A)) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2639 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (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) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,A) | k1_xboole_0 = A))) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) -> f5_s4_ordinal2 = f6_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2640 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2641 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k1_relat_1(A) = k1_relat_1(C) & B = k9_ordinal2(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))) <-> k10_ordinal2(A) = B))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2642 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2643 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> (A != k1_xboole_0 -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -(r2_hidden(E,k1_relat_1(B)) & (all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,F),D) & r2_hidden(C,k1_funct_1(B,F)))))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))) & (k1_xboole_0 = A -> ((exists C ((all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) & r1_ordinal1(C,D) -> k1_xboole_0 = k1_funct_1(B,D)))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2644 (all A (v3_ordinal1(A) -> (all B all C (r1_tarski(B,C) & r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2645 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2646 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k14_ordinal2(A,B) <-> (exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & C = k1_ordinal2(D) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> 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_ordinal1(k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & k1_funct_1(D,k1_xboole_0) = A & k1_relat_1(D) = k1_ordinal1(B)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2647 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s9_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f3_s9_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & k1_ordinal2(C) = B & v1_relat_1(C))) <-> f4_s9_ordinal2(A) = B)))) -> (all A (v3_ordinal1(A) -> f2_s9_ordinal2(A,f4_s9_ordinal2(A)) = f4_s9_ordinal2(k1_ordinal1(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2648 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2649 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2650 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2651 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2652 (all A (v3_ordinal1(A) -> (all B ((exists C (k1_funct_1(C,k1_xboole_0) = f2_s8_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s8_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_relat_1(C) = k1_ordinal1(A) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> f1_s8_ordinal2(A) = B)))) -> f1_s8_ordinal2(k1_xboole_0) = f2_s8_ordinal2 # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2653 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) & A = k1_relat_1(C) -> k15_ordinal2(A,B) = k3_tarski(k8_ordinal2(C))))) | k1_xboole_0 = A))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2654 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (v4_ordinal1(B) & C = k1_funct_1(A,B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | B = k1_xboole_0))))) <-> v3_ordinal2(A)))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.24 2655 (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]. 23.11/22.24 2656 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = k11_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & B = k8_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k1_relat_1(A) = k1_relat_1(C) & v1_funct_1(C)))))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.25 2657 (exists A (v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & k1_relat_1(A) = f1_s3_ordinal2 & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.25 2658 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.25 2659 (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]. 23.11/22.25 2660 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_tarski(k2_relat_1(A),B))) <-> v1_ordinal2(A)))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.25 2661 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f3_s16_ordinal2(A) <-> (exists C (v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s16_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & f4_s16_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C)))))))) & f2_s16_ordinal2 != k1_xboole_0 & v4_ordinal1(f2_s16_ordinal2) & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2662 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & k1_ordinal2(B) = A & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2) & (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))) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s7_ordinal2(C,k1_funct_1(B,C))))) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & v5_ordinal1(B))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2663 (all A all B -(A != B & (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D))))) & (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_ordinal2(C) = B & v1_relat_1(C))) & (exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & 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)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D))))) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & v1_funct_1(C))))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2664 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2665 (all A (k5_ordinal2 = A <-> v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v4_ordinal1(A) & r2_hidden(k1_xboole_0,A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2666 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2667 (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) & f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & v5_ordinal1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> f6_s10_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(A)) -> f5_s10_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v1_relat_1(C))) <-> B = f3_s10_ordinal2(A))))) -> f3_s10_ordinal2(f2_s10_ordinal2) = f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2668 (all A -((all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & v6_ordinal1(A) & A != k1_xboole_0 & v1_finset_1(A))) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2669 (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(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2670 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2671 (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]. 23.11/22.26 2672 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2673 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2674 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & v1_finset_1(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2675 (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]. 23.11/22.26 2676 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2677 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> A = k1_xboole_0 | v1_finset_1(B))) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2678 (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]. 23.11/22.26 2679 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2680 (all A -(v1_finset_1(A) & k1_xboole_0 != A & v6_ordinal1(A) & (all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(B,C))))))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2681 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2682 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (-p1_s1_finset_1(B) -> f3_s1_finset_1(B) = k1_funct_1(A,B)) & (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B))))) & f1_s1_finset_1 = k1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2683 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2684 (all A all B (v1_finset_1(k2_tarski(A,B)) & -v1_xboole_0(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2685 (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]. 23.11/22.26 2686 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(A) <-> v1_finset_1(k1_relat_1(A))))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2687 p1_s2_finset_1(k1_xboole_0) & (all A all B (r1_tarski(B,f1_s2_finset_1) & p1_s2_finset_1(B) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & 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]. 23.11/22.26 2688 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2689 (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]. 23.11/22.26 2690 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2691 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2692 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2693 (all A all B (v1_relat_1(A) & v1_finset_1(B) & v1_funct_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2694 (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]. 23.11/22.26 2695 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2696 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2697 (all A (v1_finset_1(A) <-> (exists B (r2_hidden(k1_relat_1(B),k5_ordinal2) & A = k2_relat_1(B) & v1_funct_1(B) & v1_relat_1(B))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2698 (all A (v1_finset_1(A) <-> v1_finset_1(k1_zfmisc_1(A)))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2699 (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]. 23.11/22.26 2700 (all A all B all C all D (v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2701 (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]. 23.11/22.26 2702 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2703 (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]. 23.11/22.26 2704 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2705 (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]. 23.11/22.26 2706 (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]. 23.11/22.26 2707 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2708 (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]. 23.11/22.26 2709 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2710 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2711 (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]. 23.11/22.26 2712 (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]. 23.11/22.26 2713 (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]. 23.11/22.26 2714 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_ordinal1(B) & v3_ordinal1(B) & v1_finset_1(B) & v4_ordinal2(B) & v2_ordinal1(B) & v2_funct_1(B) & v1_funct_1(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2715 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2716 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2717 (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]. 23.11/22.26 2718 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2719 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_xboole_0(A,B)))) # label(t14_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2720 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -((all C -((all D (r2_hidden(D,B) & r1_tarski(C,D) -> D = C)) & r2_hidden(C,B))) & B != k1_xboole_0))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2721 (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]. 23.11/22.26 2722 (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]. 23.11/22.26 2723 (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]. 23.11/22.26 2724 (all A ((all B (r2_hidden(B,A) -> v1_finset_1(B))) & v1_finset_1(A) <-> v1_finset_1(k3_tarski(A)))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2725 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2726 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_finsub_1(A),k5_finsub_1(B)))) # label(t23_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2727 (all A (v4_finsub_1(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t18_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2728 (all A (v3_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A))))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2729 (all A (-v1_xboole_0(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2730 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k2_finsub_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2731 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2732 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k2_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t17_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2733 (all A all B k5_finsub_1(k3_xboole_0(A,B)) = k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B))) # label(t24_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2734 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2735 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> (all B (v4_finsub_1(B) & -v1_xboole_0(B) -> v4_finsub_1(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2736 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k3_xboole_0(B,C),A) & r2_hidden(k5_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2737 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2738 (all A all B all C (-v1_xboole_0(C) & v4_finsub_1(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2739 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k1_finsub_1(A,B,B) = B)) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2740 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2741 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k3_finsub_1(A,B,C),A))) # label(dt_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2742 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2743 (all A (v3_finsub_1(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) & v1_finsub_1(k5_finsub_1(A)) & -v1_xboole_0(k5_finsub_1(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2744 (all A all B all C (-v1_xboole_0(C) & v4_finsub_1(C) -> (m1_subset_1(A,C) & m1_subset_1(B,C) -> m1_subset_1(k5_xboole_0(A,B),C)))) # label(t14_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2745 (all A (v4_finsub_1(A) -> v3_finsub_1(A) & v1_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2746 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2747 (all A (v3_finsub_1(A) & v1_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2748 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2749 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2750 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_finset_1(A) -> m1_subset_1(B,k5_finsub_1(A))))) # label(t34_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2751 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2752 (exists A (-v1_xboole_0(A) & v4_finsub_1(A) & v3_finsub_1(A) & v2_finsub_1(A) & v1_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2753 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_finsub_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2754 (all A (v1_finset_1(A) -> k5_finsub_1(A) = k1_zfmisc_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2755 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> k3_finsub_1(A,B,B) = B)) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2756 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k4_finsub_1(A,C,B) = k4_finsub_1(A,B,C))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2757 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k3_xboole_0(B,C),A))) <-> v2_finsub_1(A))) # label(d2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2758 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> m1_subset_1(k4_finsub_1(A,B,C),A))) # label(dt_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2759 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2760 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))) <-> v4_finsub_1(A))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2761 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t15_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2762 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2763 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2764 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(t30_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2765 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2766 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k1_finsub_1(A,C,B) = k1_finsub_1(A,B,C))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2767 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2768 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2769 (all A all B (v4_finsub_1(B) -> (k5_finsub_1(A) = B <-> (all C (v1_finset_1(C) & r1_tarski(C,A) <-> r2_hidden(C,B)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2770 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k3_finsub_1(A,C,B) = k3_finsub_1(A,B,C))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2771 (all A (v1_finsub_1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k2_xboole_0(B,C),A))))) # label(d1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2772 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(B,k1_zfmisc_1(A)))) # label(t32_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2773 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2774 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2775 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2776 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2777 (all A all B r1_tarski(k2_xboole_0(k5_finsub_1(A),k5_finsub_1(B)),k5_finsub_1(k2_xboole_0(A,B)))) # label(t25_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2778 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2779 (all A (v4_finsub_1(A) <-> v3_finsub_1(A) & v1_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2780 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2781 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2782 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k5_xboole_0(B,C) = k4_finsub_1(A,B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2783 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) & v1_funct_2(C,B,A) & v1_funct_1(C) -> (all D (m1_subset_1(D,B) -> r2_hidden(D,k3_funct_2(B,A,C,k1_tarski(k8_funct_2(B,A,C,D)))))))))))) # label(t12_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2784 (all A v3_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t49_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2785 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k4_setwiseo(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2786 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k4_xboole_0(k9_relat_1(C,B),A) = k9_relat_1(C,k4_xboole_0(B,k10_relat_1(C,A))))) # label(t11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2787 (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> (all B (m1_subset_1(B,f1_s2_setwiseo) -> (p1_s2_setwiseo(A) -> p1_s2_setwiseo(k5_setwiseo(f1_s2_setwiseo,A,k2_setwiseo(f1_s2_setwiseo,B))) | r2_hidden(B,A)))))) & p1_s2_setwiseo(k1_setwiseo(f1_s2_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s2_setwiseo)) -> p1_s2_setwiseo(A))) # label(s2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2788 (all A all B all C (r2_hidden(A,B) | C = A <-> r2_hidden(A,k2_xboole_0(B,k1_tarski(C))))) # label(t6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.26 2789 (all A all B (m2_relset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_2(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & v1_funct_1(B) -> (B = k9_setwiseo(A) <-> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k5_setwiseo(A,C,D) = k2_binop_1(k5_finsub_1(A),k5_finsub_1(A),k5_finsub_1(A),B,C,D)))))))) # label(d4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2790 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k6_setwiseo(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2791 $T # label(t7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2792 (all A k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)) = k1_xboole_0) # label(t55_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2793 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) -> k10_setwiseo(B,C,k8_setwiseo(A,B,E,D),F) = k10_setwiseo(A,C,D,k7_funct_2(A,B,k5_finsub_1(C),E,F)))))))))))) # label(t63_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2794 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> B = k10_setwiseo(A,A,B,k11_setwiseo(A)))))) # label(t71_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2795 (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> (all B (m1_subset_1(B,f1_s4_setwiseo) -> (p1_s4_setwiseo(A) -> p1_s4_setwiseo(k5_setwiseo(f1_s4_setwiseo,A,k2_setwiseo(f1_s4_setwiseo,B)))))))) & p1_s4_setwiseo(k1_setwiseo(f1_s4_setwiseo)) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s4_setwiseo)) -> p1_s4_setwiseo(A))) # label(s4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2796 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k5_finsub_1(A)))))) # label(t16_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2797 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k3_setwiseo(A,C,B) = k3_setwiseo(A,B,C))) # label(commutativity_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2798 (all A all B all C -(r1_tarski(A,k2_xboole_0(B,k1_tarski(C))) & -r1_tarski(A,B) & -r2_hidden(C,A))) # label(t5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2799 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) -> k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) = k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E)))))))))))))) # label(t29_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2800 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (B = C <-> r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C))))))) # label(t68_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2801 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v3_binop_1(C,A) & v2_binop_1(C,A) & v1_setwiseo(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D)))))))))))))) # label(t42_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2802 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> k2_xboole_0(B,C) = k5_setwiseo(A,B,C))) # label(redefinition_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2803 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (v2_binop_1(C,B) & v1_binop_1(C,B) -> D = k1_xboole_0 & -v1_setwiseo(C,B) | (all F (m1_subset_1(F,B) -> ((exists G (v1_funct_1(G) & v1_funct_2(G,k5_finsub_1(A),B) & m2_relset_1(G,k5_finsub_1(A),B) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> (all I (m1_subset_1(I,A) -> (r2_hidden(I,k6_setwiseo(A,D,H)) -> k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))) = k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I))))) | k1_xboole_0 = H))) & (all H (m1_subset_1(H,A) -> k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)) = k8_funct_2(A,B,E,H))) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> H = k1_funct_1(G,k1_xboole_0)))) & k8_funct_2(k5_finsub_1(A),B,G,D) = F)) <-> k7_setwiseo(A,B,C,D,E) = F)))))))))))))) # label(d3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2804 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (v2_binop_1(D,A) & v3_binop_1(D,A) & v1_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_2(F,B,k5_finsub_1(C)) & m2_relset_1(F,B,k5_finsub_1(C)) & v1_funct_1(F) -> (all G (v1_funct_2(G,k5_finsub_1(C),A) & m2_relset_1(G,k5_finsub_1(C),A) & v1_funct_1(G) -> ((all H (m1_subset_1(H,k5_finsub_1(C)) -> (all I (m1_subset_1(I,k5_finsub_1(C)) -> k8_funct_2(k5_finsub_1(C),A,G,k5_setwiseo(C,H,I)) = k2_binop_1(A,A,A,D,k8_funct_2(k5_finsub_1(C),A,G,H),k8_funct_2(k5_finsub_1(C),A,G,I)))))) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,k5_finsub_1(C),A,F,G)) = k8_funct_2(k5_finsub_1(C),A,G,k10_setwiseo(B,C,E,F))))))))))))))))) # label(t64_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2805 $T # label(t2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2806 $T # label(t24_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2807 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k5_setwiseo(A,B,B) = B)) # label(idempotence_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2808 (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,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v1_binop_1(D,A) & v2_binop_1(D,A) & v3_binop_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (k1_xboole_0 != E -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> (all G (v1_funct_2(G,C,A) & m2_relset_1(G,C,A) & v1_funct_1(G) -> k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G)) = k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G))))))))))))))))) # label(t38_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2809 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_binop_1(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> -(k1_xboole_0 != F & k7_setwiseo(B,A,C,k5_setwiseo(B,E,F),D) != k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) & k1_xboole_0 != E)))))))))))))) # label(t30_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2810 (all A (v1_funct_1(k9_setwiseo(A)) & v1_funct_2(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)) & m2_relset_1(k9_setwiseo(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k5_finsub_1(A)))) # label(dt_k9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2811 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(k5_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2812 $T # label(t20_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.27 2813 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)))) # label(dt_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2814 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k10_setwiseo(A,B,k4_setwiseo(A,D,E,F),C) = k5_setwiseo(B,k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)),k8_funct_2(A,k5_finsub_1(B),C,F)))))))))))) # label(t58_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2815 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k5_setwiseo(B,k10_setwiseo(A,B,D,C),k10_setwiseo(A,B,E,C)) = k10_setwiseo(A,B,k5_setwiseo(A,D,E),C))))))))) # label(t62_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2816 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (v1_binop_1(C,A) & v1_setwiseo(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,D,E),k8_funct_2(B,A,E,F)) = k7_setwiseo(B,A,C,k5_setwiseo(B,D,k2_setwiseo(B,F)),E)))))))))))))) # label(t41_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2817 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k5_finsub_1(A)))))) # label(rc2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2818 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (r2_hidden(C,B) -> m1_subset_1(C,A))))))) # label(t14_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2819 (all A all B all C r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C))) # label(t4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2820 (all A (-v1_xboole_0(A) -> (all B all C (m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k5_setwiseo(B,k10_setwiseo(A,B,E,C),k8_funct_2(A,k5_finsub_1(B),C,D)) = k10_setwiseo(A,B,k5_setwiseo(A,E,k2_setwiseo(A,D)),C))))))))) # label(t60_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2821 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(F,D) -> k7_setwiseo(B,A,C,D,E) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,F),k7_setwiseo(B,A,C,D,E)))))))))))))))) # label(t31_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2822 (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 (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (v1_binop_1(C,B) & v2_binop_1(C,B) & v3_binop_1(C,B) -> -v1_setwiseo(C,B) & k1_xboole_0 = D | (all F (m1_subset_1(F,B) -> (k7_setwiseo(A,B,C,D,E) = F <-> (exists G (v1_funct_1(G) & m2_relset_1(G,k5_finsub_1(A),B) & (all H (m1_subset_1(H,B) -> (r3_binop_1(B,H,C) -> k1_funct_1(G,k1_xboole_0) = H))) & (all H (m1_subset_1(H,k5_finsub_1(A)) -> (r1_tarski(H,D) -> H = k1_xboole_0 | (all I (m1_subset_1(I,A) -> (r2_hidden(I,D) -> k2_binop_1(B,B,B,C,k8_funct_2(k5_finsub_1(A),B,G,H),k8_funct_2(A,B,E,I)) = k8_funct_2(k5_finsub_1(A),B,G,k5_setwiseo(A,H,k2_setwiseo(A,I))))))))) & (all H (m1_subset_1(H,A) -> k8_funct_2(A,B,E,H) = k8_funct_2(k5_finsub_1(A),B,G,k2_setwiseo(A,H)))) & F = k8_funct_2(k5_finsub_1(A),B,G,D) & v1_funct_2(G,k5_finsub_1(A),B))))))))))))))))) # label(t25_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2823 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (r6_binop_1(A,D,C) & v2_binop_1(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (v1_funct_2(F,B,A) & m2_relset_1(F,B,A) & v1_funct_1(F) -> (all G (m1_subset_1(G,A) -> k2_binop_1(A,A,A,D,k7_setwiseo(B,A,C,E,F),G) = k7_setwiseo(B,A,C,E,k7_funcop_1(A,B,D,F,G)))))))))))))))))) # label(t37_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2824 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,B,A) & m2_relset_1(C,B,A) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (k2_funct_2(B,A,C,D) = k1_xboole_0 -> D = k1_xboole_0))))))))) # label(t19_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2825 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(B,A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,k3_binop_1(A,B),C) = C & k2_binop_1(A,A,A,B,C,k3_binop_1(A,B)) = C))))))) # label(t23_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2826 (all A (v1_xboole_0(k1_setwiseo(A)) & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)))) # label(dt_k1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2827 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_2(C,A,B) -> k8_setwiseo(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2828 (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 (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> D = k1_xboole_0 | (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> (r2_hidden(G,D) -> F = k8_funct_2(B,A,E,G)))) -> k7_setwiseo(B,A,C,D,E) = F)))))))))))))) # label(t33_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2829 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k3_setwiseo(A,B,C) = k2_tarski(B,C))) # label(redefinition_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2830 $T # label(t46_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2831 (all A all B all C (m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k6_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2832 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> k7_setwiseo(B,A,C,k2_setwiseo(B,E),D) = k8_funct_2(B,A,D,E)))))))))))) # label(t26_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2833 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s1_setwiseo) -> (all C (m1_subset_1(C,f1_s1_setwiseo) -> (r2_hidden(C,f2_s1_setwiseo) & p1_s1_setwiseo(C,B) <-> r2_hidden(C,k8_funct_2(f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo),A,B))))))) & m2_relset_1(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)) & v1_funct_2(A,f1_s1_setwiseo,k5_finsub_1(f1_s1_setwiseo)))) # label(s1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2834 (all A all B all C (r2_hidden(B,C) & r1_tarski(A,C) <-> r1_tarski(k2_xboole_0(A,k1_tarski(B)),C))) # label(t8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2835 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(B,A) <-> (exists C (r3_binop_1(A,C,B) & m1_subset_1(C,A)))))))) # label(d2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2836 (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) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_2(E,k2_zfmisc_1(D,D),D) -> (v3_binop_1(E,D) & v2_binop_1(E,D) & v1_binop_1(E,D) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,B,D) & v1_funct_2(G,B,D) -> ((all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> (H != k1_xboole_0 -> k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G)))))))))))))))))))))) # label(t39_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2837 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_2(D,A,k5_finsub_1(B)) & v1_funct_1(D) -> k7_setwiseo(A,k5_finsub_1(B),k9_setwiseo(B),C,D) = k10_setwiseo(A,B,C,D))))))) # label(d5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2838 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v1_setwiseo(B,A) <-> r3_binop_1(A,k3_binop_1(A,B),B)))))) # label(t22_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2839 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k3_setwiseo(A,B,C),k5_finsub_1(A)))) # label(dt_k3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2840 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_2(B,A,k5_finsub_1(A)) -> ((all C (m1_subset_1(C,A) -> k8_funct_2(A,k5_finsub_1(A),B,C) = k2_setwiseo(A,C))) <-> B = k11_setwiseo(A)))))) # label(t67_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2841 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> r2_hidden(k8_funct_2(A,B,E,F),D)))) -> r1_tarski(k2_funct_2(A,B,E,C),D)))))))))) # label(t15_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2842 (all A (-v1_xboole_0(A) -> (all B all C all D (v1_funct_2(D,A,k5_finsub_1(B)) & m2_relset_1(D,A,k5_finsub_1(B)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k5_finsub_1(B),k5_finsub_1(C)) & v1_funct_2(E,k5_finsub_1(B),k5_finsub_1(C)) -> (k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k1_setwiseo(B)) = k1_setwiseo(C) & (all F (m1_subset_1(F,k5_finsub_1(B)) -> (all G (m1_subset_1(G,k5_finsub_1(B)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k5_setwiseo(B,F,G)) = k5_setwiseo(C,k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,F),k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,G)))))) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> k8_funct_2(k5_finsub_1(B),k5_finsub_1(C),E,k10_setwiseo(A,B,F,D)) = k10_setwiseo(A,C,F,k7_funct_2(A,k5_finsub_1(B),k5_finsub_1(C),D,E))))))))))) # label(t72_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2843 (all A k1_xboole_0 = k1_setwiseo(A)) # label(d1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2844 (all A exists B (m1_subset_1(B,k5_finsub_1(A)) & v1_xboole_0(B) & v1_finset_1(B))) # label(rc1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2845 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all F (m1_subset_1(F,B) -> (k2_setwiseo(B,F) = k2_funct_2(A,B,E,D) -> F = k7_setwiseo(A,B,C,D,E))))))))))))))) # label(t34_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2846 $T # label(t21_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2847 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,B,A) & v1_funct_2(C,B,A) -> (all D (m1_subset_1(D,B) -> k2_funct_2(B,A,C,k1_tarski(D)) = k1_tarski(k8_funct_2(B,A,C,D)))))))))) # label(t13_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2848 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v3_binop_1(D,A) & v1_binop_1(D,A) & v2_binop_1(D,A) & v1_setwiseo(D,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> (all G (v1_funct_2(G,C,A) & m2_relset_1(G,C,A) & v1_funct_1(G) -> k7_setwiseo(C,A,D,k8_setwiseo(B,C,F,E),G) = k7_setwiseo(B,A,D,E,k7_funct_2(B,C,A,F,G))))))))))))))))) # label(t44_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2849 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(D) & v1_funct_2(D,A,k5_finsub_1(B)) & m1_relset_1(D,A,k5_finsub_1(B)) & m1_subset_1(C,k5_finsub_1(A)) -> m1_subset_1(k10_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2850 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k1_tarski(B) = k2_setwiseo(A,B))) # label(redefinition_k2_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2851 $T # label(t48_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2852 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> (all E (r2_hidden(E,k10_setwiseo(A,B,D,C)) <-> (exists F (r2_hidden(F,D) & r2_hidden(E,k8_funct_2(A,k5_finsub_1(B),C,F)) & m1_subset_1(F,A))))))))))) # label(t70_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2853 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,k5_finsub_1(A)) & v1_funct_1(C) & -v1_xboole_0(A) -> m1_subset_1(k8_setwiseo(A,B,C,D),k5_finsub_1(B)))) # label(dt_k8_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2854 $T # label(t66_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2855 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> m1_subset_1(k4_setwiseo(A,B,C,D),k5_finsub_1(A)))) # label(dt_k4_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2856 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> k10_setwiseo(A,B,D,C) = k3_tarski(k8_setwiseo(A,k5_finsub_1(B),C,D)))))))) # label(t61_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2857 (all A v2_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t51_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2858 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & k1_xboole_0 != B))))) # label(t18_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2859 $T # label(t17_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2860 (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) -> (v3_binop_1(C,B) & v1_setwiseo(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k8_setwiseo(A,B,E,G) = k8_setwiseo(A,B,D,F) -> k7_setwiseo(A,B,C,G,E) = k7_setwiseo(A,B,C,F,D))))))))))))))))) # label(t43_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2861 (all A r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A))) # label(t52_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2862 $T # label(t1_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2863 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,A) -> k10_setwiseo(A,B,k2_setwiseo(A,D),C) = k8_funct_2(A,k5_finsub_1(B),C,D))))))) # label(t56_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2864 $T # label(t47_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2865 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (v3_binop_1(C,B) & v2_binop_1(C,B) & v1_binop_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,k5_finsub_1(A)) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> (k2_funct_2(A,B,E,G) = k2_funct_2(A,B,D,F) -> k1_xboole_0 = F | k7_setwiseo(A,B,C,G,E) = k7_setwiseo(A,B,C,F,D))))))))))))))))) # label(t35_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2866 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C all D (m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v2_binop_1(D,B) & v1_setwiseo(D,B) & v3_binop_1(D,B) & v1_binop_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,k5_finsub_1(C)) & m2_relset_1(E,A,k5_finsub_1(C)) -> (all F (v1_funct_1(F) & v1_funct_2(F,k5_finsub_1(C),B) & m2_relset_1(F,k5_finsub_1(C),B) -> (k3_binop_1(B,D) = k8_funct_2(k5_finsub_1(C),B,F,k1_setwiseo(C)) & (all G (m1_subset_1(G,k5_finsub_1(C)) -> (all H (m1_subset_1(H,k5_finsub_1(C)) -> k2_binop_1(B,B,B,D,k8_funct_2(k5_finsub_1(C),B,F,G),k8_funct_2(k5_finsub_1(C),B,F,H)) = k8_funct_2(k5_finsub_1(C),B,F,k5_setwiseo(C,G,H)))))) -> (all G (m1_subset_1(G,k5_finsub_1(A)) -> k7_setwiseo(A,B,D,G,k7_funct_2(A,k5_finsub_1(C),B,E,F)) = k8_funct_2(k5_finsub_1(C),B,F,k10_setwiseo(A,C,G,E)))))))))))))))) # label(t65_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2867 (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) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v1_setwiseo(C,A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> k3_binop_1(A,C) = k7_setwiseo(B,A,C,k1_setwiseo(B),D)))))))))) # label(t40_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2868 (all A all B all C (m1_subset_1(C,k5_finsub_1(A)) & m1_subset_1(B,k5_finsub_1(A)) -> k5_setwiseo(A,B,C) = k5_setwiseo(A,C,B))) # label(commutativity_k5_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2869 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_hidden(B,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) & r2_hidden(C,k8_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),D)) -> B = C))))))))) # label(t69_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2870 (all A r3_binop_1(k5_finsub_1(A),k3_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A))) # label(t54_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2871 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (v1_binop_1(C,A) & v2_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (all F (m1_subset_1(F,k5_finsub_1(B)) -> (r1_tarski(E,F) -> k2_binop_1(A,A,A,C,k7_setwiseo(B,A,C,E,D),k7_setwiseo(B,A,C,F,D)) = k7_setwiseo(B,A,C,F,D) | E = k1_xboole_0)))))))))))))) # label(t32_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2872 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (v1_binop_1(C,B) & v3_binop_1(C,B) & v1_setwiseo(C,B) & v2_binop_1(C,B) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(D,D),D) & v1_funct_2(E,k2_zfmisc_1(D,D),D) -> (v1_binop_1(E,D) & v3_binop_1(E,D) & v1_setwiseo(E,D) & v2_binop_1(E,D) -> (all F (m2_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) -> (all G (m2_relset_1(G,B,D) & v1_funct_2(G,B,D) & v1_funct_1(G) -> (k8_funct_2(B,D,G,k3_binop_1(B,C)) = k3_binop_1(D,E) & (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> k8_funct_2(B,D,G,k2_binop_1(B,B,B,C,H,I)) = k2_binop_1(D,D,D,E,k8_funct_2(B,D,G,H),k8_funct_2(B,D,G,I)))))) -> (all H (m1_subset_1(H,k5_finsub_1(A)) -> k8_funct_2(B,D,G,k7_setwiseo(A,B,C,H,F)) = k7_setwiseo(A,D,E,H,k7_funct_2(A,B,D,F,G))))))))))))))))))))) # label(t45_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2873 (all A v1_binop_1(k9_setwiseo(A),k5_finsub_1(A))) # label(t50_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2874 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & m2_relset_1(C,A,k5_finsub_1(B)) & v1_funct_2(C,A,k5_finsub_1(B)) -> k10_setwiseo(A,B,k1_setwiseo(A),C) = k1_xboole_0)))) # label(t59_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2875 (all A all B all C r1_tarski(k1_tarski(A),k1_enumset1(A,B,C))) # label(t3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2876 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,k5_finsub_1(A)) & m1_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) & -v1_xboole_0(A) -> m1_subset_1(k7_setwiseo(A,B,C,D,E),B))) # label(dt_k7_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2877 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (v3_binop_1(C,A) & r6_binop_1(A,D,C) & v2_binop_1(C,A) & v1_binop_1(C,A) -> (all E (m1_subset_1(E,k5_finsub_1(B)) -> (E != k1_xboole_0 -> (all F (m2_relset_1(F,B,A) & v1_funct_2(F,B,A) & v1_funct_1(F) -> (all G (m1_subset_1(G,A) -> k7_setwiseo(B,A,C,E,k8_funcop_1(A,B,D,G,F)) = k2_binop_1(A,A,A,D,G,k7_setwiseo(B,A,C,E,F)))))))))))))))))) # label(t36_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2878 (all A (v1_funct_1(k11_setwiseo(A)) & m2_relset_1(k11_setwiseo(A),A,k5_finsub_1(A)) & v1_funct_2(k11_setwiseo(A),A,k5_finsub_1(A)))) # label(dt_k11_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2879 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (v2_binop_1(C,A) & v1_binop_1(C,A) & v3_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F)),k8_funct_2(B,A,D,G)) = k7_setwiseo(B,A,C,k4_setwiseo(B,E,F,G),D)))))))))))))))) # label(t28_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2880 (all A (-v1_xboole_0(A) -> (all B all C (v1_funct_1(C) & v1_funct_2(C,A,k5_finsub_1(B)) & m2_relset_1(C,A,k5_finsub_1(B)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k10_setwiseo(A,B,k3_setwiseo(A,D,E),C) = k5_setwiseo(B,k8_funct_2(A,k5_finsub_1(B),C,D),k8_funct_2(A,k5_finsub_1(B),C,E)))))))))) # label(t57_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2881 $T # label(t9_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2882 $T # label(t10_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2883 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k5_finsub_1(A)) & v1_funct_2(B,A,k5_finsub_1(A)) -> ((all C (r2_hidden(C,A) -> k1_tarski(C) = k1_funct_1(B,C))) <-> k11_setwiseo(A) = B))) # label(d6_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2884 (all A v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A))) # label(t53_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.28 2885 (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) -> (v3_binop_1(C,A) & v1_binop_1(C,A) & v2_binop_1(C,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> k7_setwiseo(B,A,C,k3_setwiseo(B,E,F),D) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,E),k8_funct_2(B,A,D,F))))))))))))))) # label(t27_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2886 (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (all B (m1_subset_1(B,k5_finsub_1(f1_s3_setwiseo)) -> (p1_s3_setwiseo(B) & p1_s3_setwiseo(A) -> k1_xboole_0 = A | k1_xboole_0 = B | p1_s3_setwiseo(k5_setwiseo(f1_s3_setwiseo,A,B))))))) & (all A (m1_subset_1(A,f1_s3_setwiseo) -> p1_s3_setwiseo(k2_setwiseo(f1_s3_setwiseo,A)))) -> (all A (m1_subset_1(A,k5_finsub_1(f1_s3_setwiseo)) -> (k1_xboole_0 != A -> p1_s3_setwiseo(A)))) # label(s3_setwiseo) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2887 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p2_s8_fraenkel(A,B) <-> p1_s8_fraenkel(A,B)))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(B,A) = f3_s8_fraenkel(A,B))))) -> a_0_14_fraenkel = a_0_15_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2888 (all A (r2_hidden(A,a_0_30_fraenkel) <-> (exists B exists C (p1_s16_fraenkel(B,C) & A = f3_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2889 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p1_s19_fraenkel(A,B) & B = f4_s19_fraenkel <-> p2_s19_fraenkel(A,B)))))) -> a_0_34_fraenkel = a_0_35_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2890 (all A ((exists B exists C (p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(C,f2_s13_fraenkel) & m1_subset_1(B,f1_s13_fraenkel))) <-> r2_hidden(A,a_0_22_fraenkel))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2891 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(f3_s25_fraenkel) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2892 (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]. 23.11/22.29 2893 (all A ((exists B exists C (m1_subset_1(C,f2_s12_fraenkel) & f3_s12_fraenkel(B,C) = A & p1_s12_fraenkel(B,C) & m1_subset_1(B,f1_s12_fraenkel))) <-> r2_hidden(A,a_0_20_fraenkel))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2894 (all A ((exists B (m1_subset_1(B,f3_s13_fraenkel) & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & B = A)) <-> r2_hidden(A,a_0_21_fraenkel))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2895 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,C,F) = k8_funct_2(A,B,D,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2896 (all A ((exists B exists C (A = f3_s20_fraenkel(B,C) & C = f4_s20_fraenkel & p1_s20_fraenkel(B,C) & m1_subset_1(C,f2_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_36_fraenkel))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2897 (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]. 23.11/22.29 2898 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (p1_s8_fraenkel(B,C) & f3_s8_fraenkel(B,C) = A & m1_subset_1(C,f2_s8_fraenkel) & m1_subset_1(B,f1_s8_fraenkel))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2899 k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) & (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p2_s9_fraenkel(A) <-> p1_s9_fraenkel(A))))) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2900 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> ((all D (m1_subset_1(D,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))) <-> m1_fraenkel(C,A,B)))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2901 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2902 (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]. 23.11/22.29 2903 (all A ((exists B (A = f5_s25_fraenkel(B) & r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel) & m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2904 (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]. 23.11/22.29 2905 (all A ((exists B (m1_subset_1(B,f1_s17_fraenkel) & f3_s17_fraenkel(B) = A & p1_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel))) <-> r2_hidden(A,a_0_32_fraenkel))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2906 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> k1_xboole_0 = k1_funct_2(C,D) | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2907 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2908 (all A (r2_hidden(A,a_0_29_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & p2_s15_fraenkel(B) & p1_s15_fraenkel(B,C) & A = f3_s15_fraenkel(B,C) & m1_subset_1(B,f1_s15_fraenkel))))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2909 (all A ((exists B (m1_subset_1(B,f1_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) = A & r2_hidden(B,f3_s9_fraenkel) & p1_s9_fraenkel(B))) <-> r2_hidden(A,a_0_16_fraenkel))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2910 (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]. 23.11/22.29 2911 (all A ((exists B exists C (m1_subset_1(B,f1_s2_fraenkel) & m1_subset_1(C,f2_s2_fraenkel) & p2_s2_fraenkel(B,C) & f3_s2_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_3_fraenkel))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2912 (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]. 23.11/22.29 2913 (all A all B (-v1_xboole_0(B) -> k1_funct_2(A,B) = k1_fraenkel(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.11/22.29 2914 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p2_s4_fraenkel(A,B) <-> p1_s4_fraenkel(A,B)))))) -> a_0_6_fraenkel = a_0_7_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2915 (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]. 23.21/22.29 2916 (exists A (m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)) & (all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (p1_s24_fraenkel(B,C) & B = f4_s24_fraenkel(C) & r2_hidden(C,f3_s24_fraenkel) & m1_subset_1(C,f2_s24_fraenkel))) <-> r2_hidden(B,A)))))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2917 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2918 (all A (r2_hidden(A,a_0_19_fraenkel) <-> (exists B exists C (p1_s11_fraenkel(B,C) & f3_s11_fraenkel(B,C) = A & m1_subset_1(C,f2_s11_fraenkel) & m1_subset_1(B,f1_s11_fraenkel))))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2919 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2920 (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]. 23.21/22.29 2921 (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]. 23.21/22.29 2922 (all A (v1_fraenkel(A) <-> (all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2923 v1_finset_1(f3_s22_fraenkel) & v1_finset_1(f4_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2924 (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]. 23.21/22.29 2925 (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]. 23.21/22.29 2926 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2927 (all A (r2_hidden(A,a_0_26_fraenkel) <-> (exists B (A = f2_s14_fraenkel(B) & p2_s14_fraenkel(B) & p1_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2928 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m1_subset_1(D,C) <-> m2_fraenkel(D,A,B,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2929 (all A (r2_hidden(A,a_0_23_fraenkel) <-> (exists B exists C (A = f4_s13_fraenkel(B,C) & p1_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & m1_subset_1(C,f2_s13_fraenkel) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2930 (all A ((exists B exists C (f3_s16_fraenkel(B,C) = A & p2_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel) & m1_subset_1(B,f1_s16_fraenkel))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2931 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f3_s5_fraenkel(A) = f2_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2932 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2933 (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]. 23.21/22.29 2934 (all A (r2_hidden(A,a_0_15_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & m1_subset_1(C,f2_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & p2_s8_fraenkel(B,C))))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2935 (all A ((exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & p1_s4_fraenkel(B,C) & A = f3_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel))) <-> r2_hidden(A,a_0_6_fraenkel))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2936 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & k7_relat_1(F,C) = E)))) | k1_xboole_0 = k1_funct_2(C,D))))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2937 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & p1_s7_fraenkel(B,C) & A = f4_s7_fraenkel(B,C) & m1_subset_1(C,f2_s7_fraenkel))))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2938 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2939 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2940 (all A (r2_hidden(A,a_0_27_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & m1_subset_1(C,f2_s15_fraenkel) & f3_s15_fraenkel(B,C) = A & r2_hidden(B,a_0_28_fraenkel) & p1_s15_fraenkel(B,C))))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2941 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p1_s3_fraenkel(B))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2942 (all A (r2_hidden(A,a_0_28_fraenkel) <-> (exists B (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & A = B)))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2943 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2944 (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]. 23.21/22.29 2945 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2946 (all A (r2_hidden(A,a_0_39_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s22_fraenkel) & m1_subset_1(C,f2_s22_fraenkel) & f5_s22_fraenkel(B,C) = A & r2_hidden(B,f3_s22_fraenkel) & r2_hidden(C,f4_s22_fraenkel))))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2947 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -(r2_hidden(A,f3_s26_fraenkel) & (all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B)))))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel) & v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2948 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p2_s3_fraenkel(A) <-> p1_s3_fraenkel(A)))) -> a_0_4_fraenkel = a_0_5_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2949 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s19_fraenkel) & m1_subset_1(C,f2_s19_fraenkel) & p2_s19_fraenkel(B,C) & A = f3_s19_fraenkel(B,C))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2950 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (p1_s5_fraenkel(B) & A = f3_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2951 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (p1_s2_fraenkel(B,C) & f3_s2_fraenkel(B,C) = A & m1_subset_1(C,f2_s2_fraenkel) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2952 (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) -> p1_s23_fraenkel(A,A))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -((all B (m1_subset_1(B,f1_s23_fraenkel) -> -(r2_hidden(B,f2_s23_fraenkel) & p1_s23_fraenkel(B,A) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(C,B) & r2_hidden(C,f2_s23_fraenkel) -> p1_s23_fraenkel(B,C))))))) & r2_hidden(A,f2_s23_fraenkel)))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2953 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (r2_hidden(B,a_0_25_fraenkel) & p1_s14_fraenkel(B) & f2_s14_fraenkel(B) = A & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2954 (all A ((exists B (p1_s6_fraenkel(B) & A = f2_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]. 23.21/22.29 2955 (all A (r2_hidden(A,a_0_12_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & f3_s7_fraenkel(B,C) = A & m1_subset_1(B,f1_s7_fraenkel))))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2956 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2957 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -(p1_s16_fraenkel(A,B) & (all C (m1_subset_1(C,f1_s16_fraenkel) -> -(p2_s16_fraenkel(C,B) & f3_s16_fraenkel(A,B) = f3_s16_fraenkel(C,B))))))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2958 (all A ((exists B (f3_s18_fraenkel(B) = A & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel) & p1_s18_fraenkel(B) & m1_subset_1(B,f1_s18_fraenkel))) <-> r2_hidden(A,a_0_33_fraenkel))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2959 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2960 (all A (r2_hidden(A,a_0_18_fraenkel) <-> (exists B (m1_subset_1(B,f1_s10_fraenkel) & p1_s10_fraenkel(B) & A = B)))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2961 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2962 (all A ((exists B exists C (m1_subset_1(C,f2_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & 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]. 23.21/22.29 2963 (all A (r2_hidden(A,a_0_25_fraenkel) <-> (exists B (p2_s14_fraenkel(B) & B = A & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2964 (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]. 23.21/22.29 2965 (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]. 23.21/22.29 2966 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_relat_1(B) & v1_funct_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2967 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & p1_s6_fraenkel(B) & A = f3_s6_fraenkel(B))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2968 (all A ((exists B (m1_subset_1(B,f1_s5_fraenkel) & A = f2_s5_fraenkel(B) & p1_s5_fraenkel(B))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2969 (all A ((exists B (f2_s1_fraenkel(B) = A & p2_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]. 23.21/22.29 2970 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (m1_subset_1(B,f1_s1_fraenkel) & p1_s1_fraenkel(B) & f2_s1_fraenkel(B) = A)))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2971 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2972 (all A (r2_hidden(A,a_0_5_fraenkel) <-> (exists B (p2_s3_fraenkel(B) & f2_s3_fraenkel(B) = A & m1_subset_1(B,f1_s3_fraenkel))))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2973 (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]. 23.21/22.29 2974 (all A (r2_hidden(A,a_0_38_fraenkel) <-> (exists B (f3_s21_fraenkel(B) = A & r2_hidden(B,f2_s21_fraenkel) & m1_subset_1(B,f1_s21_fraenkel))))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2975 (all A ((exists B (m1_subset_1(B,f1_s19_fraenkel) & A = f3_s19_fraenkel(B,f4_s19_fraenkel) & 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]. 23.21/22.29 2976 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m2_fraenkel(D,A,B,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2977 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f4_s7_fraenkel(A,B) = f3_s7_fraenkel(A,B))))) -> a_0_13_fraenkel = a_0_12_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2978 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2979 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2980 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2981 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2982 (all A ((exists B (m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)) & B = A & k1_funct_1(B,k13_arytm_3) = np__0)) <-> r2_hidden(A,a_0_0_numbers))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2983 (exists A (-v1_xboole_0(A) & v3_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2984 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2985 (all A all B (v2_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2986 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2987 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2988 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2989 (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]. 23.21/22.29 2990 (all A (v1_xboole_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2991 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v2_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2992 (all A all B (v2_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2993 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> -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(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2994 (all A all B (-v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2995 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v3_xreal_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2996 (all A (-v1_xboole_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(A) & v2_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2997 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 2998 (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]. 23.21/22.29 2999 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3000 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3001 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3002 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3003 (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]. 23.21/22.29 3004 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) -> -v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3005 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3006 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3007 (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]. 23.21/22.29 3008 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3009 (all A all B (v1_xreal_0(A) & -v3_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3010 (all A all B (-v2_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3011 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3012 (all A (v1_xreal_0(A) & v3_xreal_0(A) -> v1_xcmplx_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3013 (exists A (v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3014 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xcmplx_0(A) & v3_xreal_0(A) & v1_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3015 (exists A (-v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v1_xboole_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3016 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k3_xcmplx_0(A,B)) & -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3017 (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]. 23.21/22.29 3018 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) -> ((exists C (m1_subset_1(C,k2_arytm_2) & (exists D (B = D & r1_arytm_2(C,D) & A = C & m1_subset_1(D,k2_arytm_2))))) <-> r1_xreal_0(A,B))) & -(-(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(B,k2_arytm_2) <-> r1_xreal_0(A,B)) & -(r2_hidden(B,k2_arytm_2) & r2_hidden(A,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)) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (m1_subset_1(D,k2_arytm_2) & k4_tarski(np__0,D) = B & r1_arytm_2(D,C) & A = k4_tarski(np__0,C))))))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3019 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) -> -v2_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3020 (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]. 23.21/22.29 3021 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3022 (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]. 23.21/22.29 3023 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> r1_xreal_0(B,A) | r1_xreal_0(A,B))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3024 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3025 (all A (-v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v1_xboole_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3026 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3027 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & v3_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(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3028 (all A all B (v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3029 (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]. 23.21/22.29 3030 (all A all B (-v2_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_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]. 23.21/22.29 3031 (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]. 23.21/22.29 3032 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (k3_xcmplx_0(C,D) = k6_xcmplx_0(A,B) & v1_int_1(D))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3033 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3034 (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]. 23.21/22.29 3035 (all A (v1_xreal_0(A) -> -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)) & -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3036 (all A (v1_xreal_0(A) -> np__0 = k1_int_1(k4_int_1(A)))) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3037 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3038 (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]. 23.21/22.29 3039 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3040 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3041 (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]. 23.21/22.29 3042 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_int_1(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3043 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_int_1(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3044 (all A (m1_subset_1(A,k5_numbers) -> v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3045 (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]. 23.21/22.29 3046 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3047 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3048 (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]. 23.21/22.29 3049 (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]. 23.21/22.29 3050 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3051 (all A (v1_int_1(A) <-> r2_hidden(A,k4_numbers))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3052 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3053 (all A (v1_xreal_0(A) -> v1_xreal_0(k3_int_1(A)) & v1_xcmplx_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3054 (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]. 23.21/22.29 3055 (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]. 23.21/22.29 3056 (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]. 23.21/22.29 3057 (all A (v1_int_1(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3058 (all A (v1_int_1(A) -> r1_int_1(np__0,A,A) & r1_int_1(A,np__0,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3059 (all A (v1_xreal_0(A) -> k1_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3060 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3061 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3062 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3063 (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]. 23.21/22.29 3064 (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]. 23.21/22.29 3065 (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]. 23.21/22.29 3066 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3067 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k1_int_1(A)) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & r1_xreal_0(np__0,k2_int_1(A))))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3068 (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]. 23.21/22.29 3069 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3070 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3071 (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]. 23.21/22.29 3072 (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]. 23.21/22.29 3073 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & m1_subset_1(A,k1_numbers))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3074 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3075 (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) <-> B = k2_int_1(A)))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3076 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3077 (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]. 23.21/22.29 3078 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3079 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3080 (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]. 23.21/22.29 3081 (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]. 23.21/22.29 3082 (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]. 23.21/22.29 3083 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3084 (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]. 23.21/22.29 3085 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3086 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3087 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> A = k1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3088 (all A (v1_xreal_0(A) -> (k4_int_1(A) = np__0 <-> v1_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.29 3089 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3090 (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]. 23.21/22.30 3091 (all A (v1_int_1(A) -> (p1_s2_int_1(A) & r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) & p1_s2_int_1(f1_s2_int_1) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3092 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k6_xcmplx_0(A,np__1)) & v1_int_1(k2_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3093 (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]. 23.21/22.30 3094 (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]. 23.21/22.30 3095 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3096 (all A (v1_xreal_0(A) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> B != A & A != k1_real_1(B))) & v1_int_1(A)))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3097 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3098 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3099 (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]. 23.21/22.30 3100 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s1_int_1(B)))) & m1_subset_1(A,k1_zfmisc_1(k4_numbers)))) # label(s1_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3101 (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]. 23.21/22.30 3102 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = B | k4_xcmplx_0(B) = A -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3103 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k4_int_1(A)) & -r1_xreal_0(np__1,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3104 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (np__1 = k3_xcmplx_0(A,B) <-> A = k1_real_1(np__1) & k1_real_1(np__1) = B | B = np__1 & A = np__1))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3105 (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) & p1_s3_int_1(A) -> 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]. 23.21/22.30 3106 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k1_int_1(k7_xcmplx_0(A,B)) = k5_int_1(A,B))))) # label(d7_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3107 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3108 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3109 (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]. 23.21/22.30 3110 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3111 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(B,D,C) & r1_int_1(A,B,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3112 (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]. 23.21/22.30 3113 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3114 (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]. 23.21/22.30 3115 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,C) & r1_xreal_0(A,B) -> B = C | r1_xreal_0(k2_xcmplx_0(A,np__1),C) | r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3116 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3117 (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]. 23.21/22.30 3118 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3119 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3120 (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]. 23.21/22.30 3121 (all A (v1_xreal_0(A) -> (k1_int_1(A) = k2_int_1(A) <-> k2_xcmplx_0(k1_int_1(A),np__1) != k2_int_1(A)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3122 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3123 (all A (v1_xreal_0(A) -> k6_xcmplx_0(A,k1_int_1(A)) = k3_int_1(A))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3124 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(A,k1_int_1(A)) & v1_int_1(A)) & -(r1_xreal_0(A,k1_int_1(A)) & -v1_int_1(A)))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3125 (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]. 23.21/22.30 3126 (all A (A = k4_numbers <-> (all B (-(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_real_1(C) != B & B != C)) <-> r2_hidden(B,A))))) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3127 (exists A (p1_s6_int_1(A) & v1_int_1(A))) & (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) -> (exists A (v1_int_1(A) & (all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))) & p1_s6_int_1(A))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3128 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3129 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3130 (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]. 23.21/22.30 3131 (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]. 23.21/22.30 3132 (all A (m1_subset_1(A,k5_numbers) -> v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_int_1(A) & v1_xreal_0(A) & v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3133 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3134 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3135 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3136 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3137 (all A (v1_int_1(A) -> (np__0 != A -> np__1 = k5_int_1(A,A)))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3138 (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]. 23.21/22.30 3139 (all A (v1_xreal_0(A) -> (A = k2_int_1(A) <-> v1_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3140 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3141 (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]. 23.21/22.30 3142 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__0 -> np__0 = k6_int_1(A,B)) & (np__0 != B -> 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]. 23.21/22.30 3143 p1_s4_int_1(f1_s4_int_1) & (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k2_xcmplx_0(A,np__1)) & p1_s4_int_1(k6_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3144 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3145 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3146 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),k1_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]. 23.21/22.30 3147 (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]. 23.21/22.30 3148 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(B,A) & r1_xreal_0(C,A) -> r1_xreal_0(B,k6_xcmplx_0(A,np__1)) | B = C | r1_xreal_0(C,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3149 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = k3_xcmplx_0(A,B) <-> np__1 = B & k1_real_1(np__1) = A | B = k1_real_1(np__1) & A = np__1))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3150 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k2_int_1(A),B) = k2_int_1(k2_xcmplx_0(A,B)))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3151 (all A (v1_xreal_0(A) -> (np__0 != A -> np__1 = k1_int_1(k7_xcmplx_0(A,A))))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3152 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> (k34_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k10_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d10_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3153 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k11_binop_2(B,A) = k11_binop_2(A,B))) # label(commutativity_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3154 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k10_binop_2(A,B),k1_numbers))) # label(dt_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3155 (all A (m1_subset_1(A,k3_numbers) -> A = k13_binop_2(k13_binop_2(A)))) # label(involutiveness_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3156 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k20_binop_2(A,B),k4_numbers))) # label(dt_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3157 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k11_binop_2(A,B),k1_numbers))) # label(dt_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3158 (all A (m1_subset_1(A,k2_numbers) -> A = k2_binop_2(k2_binop_2(A)))) # label(involutiveness_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3159 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k8_binop_2(A),k1_numbers))) # label(dt_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3160 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k3_binop_2(A,B) = k3_binop_2(B,A))) # label(commutativity_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3161 (all A (v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k5_binop_2(B,C))))) <-> k29_binop_2 = A))) # label(d5_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3162 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> (A = k36_binop_2 <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k12_binop_2(B,C)))))))) # label(d12_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3163 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k4_binop_2(B,C) = k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C))))) <-> A = k28_binop_2))) # label(d4_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3164 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k15_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3165 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k3_xcmplx_0(A,B) = k22_binop_2(A,B))) # label(redefinition_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3166 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k9_binop_2(B,A) = k9_binop_2(A,B))) # label(commutativity_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3167 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k11_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C))))) <-> k35_binop_2 = A))) # label(d11_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3168 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k4_binop_2(A,B),k2_numbers))) # label(dt_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3169 (all A (v1_funct_2(A,k2_numbers,k2_numbers) & m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_1(A) -> (k26_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> k2_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B)))))) # label(d2_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3170 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k2_xcmplx_0(A,B) = k9_binop_2(A,B))) # label(redefinition_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3171 (all A (m1_subset_1(A,k3_numbers) -> A = k14_binop_2(k14_binop_2(A)))) # label(involutiveness_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3172 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> m1_subset_1(k12_binop_2(A,B),k1_numbers))) # label(dt_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3173 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k20_binop_2(B,A) = k20_binop_2(A,B))) # label(commutativity_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3174 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k5_binop_2(A,B),k2_numbers))) # label(dt_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3175 (all A (m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C) = k3_binop_2(B,C))))) <-> A = k27_binop_2))) # label(d3_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3176 (all A (m1_subset_1(A,k1_numbers) -> A = k8_binop_2(k8_binop_2(A)))) # label(involutiveness_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3177 (all A (v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) -> (A = k47_binop_2 <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k23_binop_2(B,C) = k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C)))))))) # label(d23_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3178 (all A (m1_subset_1(A,k1_numbers) -> k7_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3179 (all A (v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) & v1_funct_1(A) -> (k32_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> k8_funct_2(k1_numbers,k1_numbers,A,B) = k8_binop_2(B)))))) # label(d8_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3180 (all A (m1_subset_1(A,k3_numbers) -> k13_binop_2(A) = k4_xcmplx_0(A))) # label(redefinition_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3181 (all A (m1_subset_1(A,k1_numbers) -> k5_xcmplx_0(A) = k8_binop_2(A))) # label(redefinition_k8_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3182 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (A = k39_binop_2 <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C) = k15_binop_2(B,C)))))))) # label(d15_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3183 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k17_binop_2(A,B) = k17_binop_2(B,A))) # label(commutativity_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3184 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> m1_subset_1(k6_binop_2(A,B),k2_numbers))) # label(dt_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3185 (all A (m1_subset_1(A,k4_numbers) -> k4_xcmplx_0(A) = k19_binop_2(A))) # label(redefinition_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3186 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k3_xcmplx_0(A,B) = k5_binop_2(A,B))) # label(redefinition_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3187 (all A all B (m1_subset_1(B,k3_numbers) & m1_subset_1(A,k3_numbers) -> k18_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3188 (all A (v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k16_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C))))) <-> A = k40_binop_2))) # label(d16_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3189 (all A (m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C) = k21_binop_2(B,C))))) <-> k45_binop_2 = A))) # label(d21_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3190 (all A (v1_funct_1(A) & v1_funct_2(A,k4_numbers,k4_numbers) & m2_relset_1(A,k4_numbers,k4_numbers) -> (k43_binop_2 = A <-> (all B (m1_subset_1(B,k4_numbers) -> k8_funct_2(k4_numbers,k4_numbers,A,B) = k19_binop_2(B)))))) # label(d19_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3191 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k23_binop_2(A,B) = k23_binop_2(B,A))) # label(commutativity_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3192 (all A (v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) & m2_relset_1(B,k2_zfmisc_1(f1_s2_binop_2,f1_s2_binop_2),f1_s2_binop_2) -> ((all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> f2_s2_binop_2(C,D) = k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,A,C,D))))) & (all C (m1_subset_1(C,f1_s2_binop_2) -> (all D (m1_subset_1(D,f1_s2_binop_2) -> f2_s2_binop_2(C,D) = k2_binop_1(f1_s2_binop_2,f1_s2_binop_2,f1_s2_binop_2,B,C,D))))) -> B = A))))) # label(s2_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3193 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k17_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3194 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k6_xcmplx_0(A,B) = k21_binop_2(A,B))) # label(redefinition_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3195 (all A (m1_subset_1(A,k1_numbers) -> A = k7_binop_2(k7_binop_2(A)))) # label(involutiveness_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3196 (all A (m1_subset_1(A,k3_numbers) -> k14_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3197 (all A (m1_subset_1(A,k2_numbers) -> k2_binop_2(A) = k5_xcmplx_0(A))) # label(redefinition_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3198 (all A (v1_funct_1(A) & m2_relset_1(A,k2_numbers,k2_numbers) & v1_funct_2(A,k2_numbers,k2_numbers) -> ((all B (m1_subset_1(B,k2_numbers) -> k1_binop_2(B) = k8_funct_2(k2_numbers,k2_numbers,A,B))) <-> A = k25_binop_2))) # label(d1_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3199 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k2_xcmplx_0(A,B) = k3_binop_2(A,B))) # label(redefinition_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3200 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k2_binop_2(A),k2_numbers))) # label(dt_k2_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3201 (all A (m1_subset_1(A,k3_numbers) -> v1_xcmplx_0(A) & v1_rat_1(A) & v1_xreal_0(A))) # label(cc1_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3202 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k22_binop_2(A,B),k4_numbers))) # label(dt_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3203 (all A (v1_funct_1(A) & v1_funct_2(A,k3_numbers,k3_numbers) & m2_relset_1(A,k3_numbers,k3_numbers) -> ((all B (m1_subset_1(B,k3_numbers) -> k8_funct_2(k3_numbers,k3_numbers,A,B) = k14_binop_2(B))) <-> k38_binop_2 = A))) # label(d14_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3204 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k6_xcmplx_0(A,B) = k4_binop_2(A,B))) # label(redefinition_k4_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3205 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k12_binop_2(A,B) = k7_xcmplx_0(A,B))) # label(redefinition_k12_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3206 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> k22_binop_2(B,A) = k22_binop_2(A,B))) # label(commutativity_k22_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3207 (all A (v1_funct_1(A) & v1_funct_2(A,f1_s1_binop_2,f2_s1_binop_2) & m2_relset_1(A,f1_s1_binop_2,f2_s1_binop_2) -> (all B (m2_relset_1(B,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_2(B,f1_s1_binop_2,f2_s1_binop_2) & v1_funct_1(B) -> ((all C (m1_subset_1(C,f1_s1_binop_2) -> f3_s1_binop_2(C) = k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,B,C))) & (all C (m1_subset_1(C,f1_s1_binop_2) -> f3_s1_binop_2(C) = k8_funct_2(f1_s1_binop_2,f2_s1_binop_2,A,C))) -> A = B))))) # label(s1_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3208 (all A (m1_subset_1(A,k4_numbers) -> A = k19_binop_2(k19_binop_2(A)))) # label(involutiveness_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3209 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) -> (k44_binop_2 = A <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k20_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d20_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3210 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> k24_binop_2(B,A) = k24_binop_2(A,B))) # label(commutativity_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3211 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k24_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3212 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k13_binop_2(A),k3_numbers))) # label(dt_k13_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3213 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> k10_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k10_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3214 (all A all B (m1_subset_1(B,k4_numbers) & m1_subset_1(A,k4_numbers) -> k20_binop_2(A,B) = k2_xcmplx_0(A,B))) # label(redefinition_k20_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3215 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k24_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k24_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3216 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k2_xcmplx_0(A,B) = k23_binop_2(A,B))) # label(redefinition_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3217 (all A (v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) -> (k41_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k17_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C)))))))) # label(d17_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3218 (all A all B (m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) -> m1_subset_1(k21_binop_2(A,B),k4_numbers))) # label(dt_k21_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3219 (all A (m1_subset_1(A,k2_numbers) -> m1_subset_1(k1_binop_2(A),k2_numbers))) # label(dt_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3220 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k15_binop_2(A,B),k3_numbers))) # label(dt_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3221 (all A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) -> (k33_binop_2 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k9_binop_2(B,C) = k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C)))))))) # label(d9_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3222 (all A (v1_funct_2(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m2_relset_1(A,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_funct_1(A) -> (k30_binop_2 = A <-> (all B (m1_subset_1(B,k2_numbers) -> (all C (m1_subset_1(C,k2_numbers) -> k6_binop_2(B,C) = k2_binop_1(k2_numbers,k2_numbers,k2_numbers,A,B,C)))))))) # label(d6_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3223 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers))) # label(dt_k23_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3224 (all A (v1_funct_2(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & m2_relset_1(A,k2_zfmisc_1(k5_numbers,k5_numbers),k5_numbers) & v1_funct_1(A) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k2_binop_1(k5_numbers,k5_numbers,k5_numbers,A,B,C) = k24_binop_2(B,C))))) <-> A = k48_binop_2))) # label(d24_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3225 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> m1_subset_1(k3_binop_2(A,B),k2_numbers))) # label(dt_k3_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3226 (all A all B (m1_subset_1(B,k1_numbers) & m1_subset_1(A,k1_numbers) -> k11_binop_2(A,B) = k3_xcmplx_0(A,B))) # label(redefinition_k11_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3227 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k18_binop_2(A,B),k3_numbers))) # label(dt_k18_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3228 (all A (m1_subset_1(A,k1_numbers) -> m1_subset_1(k7_binop_2(A),k1_numbers))) # label(dt_k7_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3229 (all A (m1_subset_1(A,k3_numbers) -> m1_subset_1(k14_binop_2(A),k3_numbers))) # label(dt_k14_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3230 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k16_binop_2(A,B) = k6_xcmplx_0(A,B))) # label(redefinition_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3231 (all A all B (m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) -> m1_subset_1(k9_binop_2(A,B),k1_numbers))) # label(dt_k9_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3232 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k17_binop_2(A,B),k3_numbers))) # label(dt_k17_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3233 (all A (m1_subset_1(A,k4_numbers) -> m1_subset_1(k19_binop_2(A),k4_numbers))) # label(dt_k19_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3234 (all A (v1_funct_1(A) & v1_funct_2(A,k1_numbers,k1_numbers) & m2_relset_1(A,k1_numbers,k1_numbers) -> ((all B (m1_subset_1(B,k1_numbers) -> k8_funct_2(k1_numbers,k1_numbers,A,B) = k7_binop_2(B))) <-> k31_binop_2 = A))) # label(d7_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3235 (all A all B (m1_subset_1(B,k2_numbers) & m1_subset_1(A,k2_numbers) -> k5_binop_2(B,A) = k5_binop_2(A,B))) # label(commutativity_k5_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3236 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> m1_subset_1(k16_binop_2(A,B),k3_numbers))) # label(dt_k16_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3237 (all A (v1_funct_2(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m2_relset_1(A,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_funct_1(A) -> (A = k46_binop_2 <-> (all B (m1_subset_1(B,k4_numbers) -> (all C (m1_subset_1(C,k4_numbers) -> k22_binop_2(B,C) = k2_binop_1(k4_numbers,k4_numbers,k4_numbers,A,B,C)))))))) # label(d22_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3238 (all A (v1_funct_2(A,k3_numbers,k3_numbers) & m2_relset_1(A,k3_numbers,k3_numbers) & v1_funct_1(A) -> ((all B (m1_subset_1(B,k3_numbers) -> k13_binop_2(B) = k8_funct_2(k3_numbers,k3_numbers,A,B))) <-> k37_binop_2 = A))) # label(d13_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3239 (all A (v1_funct_2(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m2_relset_1(A,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_funct_1(A) -> (k42_binop_2 = A <-> (all B (m1_subset_1(B,k3_numbers) -> (all C (m1_subset_1(C,k3_numbers) -> k18_binop_2(B,C) = k2_binop_1(k3_numbers,k3_numbers,k3_numbers,A,B,C)))))))) # label(d18_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3240 (all A (m1_subset_1(A,k2_numbers) -> k1_binop_2(k1_binop_2(A)) = A)) # label(involutiveness_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3241 (all A (m1_subset_1(A,k2_numbers) -> k4_xcmplx_0(A) = k1_binop_2(A))) # label(redefinition_k1_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3242 (all A all B (m1_subset_1(A,k2_numbers) & m1_subset_1(B,k2_numbers) -> k7_xcmplx_0(A,B) = k6_binop_2(A,B))) # label(redefinition_k6_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3243 (all A all B (m1_subset_1(A,k3_numbers) & m1_subset_1(B,k3_numbers) -> k15_binop_2(B,A) = k15_binop_2(A,B))) # label(commutativity_k15_binop_2) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3244 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3245 (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]. 23.21/22.30 3246 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_rat_1(B) & v1_xreal_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3247 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(C) & v4_ordinal2(B) -> v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3248 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3249 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3250 (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]. 23.21/22.30 3251 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3252 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3253 (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]. 23.21/22.30 3254 (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]. 23.21/22.30 3255 (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]. 23.21/22.30 3256 (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]. 23.21/22.30 3257 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xcmplx_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3258 (all A (v1_xboole_0(A) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3259 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3260 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3261 (all A all B (v5_membered(A) -> v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3262 (all A all B (v4_membered(A) & v4_membered(B) -> v4_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3263 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3264 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3265 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3266 (exists A (-v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v4_membered(A) & v5_membered(A) & v3_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3267 (all A all B (v3_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3268 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3269 (all A all B all C (v1_rat_1(B) & v1_rat_1(C) & v1_rat_1(A) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3270 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> k2_numbers = A))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3271 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 23.21/22.30 3272 (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]. 23.21/22.30 3273 (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]. 23.21/22.30 3274 (all A ((all B (r2_hidden(B,A) -> v1_xreal_0(B))) <-> v2_membered(A))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3275 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3276 (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]. 23.24/22.30 3277 (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]. 23.24/22.30 3278 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3279 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3280 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3281 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3282 (exists A ((all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))) & v5_membered(A))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3283 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3284 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3285 (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]. 23.24/22.30 3286 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3287 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v4_ordinal2(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3288 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3289 (all A (v4_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_int_1(B))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3290 (all A (v1_int_1(A) -> v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3291 (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]. 23.24/22.30 3292 (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]. 23.24/22.30 3293 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3294 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3295 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (B = A <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3296 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v4_membered(B) & v3_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3297 (all A all B (v4_membered(A) & v4_membered(B) -> v4_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3298 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3299 (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]. 23.24/22.30 3300 (all A (v1_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_xcmplx_0(B))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3301 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_rat_1(B) & v1_int_1(B) & v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3302 (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]. 23.24/22.30 3303 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3304 (all A all B (v2_membered(A) & v2_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3305 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3306 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3307 (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]. 23.24/22.30 3308 (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]. 23.24/22.30 3309 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3310 (all A all B (v1_rat_1(A) & v1_rat_1(B) -> v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3311 (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]. 23.24/22.30 3312 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3313 (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]. 23.24/22.30 3314 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3315 (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]. 23.24/22.30 3316 (all A (-v1_xboole_0(A) & v2_membered(A) -> (exists B (r2_hidden(B,A) & v1_xreal_0(B))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3317 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.30 3318 (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]. 23.24/22.31 3319 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3320 (all A all B (v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3321 (exists A (v1_membered(A) & (all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3322 (all A all B (v2_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3323 (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]. 23.24/22.31 3324 (all A all B (v5_membered(B) & v5_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3325 (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]. 23.24/22.31 3326 (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]. 23.24/22.31 3327 (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]. 23.24/22.31 3328 (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]. 23.24/22.31 3329 (all A all B all C (v1_xcmplx_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3330 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v1_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3331 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3332 (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]. 23.24/22.31 3333 (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]. 23.24/22.31 3334 (all A (v1_xreal_0(A) -> v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3335 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3336 (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]. 23.24/22.31 3337 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3338 (all A all B (v3_membered(B) & v3_membered(A) -> v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3339 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3340 (all A all B all C (v1_xreal_0(C) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3341 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) & v1_int_1(B) & v4_ordinal2(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3342 (all A (-v1_xboole_0(A) & v5_membered(A) -> (exists B (r2_hidden(B,A) & v4_ordinal2(B))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3343 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3344 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3345 (all A all B all C (v1_int_1(A) & v1_int_1(C) & v1_int_1(B) -> v2_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3346 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3347 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v2_membered(A) & v3_membered(A) & v4_membered(A) & v1_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3348 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s4_membered(B)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3349 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3350 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3351 (all A all B (r2_hidden(B,A) & v4_membered(B) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3352 (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]. 23.24/22.31 3353 (exists A (v3_membered(A) & (all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3354 (exists A ((all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))) & v2_membered(A))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3355 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> A = B))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3356 (all A all B (v4_membered(A) -> v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3357 (all A all B (v5_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3358 (all A all B (v5_membered(A) & v5_membered(B) -> v5_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3359 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3360 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3361 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3362 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (r1_tarski(A,k2_relat_1(C)) & B = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3363 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k3_card_1(A),k3_card_1(B))))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3364 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3365 (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]. 23.24/22.31 3366 (all A all B ((exists C k1_tarski(C) = A) <-> r2_wellord2(A,k1_tarski(B)))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3367 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3368 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3369 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B = k4_card_1(A) <-> k1_card_1(B) = k1_card_1(A)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3370 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3371 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3372 (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]. 23.24/22.31 3373 (all A all B ((exists C (k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B) & v2_funct_1(C) & v1_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]. 23.24/22.31 3374 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (A = B <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3375 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3376 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3377 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> B = A))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3378 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3379 (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]. 23.24/22.31 3380 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3381 (all A (v1_card_1(A) <-> (exists B (v3_ordinal1(B) & A = B & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))))))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3382 (all A (v1_card_1(A) -> (v2_card_1(A) <-> (all B (v1_card_1(B) -> k2_card_1(B) != A))))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3383 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3384 (all A (v1_card_1(A) -> v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3385 p1_s1_card_1(k1_xboole_0) & (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> k1_xboole_0 = A | p1_s1_card_1(A)))) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3386 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3387 (all A all B (k1_card_1(A) = k1_card_1(B) -> k2_card_1(A) = k2_card_1(B))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3388 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3389 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_card_1(A)) & v1_card_1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3390 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3391 (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]. 23.24/22.31 3392 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3393 (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]. 23.24/22.31 3394 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3395 (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]. 23.24/22.31 3396 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3397 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3398 (all A -(v1_finset_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,B))))) # label(t74_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3399 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3400 (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]. 23.24/22.31 3401 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3402 (all A all B all C all D (r1_xboole_0(A,B) & r1_xboole_0(C,D) & r2_wellord2(A,C) & r2_wellord2(B,D) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3403 (all A (m1_subset_1(A,k5_numbers) -> v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3404 (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]. 23.24/22.31 3405 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(A) = k3_card_1(B) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3406 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_tarski(k3_card_1(A),k3_card_1(B))))))) # label(t43_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3407 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_wellord2(A,B) -> k4_card_1(B) = k4_card_1(A)))))) # label(t81_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3408 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3409 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3410 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v4_ordinal2(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_xcmplx_0(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3411 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3412 (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]. 23.24/22.31 3413 (all A (v1_finset_1(A) -> k4_card_1(A) = k1_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3414 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3415 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3416 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3417 (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]. 23.24/22.31 3418 (all A all B ((exists C A = k1_tarski(C)) <-> k1_card_1(A) = k1_card_1(k1_tarski(B)))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3419 (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]. 23.24/22.31 3420 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3421 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3422 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3423 (all A all B (v1_card_1(B) -> (B = k1_card_1(A) <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3424 (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]. 23.24/22.31 3425 (all A (v1_finset_1(A) -> v1_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3426 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3427 (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]. 23.24/22.31 3428 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3429 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3430 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) & r2_wellord2(A,B) -> r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))))) # label(t61_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3431 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3432 (all A (v1_card_1(A) & v1_finset_1(A) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & A = k1_card_1(B))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3433 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_relat_1(B)) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3434 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3435 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3436 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> r2_wellord2(k4_xboole_0(B,k1_tarski(A)),k4_xboole_0(B,k1_tarski(C))))) # label(t59_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3437 (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]. 23.24/22.31 3438 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k3_card_1(C)))) & A = k1_relat_1(B) -> k1_card_1(k8_ordinal2(B)) = k3_card_1(A)))) | k1_xboole_0 = A))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3439 (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]. 23.24/22.31 3440 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_ordinal1(A,B) <-> r1_xreal_0(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3441 (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]. 23.24/22.31 3442 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3443 (all A all B (v1_card_1(B) -> (B = k2_card_1(A) <-> (all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) & r2_hidden(k1_card_1(A),B)))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3444 (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]. 23.24/22.31 3445 (all A (v3_ordinal1(A) -> (all B ((exists C (B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_card_1(k8_ordinal2(k2_ordinal1(C,D))) = k1_funct_1(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_card_1(k5_numbers) = k1_funct_1(C,k1_xboole_0) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> k3_card_1(A) = B)))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3446 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3447 (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]. 23.24/22.31 3448 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) -> B = A))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3449 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3450 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (-r1_tarski(B,A) <-> r2_hidden(A,B)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3451 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3452 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3453 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> r2_hidden(k1_card_1(A),k1_card_1(B)) & -r2_wellord2(A,B))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3454 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3455 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3456 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3457 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (A != B & r1_tarski(A,B) <-> r2_hidden(A,B)))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3458 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(A) & v1_finset_1(k1_card_1(A)))) # label(t69_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3459 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3460 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3461 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3462 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3463 (all A (A = k1_xboole_0 <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3464 (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) -> (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]. 23.24/22.31 3465 (all A (v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3466 (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) -> (k4_finseq_1(A) = k4_finseq_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) -> A = B))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3467 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3468 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (r1_tarski(k1_relat_1(A),k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> v2_finseq_1(A)))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3469 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k2_finseq_1(np__1) & A = k1_funct_1(B,np__1) <-> B = k9_finseq_1(A)))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3470 (all A (-v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3471 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (m2_finseq_1(C,B) & A = k3_finseq_1(C))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3472 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3473 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3474 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3475 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (np__1 = k3_finseq_1(B) & k2_relat_1(B) = k1_tarski(A) <-> k9_finseq_1(A) = B))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3476 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k7_finseq_1(A,k1_xboole_0) = A & A = k7_finseq_1(k1_xboole_0,A))) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3477 (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_finset_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3478 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3479 (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) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3480 (all A all B all C (v1_funct_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3481 (all A all B all C (k11_finseq_1(A,B,C) = k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) & k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3482 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3483 (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]. 23.24/22.31 3484 (exists A (v1_relat_1(A) & v1_finseq_1(A) & v1_finset_1(A) & v1_funct_1(A) & -v1_xboole_0(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3485 (all A (v1_funct_1(k9_finseq_1(A)) & v1_relat_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3486 (all A (v4_ordinal2(A) -> r2_hidden(A,k2_finseq_1(A)) | np__0 = A)) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3487 (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) -> (v2_funct_1(B) & v2_funct_1(A) & k2_relat_1(A) = k2_relat_1(B) -> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3488 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3489 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3490 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3491 (all A (v1_relat_1(A) & v1_funct_1(A) -> -((all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -r1_tarski(A,B))) & (exists B (r1_tarski(k1_relat_1(A),k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers)))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3492 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(k16_finseq_1(A,B,np__0)) & v2_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)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_xboole_0(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3493 (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]. 23.24/22.31 3494 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(D,k3_relat_1(A)) & (exists E (v1_relat_1(E) & D = k1_funct_1(E,k3_finseq_1(E)) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,F) -> r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),A) | r1_xreal_0(k3_finseq_1(E),F)))) & C = k1_funct_1(E,np__1) & r1_xreal_0(np__1,k3_finseq_1(E)) & v1_finseq_1(E) & v1_funct_1(E))) & r2_hidden(C,k3_relat_1(A)))) <-> k17_finseq_1(A) = B))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3495 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3496 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3497 (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]. 23.24/22.31 3498 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3499 (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]. 23.24/22.31 3500 (all A (v1_relat_1(A) & v1_finset_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3501 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3502 (all A all B (m2_finseq_1(B,A) -> m2_relset_1(B,k5_numbers,A) & v1_finseq_1(B) & v1_funct_1(B))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3503 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3504 (all A (v4_ordinal2(A) -> k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(A))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3505 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (B = k9_finseq_1(A) <-> A = k1_funct_1(B,np__1) & k3_finseq_1(B) = np__1))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3506 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3507 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3508 (all A (v4_ordinal2(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) -> (r1_xreal_0(A,k3_finseq_1(B)) & k7_relat_1(B,k2_finseq_1(A)) = C -> A = k3_finseq_1(C) & k2_finseq_1(A) = k4_finseq_1(C)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3509 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,A)) & v2_finseq_1(k7_relat_1(B,A)) & v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3510 (all A all B (v4_ordinal2(B) -> ((exists C (C = A & r1_xreal_0(np__1,C) & r1_xreal_0(C,B) & 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]. 23.24/22.31 3511 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> k3_finseq_1(A) = k1_card_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3512 (exists A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & C = B)) <-> r2_hidden(B,A))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3513 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v2_funct_1(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3514 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3515 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (k3_finseq_1(A) = np__0 <-> k1_xboole_0 = A))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3516 (exists A (-v1_xboole_0(A) & v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3517 (all A k9_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3518 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_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]. 23.24/22.31 3519 (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) -> -(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]. 23.24/22.31 3520 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3521 (all A all B (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_relat_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3522 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3523 (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]. 23.24/22.31 3524 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> -(k7_finseq_1(A,B) = k7_finseq_1(C,D) & 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)))))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3525 (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 (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) | r1_xreal_0(C,k3_finseq_1(A))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3526 (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]. 23.24/22.31 3527 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> 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]. 23.24/22.31 3528 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> k5_relat_1(k14_finseq_1(k1_relat_1(A)),A) = k15_finseq_1(A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3529 (all A ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(A,k2_finseq_1(B)))) -> (k1_xboole_0 = k14_finseq_1(A) <-> k1_xboole_0 = A))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3530 (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]. 23.24/22.31 3531 (all A all B k10_finseq_1(A,B) = k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B))) # label(d9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3532 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(D,k4_finseq_1(B)) & C = k1_nat_1(k3_finseq_1(A),D)))) & -r2_hidden(C,k4_finseq_1(A))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3533 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_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]. 23.24/22.31 3534 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3535 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & -v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3536 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,C) & p1_s1_finseq_1(A,B) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((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_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))))) & k2_finseq_1(f1_s1_finseq_1) = k4_finseq_1(A) & v1_funct_1(A))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3537 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> k8_finseq_1(A,B,C) = k7_finseq_1(B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3538 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (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(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D))))))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3539 (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) -> (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]. 23.24/22.31 3540 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f2_s5_finseq_1)) & (all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B)))))) -> (exists A (m2_finseq_1(A,f1_s5_finseq_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3541 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3542 (all A all B (m1_finseq_1(B,A) <-> m2_finseq_1(B,A))) # label(redefinition_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.31 3543 (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]. 23.24/22.32 3544 (all A (v4_ordinal2(A) -> k4_card_1(k2_finseq_1(A)) = A)) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3545 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_relat_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3546 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k7_finseq_1(A,B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3547 (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]. 23.24/22.32 3548 (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]. 23.24/22.32 3549 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1) = A)) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3550 (exists A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3551 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -(A != k1_xboole_0 & (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3552 (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(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3553 (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]. 23.24/22.32 3554 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) <-> r1_tarski(k2_finseq_1(A),k2_finseq_1(B))))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3555 (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]. 23.24/22.32 3556 (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) -> (k7_finseq_1(A,B) = k1_xboole_0 -> k1_xboole_0 = A & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3557 (all A (v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3558 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3559 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3560 (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]. 23.24/22.32 3561 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3562 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (C = k10_finseq_1(A,B) <-> B = k1_funct_1(C,np__2) & A = k1_funct_1(C,np__1) & k3_finseq_1(C) = np__2))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3563 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k4_finseq_1(A) = k1_relat_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3564 (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]. 23.24/22.32 3565 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_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]. 23.24/22.32 3566 (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]. 23.24/22.32 3567 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3568 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (A = k6_finseq_1(B) <-> np__0 = k3_finseq_1(A))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3569 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(k2_finseq_1(A),k2_finseq_1(B)) -> B = A))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3570 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3571 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3572 (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]. 23.24/22.32 3573 (all A all B (v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3574 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3575 (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]. 23.24/22.32 3576 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) = k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3577 (all A (v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3578 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k9_finseq_1(A) = B <-> k2_relat_1(B) = k1_tarski(A) & k4_finseq_1(B) = k2_finseq_1(np__1)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3579 (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(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) -> k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C)) = k1_funct_1(B,C)))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3580 (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]. 23.24/22.32 3581 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3582 (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]. 23.24/22.32 3583 (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]. 23.24/22.32 3584 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & v4_ordinal2(B))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k14_finseq_1(A) = B <-> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(k1_funct_1(B,C) = E & r1_xreal_0(F,E) & k1_funct_1(B,D) = F & r1_xreal_0(D,k3_finseq_1(B)) & -r1_xreal_0(D,C) & r1_xreal_0(np__1,C)))))))))) & k2_relat_1(B) = A))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3585 (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]. 23.24/22.32 3586 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3587 (all A exists B (v1_relat_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v1_funct_1(B) & m1_relset_1(B,k5_numbers,A))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3588 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (k4_finseq_1(A) = k1_xboole_0 <-> A = k1_xboole_0))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3589 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3590 (all A all B all C all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (np__3 = k3_finseq_1(D) & B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & k1_funct_1(D,np__1) = A <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3591 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & v1_finseq_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3592 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> k3_finseq_1(k16_finseq_1(A,B,C)) = C))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3593 (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]. 23.24/22.32 3594 (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) -> A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)))))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3595 (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 (v4_ordinal2(C) -> (r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) -> k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3596 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k2_finseq_1(B) = k1_relat_1(A) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3597 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3598 (all A (v4_ordinal2(A) -> a_1_0_finseq_1(A) = k1_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3599 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3600 (all A (v1_relat_1(A) -> (v1_finseq_1(A) <-> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = k1_relat_1(A)))))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3601 (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]. 23.24/22.32 3602 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -(r2_hidden(A,k4_finseq_1(B)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B))) & A = D)))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3603 (all A all B (v1_finseq_1(A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_finseq_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3604 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) = k2_finseq_1(A) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3605 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k1_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3606 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3607 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3608 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3609 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_tarski(k2_relat_1(B),A) <-> m1_finseq_1(B,A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3610 (all A k1_tarski(k4_tarski(np__1,A)) = k5_finseq_1(A)) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3611 (all A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3612 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3613 p1_s3_finseq_1(k1_xboole_0) & (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) -> (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3614 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> f2_s2_finseq_1(B) = k1_funct_1(A,B)))) & k3_finseq_1(A) = f1_s2_finseq_1 & v1_finseq_1(A))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3615 (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]. 23.24/22.32 3616 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r1_xreal_0(B,np__0) | r2_hidden(B,k2_finseq_1(A)) & r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C)))))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3617 (exists A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3618 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(k7_finseq_1(A,B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3619 (all A (v1_funct_1(A) & v1_finseq_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]. 23.24/22.32 3620 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3621 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(B,C) = k7_finseq_1(B,A) | k7_finseq_1(C,B) = k7_finseq_1(A,B) -> C = A))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3622 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k3_finseq_1(A) = k3_finseq_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3623 (all A exists B (m1_finseq_1(B,A) & v1_xboole_0(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3624 (all A k6_finseq_1(A) = k1_xboole_0) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3625 (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]. 23.24/22.32 3626 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3627 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3628 (all A (v1_relat_1(A) -> (all B (r9_orders_1(k4_relat_1(A),B) <-> r8_orders_1(A,B))))) # label(t166_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3629 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3630 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3631 (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]. 23.24/22.32 3632 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) & v1_funct_1(B) -> (m1_orders_1(B,A) <-> (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))))))))) # label(d1_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3633 (all A (v1_relat_1(A) -> (all B all C (r3_orders_1(A,B) & r1_tarski(C,B) -> r3_orders_1(A,C))))) # label(t134_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3634 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3635 (all A all B all C all D (v1_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v4_relat_2(D) -> (r2_hidden(B,A) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(C,A) -> B = C))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3636 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3637 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3638 (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) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3639 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3640 (all A (v1_relat_1(A) -> (all B (v4_relat_2(A) & r8_orders_1(A,B) -> r6_orders_1(A,B))))) # label(t158_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3641 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_hidden(A,k1_orders_1(B)) <-> m1_subset_1(A,k1_zfmisc_1(B))))))) # label(t6_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3642 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3643 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3644 (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]. 23.24/22.32 3645 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3646 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3647 (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]. 23.24/22.32 3648 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(C,B),A) | C = B)) & r2_hidden(B,k3_relat_1(A)) <-> r8_orders_1(A,B))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3649 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> (all C -((all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))) & r2_hidden(D,B))) & v3_orders_1(k2_wellord1(A,C)) & r1_tarski(C,B))))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3650 (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]. 23.24/22.32 3651 (all A (v1_relat_1(A) -> (all B -(k1_xboole_0 = B & r4_orders_1(A,B))))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3652 (all A (v1_relat_1(A) -> (all B (r6_orders_1(k4_relat_1(A),B) <-> r7_orders_1(A,B))))) # label(t163_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3653 (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]. 23.24/22.32 3654 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3655 (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]. 23.24/22.32 3656 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3657 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3658 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r8_relat_2(A,B) <-> r1_orders_1(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3659 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3660 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3661 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3662 (all A (v1_relat_1(A) -> (all B all C (v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r9_orders_1(A,B) & r2_hidden(B,C) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3663 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v1_orders_1(A) & v2_orders_1(A)))) # label(t108_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3664 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3665 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3666 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3667 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3668 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3669 (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]. 23.24/22.32 3670 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) & r6_relat_2(A,B) & r8_relat_2(A,B) & r1_relat_2(A,B) <-> r3_orders_1(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3671 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3672 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3673 (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]. 23.24/22.32 3674 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3675 (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]. 23.24/22.32 3676 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k3_relat_1(B) = A)) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3677 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3678 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3679 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v2_orders_1(A) & v3_orders_1(A) & v1_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3680 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3681 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.24/22.32 3682 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3683 (all A -(k1_xboole_0 != A & (all B -(r1_tarski(B,A) & (all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))) & v6_ordinal1(B))) & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & r1_tarski(B,C) & B != C)))))) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3684 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3685 (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]. 23.27/22.35 3686 (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]. 23.27/22.35 3687 (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]. 23.27/22.35 3688 (all A all B (v4_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> A = k3_relat_1(B))) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3689 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3690 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3691 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3692 (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]. 23.27/22.35 3693 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3694 (all A all B all C (v1_relat_1(C) -> (r1_relat_2(C,A) & r1_tarski(B,A) -> r1_relat_2(C,B)))) # label(t93_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3695 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3696 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3697 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3698 (all A (v1_relat_1(A) -> (all B k2_wellord1(k4_relat_1(A),B) = k4_relat_1(k2_wellord1(A,B))))) # label(t193_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3699 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3700 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3701 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3702 (all A (v1_relat_1(A) -> (all B (r4_orders_1(k4_relat_1(A),B) <-> r5_orders_1(A,B))))) # label(t152_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3703 (all A (-((all B -(r2_hidden(B,A) & B != k1_xboole_0)) & k1_xboole_0 != k3_tarski(A)) & -(k1_xboole_0 = k3_tarski(A) & (exists B (r2_hidden(B,A) & B != k1_xboole_0))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3704 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3705 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3706 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3707 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3708 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3709 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3710 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3711 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3712 (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,A) -> A = B))))) & (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 -((all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> -(r2_hidden(C,A) & -p1_s1_orders_1(B,C) & -p1_s1_orders_1(C,B) & r2_hidden(B,A)))))) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (r2_hidden(C,A) & -p1_s1_orders_1(C,B) & m1_subset_1(C,f1_s1_orders_1))))) & r1_tarski(A,f1_s1_orders_1))) -> (exists A ((all B (m1_subset_1(B,f1_s1_orders_1) -> -(p1_s1_orders_1(A,B) & B != A))) & m1_subset_1(A,f1_s1_orders_1))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3713 (all A (v1_orders_1(k6_partfun1(A)) & v2_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3714 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3715 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3716 (all A (v1_relat_1(A) -> (all B -(r5_orders_1(A,B) & B = k1_xboole_0)))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3717 (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]. 23.27/22.35 3718 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,k3_relat_1(A)) -> C = B | r2_hidden(k4_tarski(B,C),A))) & r2_hidden(B,k3_relat_1(A)) <-> r9_orders_1(A,B))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3719 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3720 (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]. 23.27/22.35 3721 (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]. 23.27/22.35 3722 (all A (v1_relat_1(A) -> (all B -(B = k3_relat_1(A) & (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]. 23.27/22.35 3723 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3724 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v8_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B) & v4_relat_2(k2_wellord1(A,B)) & v1_relat_2(k2_wellord1(A,B)))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3725 (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]. 23.27/22.35 3726 (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]. 23.27/22.35 3727 (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]. 23.27/22.35 3728 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3729 (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]. 23.27/22.35 3730 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C -(r2_hidden(k4_tarski(B,C),A) & C != B & r2_hidden(C,k3_relat_1(A)))) <-> r6_orders_1(A,B))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3731 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3732 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3733 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C -r7_orders_1(A,C)) & r5_orders_1(A,B) & r2_orders_1(A,B))))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3734 (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]. 23.27/22.35 3735 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3736 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3737 (all A -((all B -((all C -(r2_hidden(C,A) & B != C & r1_tarski(C,B))) & r2_hidden(B,A))) & (all B -((all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(C,D))))) & v6_ordinal1(B) & r1_tarski(B,A))) & k1_xboole_0 != A)) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3738 (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]. 23.27/22.35 3739 (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)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)))))) # label(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3740 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3741 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3742 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3743 (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]. 23.27/22.35 3744 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3745 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3746 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) & r8_relat_2(A,B) & r1_relat_2(A,B) <-> r2_orders_1(A,B))))) # label(d7_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3747 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3748 (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)) & v8_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3749 (all A (v1_relat_1(A) -> (all B all C (r2_hidden(B,C) & r8_orders_1(A,B) & r1_tarski(C,k3_relat_1(A)) & v1_relat_2(A) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3750 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3751 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3752 (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]. 23.27/22.35 3753 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3754 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3755 (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]. 23.27/22.35 3756 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3757 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3758 (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]. 23.27/22.35 3759 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3760 (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]. 23.27/22.35 3761 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (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]. 23.27/22.35 3762 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3763 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3764 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3765 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3766 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3767 (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]. 23.27/22.35 3768 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3769 (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]. 23.27/22.35 3770 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r1_orders_1(A,B) & r2_orders_1(A,B) & r3_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3771 (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]. 23.27/22.35 3772 (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]. 23.27/22.35 3773 (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]. 23.27/22.35 3774 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3775 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3776 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3777 (all A (v1_relat_1(A) -> (v4_relat_2(A) & v6_relat_2(A) & v8_relat_2(A) & v1_relat_2(A) <-> v3_orders_1(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3778 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> r2_hidden(k3_tarski(B),A) | B = k1_xboole_0)) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))))) & A != k1_xboole_0)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3779 (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]. 23.27/22.35 3780 (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]. 23.27/22.35 3781 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3782 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3783 (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]. 23.27/22.35 3784 (all A -(k1_xboole_0 != A & (all B (v6_ordinal1(B) & r1_tarski(B,A) -> r2_hidden(k1_setfam_1(B),A) | B = k1_xboole_0)) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(C,B) & C != B & r2_hidden(C,A))))))) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3785 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3786 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3787 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3788 (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]. 23.27/22.35 3789 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3790 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3791 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3792 (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]. 23.27/22.35 3793 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3794 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3795 (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]. 23.27/22.35 3796 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3797 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3798 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.35 3799 (all A (v1_relat_1(A) -> (all B ((all C -(v3_orders_1(k2_wellord1(A,C)) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))) & r2_hidden(D,B))) & r1_tarski(C,B))) <-> r5_orders_1(A,B))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3800 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3801 (all A all B (v1_relat_1(B) -> (r6_relat_2(B,A) & r1_relat_2(B,A) <-> r7_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3802 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3803 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3804 (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]. 23.27/22.38 3805 (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]. 23.27/22.38 3806 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r2_orders_1(A,B) -> r2_orders_1(A,C))))) # label(t131_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3807 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3808 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3809 (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]. 23.27/22.38 3810 (all A (v1_relat_1(A) -> (all B all C (r2_wellord1(A,B) & r1_tarski(C,B) -> r2_wellord1(A,C))))) # label(t187_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3811 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_hidden(A,k1_orders_1(B)) <-> r1_tarski(A,B)))))) # label(t5_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3812 (all A all B all C all D all E (v4_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v1_relat_2(E) -> (r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3813 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3814 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3815 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3816 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3817 (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) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3818 (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,C) -> p1_s2_orders_1(A,C)))))))) & (all A -(r1_tarski(A,f1_s2_orders_1) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (m1_subset_1(C,f1_s2_orders_1) & r2_hidden(C,A) & -p1_s2_orders_1(B,C))))) & (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 A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,A) -> B = A))))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> p1_s2_orders_1(A,A))) -> (exists A (m1_subset_1(A,f1_s2_orders_1) & (all B (m1_subset_1(B,f1_s2_orders_1) -> -(p1_s2_orders_1(B,A) & A != B))))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3819 (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]. 23.27/22.38 3820 (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]. 23.27/22.38 3821 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(C,B),A) & B != C & r2_hidden(C,k3_relat_1(A)))) & r2_hidden(B,k3_relat_1(A)) <-> r7_orders_1(A,B))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3822 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3823 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3824 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> A = k3_relat_1(B) & A = k4_relset_1(A,A,B)))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3825 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3826 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3827 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3828 (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) -> k4_relset_1(A,A,B) = A & k5_relset_1(A,A,B) = A)) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3829 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3830 (all A (v1_relat_1(A) -> (v4_relat_2(A) & v8_relat_2(A) & v1_relat_2(A) <-> v2_orders_1(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3831 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3832 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3833 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3834 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r4_relat_2(C,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3835 (all A (v1_relat_1(A) -> (all B (v1_relat_2(A) & r1_tarski(B,k3_relat_1(A)) -> k3_relat_1(k2_wellord1(A,B)) = B)))) # label(t181_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3836 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v1_relat_2(A) <-> v1_orders_1(A)))) # label(d3_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3837 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B -((all C -(r1_tarski(C,k1_relat_1(A)) & k9_relat_1(A,C) = B & v1_finset_1(C))) & r1_tarski(B,k2_relat_1(A)) & v1_finset_1(B))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3838 (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]. 23.27/22.38 3839 (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))) -> m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & 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]. 23.27/22.38 3840 (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]. 23.27/22.38 3841 (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 (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))))) # label(t23_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3842 (all A all B all C all D all E (v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) -> (r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3843 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3844 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3845 (all A (v1_relat_2(k1_eqrel_1(A)) & v3_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v8_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3846 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3847 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) -> B = k5_eqrel_1(A,B,B))) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3848 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3849 (all A all B all C all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3850 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(k4_tarski(D,B),C) <-> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3851 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3852 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3853 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> -(B != k1_eqrel_1(A) & k1_eqrel_1(A) != C & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3854 (all A all B (-v1_xboole_0(A) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(B) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3855 (all A k1_eqrel_1(A) = k2_zfmisc_1(A,A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3856 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> -((exists C r2_hidden(C,A)) & k1_xboole_0 = B))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3857 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3858 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3859 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3860 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> ((exists C A = k6_eqrel_1(A,B,C)) -> k1_eqrel_1(A) = B))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3861 (all A all B (m2_relset_1(B,A,A) -> (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) <-> A = k3_relat_1(B) & v8_relat_2(B) & v3_relat_2(B) & v1_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3862 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> k7_eqrel_1(A,B) = k8_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3863 (all A all B (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)) & v1_setfam_1(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3864 (all A all B all C (v3_relat_2(B) & 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) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3865 (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 (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (r2_hidden(E,A) & k6_eqrel_1(A,B,E) = D))))) <-> k7_eqrel_1(A,B) = C))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3866 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> B = k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)))))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3867 (all A all B all C (v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & 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]. 23.27/22.38 3868 (all A all B all C (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3869 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != A -> (k5_setfam_1(A,B) = A & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> k1_xboole_0 != C & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(D != C & -r1_xboole_0(C,D) & r2_hidden(D,B))))))) <-> m1_eqrel_1(B,A))) & (k1_xboole_0 = A -> (m1_eqrel_1(B,A) <-> B = k1_xboole_0)))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3870 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3871 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3872 (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) -> (k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B) <-> r2_hidden(B,k6_eqrel_1(A,C,D))))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3873 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> B = k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)))))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3874 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C all D -(r2_hidden(D,A) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & r2_hidden(C,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3875 (all A (v1_relat_1(k1_eqrel_1(A)) & v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3876 (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 k6_eqrel_1(A,B,C) = k10_relset_1(A,A,B,k1_tarski(C))))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3877 (all A all B all C all D (v1_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v3_relat_2(D) -> (r2_hidden(B,k6_eqrel_1(A,D,C)) <-> r2_hidden(k4_tarski(B,C),D)))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3878 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,B,B) = B)) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3879 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3880 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C -((all D -r2_hidden(C,k6_eqrel_1(A,B,D))) & r2_hidden(C,A))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3881 (all A all B all C all D all E (v1_relat_2(E) & v3_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_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]. 23.27/22.38 3882 (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]. 23.27/22.38 3883 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> k5_eqrel_1(A,B,B) = B)) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3884 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (A = k1_xboole_0 -> k1_xboole_0 = k7_eqrel_1(A,B)))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3885 (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]. 23.27/22.38 3886 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(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]. 23.27/22.38 3887 (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 (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) -> (r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v3_relat_2(E) & v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E)))) <-> k5_eqrel_1(A,B,C) = D))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3888 (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]. 23.27/22.38 3889 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k2_xboole_0(B,C) = k3_eqrel_1(A,B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3890 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3891 (all A all B (m2_relset_1(B,A,A) -> B = k2_eqrel_1(A,k1_eqrel_1(A),B))) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3892 (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]. 23.27/22.38 3893 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3894 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3895 (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]. 23.27/22.38 3896 (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) -> v3_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) & v8_relat_2(k4_eqrel_1(A,B,C)))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3897 (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]. 23.27/22.38 3898 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3899 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (all D (v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) -> (D = k3_eqrel_1(A,B,C) -> (all E -(r2_hidden(E,A) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,B,E)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3900 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3901 (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) -> k4_eqrel_1(A,B,C) = k4_eqrel_1(A,C,B))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3902 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3903 (all A all B all C (v1_partfun1(B,A,A) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> v8_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v3_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3904 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -((all D (m1_subset_1(D,B) -> A != k6_eqrel_1(B,C,D))) & r2_hidden(A,k7_eqrel_1(B,C))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3905 (all A all B (r2_hidden(B,A) -> A = k6_eqrel_1(A,k1_eqrel_1(A),B))) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3906 (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]. 23.27/22.38 3907 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3908 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,C) = k3_eqrel_1(A,C,B))) # label(commutativity_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3909 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> B = k2_eqrel_1(A,B,B))) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3910 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3911 (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 = k4_eqrel_1(A,B,B))) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3912 (all A all B (m1_eqrel_1(B,A) -> (exists C (v3_relat_2(C) & v8_relat_2(C) & B = k7_eqrel_1(A,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3913 (all A (v3_relat_2(k6_partfun1(A)) & v8_relat_2(k6_partfun1(A)) & m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3914 (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]. 23.27/22.38 3915 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3916 (all A all B all C all D (v3_relat_2(D) & v8_relat_2(D) & v1_partfun1(D,B,B) & m2_relset_1(D,B,B) -> (all E (v3_relat_2(E) & v8_relat_2(E) & m2_relset_1(E,B,B) & v1_partfun1(E,B,B) -> (r2_hidden(A,B) -> (r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)) <-> (exists F ((all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E)) | r1_xreal_0(k3_finseq_1(F),G)))) & C = k1_funct_1(F,k3_finseq_1(F)) & A = k1_funct_1(F,np__1) & r1_xreal_0(np__1,k3_finseq_1(F)) & v1_finseq_1(F) & v1_funct_1(F) & v1_relat_1(F))))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3917 (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,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))) -> (exists A (v3_relat_2(A) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & (all B all C (r2_hidden(B,f1_s1_eqrel_1) & r2_hidden(C,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3918 (all A all B (m2_relset_1(B,A,A) -> (exists C (r1_tarski(B,C) & (all D (v3_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & 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]. 23.27/22.38 3919 (all A all B all C all D (k2_tarski(A,C) = k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) & k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(B,D))) # label(t16_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3920 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_funct_5(A)) & v1_relat_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3921 (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]. 23.27/22.38 3922 (all A (k1_xboole_0 = k1_funct_5(A) <-> k2_funct_5(A) = k1_xboole_0)) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3923 (all A (v1_relat_1(A) & v1_funct_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]. 23.27/22.38 3924 (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_relat_1(k1_funct_1(k5_funct_5(C),B)) & v1_funct_1(k1_funct_1(k5_funct_5(C),B))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3925 (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)) -> C = k3_funct_5(k4_funct_5(C)) & C = k5_funct_5(k6_funct_5(C)) | A = k1_xboole_0))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3926 (all A (k1_xboole_0 = k1_funct_5(A) | k2_funct_5(A) = k1_xboole_0 -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3927 (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]. 23.27/22.38 3928 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k4_funct_5(A)) & v1_relat_1(k4_funct_5(A)))) # label(dt_k4_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3929 (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]. 23.27/22.38 3930 (all A all B all C all D (k1_card_1(A) = k1_card_1(B) & k1_card_1(C) = k1_card_1(D) -> 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]. 23.27/22.38 3931 (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(k3_funct_5(B))) & C = k1_funct_1(k3_funct_5(B),A) -> 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))) & k1_relat_1(C) = k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B)))))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3932 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A) & k2_zfmisc_1(A,k1_relat_1(C)) = k1_relat_1(k6_funct_5(C))))) # label(t33_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3933 (all A all B (r2_wellord2(A,k1_funct_2(k1_tarski(B),A)) & k1_card_1(A) = k1_card_1(k1_funct_2(k1_tarski(B),A)))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3934 (all A all B (r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3935 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3936 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> C = k3_funct_5(k4_funct_5(C)) & k5_funct_5(k6_funct_5(C)) = C | r2_hidden(k1_xboole_0,k2_relat_1(C))))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3937 (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]. 23.27/22.38 3938 (all A all B all C (r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) & k1_card_1(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))))) # label(t71_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3939 (all A (v1_relat_1(A) -> k2_funct_5(A) = k2_relat_1(A) & k1_relat_1(A) = k1_funct_5(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3940 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k4_funct_5(A) = B <-> (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (v1_funct_1(E) & (exists F (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = E & r2_hidden(F,k1_relat_1(E)) & C = k4_tarski(D,F))) & v1_relat_1(E))))) & (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k1_relat_1(B)) & k1_funct_1(A,k1_mcart_1(C)) = D -> k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C)))))))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3941 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k3_funct_5(C) = k3_funct_5(D) & k1_relat_1(D) = k2_zfmisc_1(A,B) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> D = C))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3942 (all A all B (-(k1_xboole_0 = k2_zfmisc_1(B,A) & k1_xboole_0 = k2_zfmisc_1(A,B) & k1_xboole_0 = A) -> B = k1_funct_5(k2_zfmisc_1(B,A)) & k2_funct_5(k2_zfmisc_1(A,B)) = B)) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3943 (all A all B (B = k1_funct_5(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3944 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k4_funct_5(D) = k4_funct_5(C) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_xboole_0 = A | C = D))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3945 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(D)) & D = k1_funct_1(C,A) -> 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]. 23.27/22.38 3946 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A)) & r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C)))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3947 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) & D = k1_funct_1(k3_funct_5(C),A) -> k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,B) & r2_hidden(B,k1_relat_1(D))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3948 (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(k5_funct_5(C)),B) & r1_tarski(k1_relat_1(k3_funct_5(C)),A)))) # label(t32_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3949 (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)) -> D = C))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3950 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k3_funct_5(A) <-> k1_relat_1(B) = k1_funct_5(k1_relat_1(A)) & (all C -((all D (v1_funct_1(D) & v1_relat_1(D) -> -(k1_relat_1(D) = k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E)))) & k1_funct_1(B,C) = D))) & r2_hidden(C,k1_funct_5(k1_relat_1(A)))))))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.38 3951 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_funct_5(C)) & r2_hidden(B,k2_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3952 (all A all B (k2_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(B) & k1_tarski(A) = k1_funct_5(k1_tarski(k4_tarski(A,B))))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3953 (all A k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3954 (all A all B all C (B != A -> k1_card_1(k1_funct_2(k2_tarski(A,B),C)) = k1_card_1(k2_zfmisc_1(C,C)) & r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C)))) # label(t73_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3955 (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]. 23.27/22.39 3956 (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]. 23.27/22.39 3957 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k6_funct_5(A)) & v1_relat_1(k6_funct_5(A)))) # label(dt_k6_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3958 (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]. 23.27/22.39 3959 (all A all B all C (r1_xboole_0(A,B) -> r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) & k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3960 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3961 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(r2_hidden(B,k1_relat_1(A)) & v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) -> k4_funct_5(A) = k1_xboole_0 & k6_funct_5(A) = k1_xboole_0))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3962 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> r1_tarski(k2_relat_1(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]. 23.27/22.39 3963 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t47_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3964 (exists 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) & v1_relat_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3965 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = k6_funct_5(k5_funct_5(C)) & C = k4_funct_5(k3_funct_5(C))))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3966 (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)) -> k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,A) & r2_hidden(A,k1_relat_1(D))))))) # label(t29_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3967 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3968 (all A all B all 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)) & r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C))))) # label(t70_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3969 (all A all B all C all D (r2_wellord2(C,D) & r2_wellord2(A,B) -> r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)) & k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3970 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & k5_funct_5(D) = k5_funct_5(C) -> D = C))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3971 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_4(k4_funct_5(A)) = k6_funct_5(A))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3972 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> B = k1_relat_1(k5_funct_5(C)) & k1_relat_1(k3_funct_5(C)) = A | k2_zfmisc_1(A,B) = k1_xboole_0))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3973 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(k5_funct_5(A)) = k2_funct_5(k1_relat_1(A)))) # label(t30_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3974 (all A all B (v1_funct_1(B) & v1_relat_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]. 23.27/22.39 3975 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_funct_1(C,A) = D & r2_hidden(B,k1_relat_1(D)) & r2_hidden(A,k1_relat_1(C)) -> k1_funct_1(D,B) = k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C))) & r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C)))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3976 (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]. 23.27/22.39 3977 (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)) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & k4_funct_5(C) = k4_funct_5(D) -> C = D | r2_hidden(k1_xboole_0,k2_relat_1(D)) | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3978 (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_funct_1(k1_funct_1(k3_funct_5(C),A)) & v1_relat_1(k1_funct_1(k3_funct_5(C),A))))) # label(t26_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3979 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3980 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A))) & k1_funct_5(k1_relat_1(k2_funct_4(A))) = k2_funct_5(k1_relat_1(A)))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3981 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3982 (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]. 23.27/22.39 3983 (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(C),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(D)) | D = C | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3984 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3985 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = k6_funct_5(k5_funct_5(C)) & k4_funct_5(k3_funct_5(C)) = C))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3986 (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]. 23.27/22.39 3987 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funct_5(A)) & v1_relat_1(k3_funct_5(A)))) # label(dt_k3_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3988 (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)) -> 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]. 23.27/22.39 3989 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k1_xboole_0 = k3_funct_5(A) & k5_funct_5(A) = k1_xboole_0))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3990 (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(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(D) = k6_funct_5(C) -> k1_xboole_0 = A | D = C))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3991 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(D) & k5_funct_5(D) = k5_funct_5(C) & k1_relat_1(C) = k2_zfmisc_1(A,B) -> C = D))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3992 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> -(k1_relat_1(D) = k2_zfmisc_1(A,B) & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,A) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)))) & k1_relat_1(E) = A & E = k1_funct_1(k5_funct_5(D),C)))) & r2_hidden(C,B) & k2_zfmisc_1(A,B) != k1_xboole_0))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3993 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3994 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) & C = k1_funct_1(k5_funct_5(B),A) -> 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)))) & 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(B,k4_tarski(D,A)) = k1_funct_1(C,D) & r2_hidden(k4_tarski(D,A),k1_relat_1(B)))) & r1_tarski(k2_relat_1(C),k2_relat_1(B))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3995 (all A all B (B = k2_funct_5(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))))) # label(d2_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3996 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3997 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3998 (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,A) & (all E (v1_funct_1(E) & v1_relat_1(E) -> -(E = k1_funct_1(k3_funct_5(D),C) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,B) -> k1_funct_1(D,k4_tarski(C,F)) = k1_funct_1(E,F))) & k1_relat_1(E) = B)))))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 3999 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_funct_5(A) = k1_xboole_0 & k2_funct_5(A) = k1_xboole_0)) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4000 (all A (v1_relat_1(A) & v1_funct_1(A) -> k5_funct_5(A) = k3_funct_5(k2_funct_4(A)))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4001 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__3,A) = a_1_2_finseq_2(A))) # label(t122_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4002 (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]. 23.27/22.39 4003 (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 (v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)))))))))) # label(t135_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4004 (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]. 23.27/22.39 4005 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4006 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (E = k4_funcop_1(F,G,D) -> k3_finseq_1(G) = k3_finseq_1(E)))))))))))))))) # label(t98_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4007 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (all J (m2_finseq_1(J,B) -> (k10_finseq_1(D,E) = I & J = k10_finseq_1(F,G) -> 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]. 23.27/22.39 4008 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4009 (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]. 23.27/22.39 4010 (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]. 23.27/22.39 4011 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (v1_funct_1(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)) -> 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]. 23.27/22.39 4012 (all A (v4_ordinal2(A) -> (all B all C (r2_hidden(B,k2_finseq_1(A)) -> k1_funct_1(k2_finseq_2(A,C),B) = C)))) # label(t70_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4013 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4014 (all A all B all C (v4_ordinal2(B) -> (r2_hidden(A,a_2_0_finseq_2(B,C)) <-> (exists D (B = k3_finseq_1(D) & A = D & m2_finseq_2(D,C,k3_finseq_2(C))))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4015 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k2_finseq_2(k1_nat_1(A,np__1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B))))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4016 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k1_finseq_2(A)))) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4017 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4018 (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]. 23.27/22.39 4019 (all A all B ((all C (r2_hidden(C,B) -> m2_finseq_1(C,A))) <-> m1_finseq_2(B,A))) # label(d3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4020 (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]. 23.27/22.39 4021 (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) -> (k5_relat_1(A,C) = B & r1_tarski(k2_relat_1(A),k1_relat_1(C)) -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4022 (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]. 23.27/22.39 4023 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (k11_finseq_1(D,E,F) = I -> k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) = k4_funcop_1(H,I,G)))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4024 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (np__0 != A -> (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]. 23.27/22.39 4025 (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]. 23.27/22.39 4026 (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) -> (k3_finseq_1(B) = A & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k2_finseq_1(A)) -> k1_funct_1(B,D) = k1_funct_1(C,D)))) & A = k3_finseq_1(C) -> B = C))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4027 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (C = k1_partfun1(k5_numbers,A,A,B,D,E) -> k3_finseq_1(C) = k3_finseq_1(D)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4028 (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]. 23.27/22.39 4029 (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]. 23.27/22.39 4030 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_relat_1(k2_funcop_1(k2_finseq_1(A),B)))))) # label(t66_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4031 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> 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]. 23.27/22.39 4032 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),B)))) -> m2_finseq_1(A,B))))) # label(t14_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4033 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4034 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_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_relat_1(E) & v1_finseq_1(E) & v1_funct_1(E) -> -(B = k3_finseq_1(E) & k7_finseq_1(D,E) = C & k3_finseq_1(D) = A)))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4035 (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) -> (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)) -> (r1_xreal_0(A,k3_finseq_1(B)) & C = k5_relat_1(D,B) & k2_finseq_1(A) = k2_relat_1(D) -> A = k3_finseq_1(C)))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4036 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C k2_finseq_2(k1_nat_1(A,B),C) = k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C))))))) # label(t143_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4037 (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]. 23.27/22.39 4038 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r1_tarski(A,C) & r1_tarski(B,C) & k3_finseq_1(B) = k3_finseq_1(A) -> B = A))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4039 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(k3_finseq_1(B) != np__0 & (all C (m2_finseq_1(C,A) -> (all D (m1_subset_1(D,A) -> k8_finseq_1(A,C,k12_finseq_1(A,D)) != B))))))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4040 (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) -> (k10_finseq_1(D,E) = H -> k4_funcop_1(G,H,F) = k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F))))))))))))))))))) # label(t101_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4041 (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]. 23.27/22.39 4042 (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]. 23.27/22.39 4043 (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]. 23.27/22.39 4044 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> r1_tarski(B,k3_finseq_2(A)))) # label(t105_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4045 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B)) -> (r1_xreal_0(B,k3_finseq_1(C)) -> np__0 != A & B = np__0 | v1_relat_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C))))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4046 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k5_relat_1(k10_finseq_1(B,C),A) = k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4047 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(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]. 23.27/22.39 4048 (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]. 23.27/22.39 4049 (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]. 23.27/22.39 4050 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) -> (r1_xreal_0(B,k3_finseq_1(D)) -> B = np__0 & np__0 != A | m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C)))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4051 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_square_1(B,C) = A -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C)) = k2_finseq_1(A)))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4052 (all A (v4_ordinal2(A) -> k1_finseq_2(A) = k6_partfun1(k2_finseq_1(A)))) # label(d1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4053 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> v1_funct_1(B) & m2_relset_1(B,k4_finseq_1(B),A) & v1_funct_2(B,k4_finseq_1(B),A))))) # label(t30_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4054 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__1,A) = a_1_0_finseq_2(A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4055 (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]. 23.27/22.39 4056 (all A k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A)) = k4_finseq_2(np__0,A)) # label(t112_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4057 (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]. 23.27/22.39 4058 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k5_numbers,B) & m2_relset_1(C,k5_numbers,B) & v1_funct_1(C) -> m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B))))))) # label(t31_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4059 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4060 (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]. 23.27/22.39 4061 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,B) -> (k12_finseq_1(B,E) = G -> 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]. 23.27/22.39 4062 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4063 (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]. 23.27/22.39 4064 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k3_funcop_1(D,E,F),C))))))))))))) # label(t84_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4065 (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,C,D) = D & D = k8_finseq_1(B,D,C))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4066 (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]. 23.27/22.39 4067 (all A all B all C (m2_finseq_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B))))) # label(t36_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4068 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -(k3_finseq_1(B) = k1_nat_1(A,np__1) & (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D B != k7_finseq_1(C,k9_finseq_1(D)))))))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4069 (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]. 23.27/22.39 4070 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> np__0 = k3_square_1(A,np__0) & A = k4_square_1(A,np__0) & A = k4_square_1(np__0,A) & np__0 = k3_square_1(np__0,A))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4071 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C)) -> (exists E (m2_finseq_2(E,C,k4_finseq_2(A,C)) & (exists F (m2_finseq_2(F,C,k4_finseq_2(B,C)) & k8_finseq_1(C,E,F) = D)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4072 (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 (m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) -> v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B)) & v1_relat_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4073 (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_funct_1(k1_finseq_2(B),A) = A))))) # label(t56_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4074 (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]. 23.27/22.39 4075 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__2,A) = a_1_1_finseq_2(A))) # label(t119_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4076 (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 (m2_relset_1(G,D,E) & v1_funct_2(G,D,E) & v1_funct_1(G) -> (F = k11_finseq_1(A,B,C) -> k1_partfun1(k5_numbers,D,D,E,F,G) = k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C))))))))))) # label(t41_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4077 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (k2_relat_1(C) = k4_finseq_1(A) & k5_relat_1(C,A) = B -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4078 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) & r1_xreal_0(k3_finseq_1(C),A) -> B = C))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4079 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4080 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_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_square_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(C)))))))))) # label(t79_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4081 (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]. 23.27/22.39 4082 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C)) -> v1_relat_1(k4_funcop_1(C,B,A)) & v1_funct_1(k4_funcop_1(C,B,A)) & v1_finseq_1(k4_funcop_1(C,B,A))))))) # label(t82_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4083 (all A all B all C all D (m2_subset_1(B,k1_numbers,k5_numbers) & -v1_xboole_0(D) & m2_subset_1(C,k1_numbers,k5_numbers) -> ((exists E exists F (A = k8_finseq_1(D,E,F) & m2_finseq_2(F,D,k4_finseq_2(C,D)) & m2_finseq_2(E,D,k4_finseq_2(B,D)))) <-> r2_hidden(A,a_3_0_finseq_2(B,C,D))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4084 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4085 (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]. 23.27/22.39 4086 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_finseq_1(k5_funcop_1(C,A,B)) & v1_funct_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]. 23.27/22.39 4087 (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) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_square_1(A,k3_finseq_1(C)) = k3_finseq_1(B)))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4088 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4089 (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) -> -(k1_nat_1(A,B) = k3_finseq_1(D) & (all E (m2_finseq_1(E,C) -> (all F (m2_finseq_1(F,C) -> -(k3_finseq_1(E) = A & k3_finseq_1(F) = B & k8_finseq_1(C,E,F) = D)))))))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4090 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (-v1_xboole_0(C) & m1_finseq_2(C,B) -> -v1_xboole_0(C) & m1_finseq_2(C,A))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4091 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_2(E,k2_zfmisc_1(B,C),D) -> (all F (m2_finseq_2(F,B,k4_finseq_2(A,B)) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t140_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4092 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (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]. 23.27/22.39 4093 (all A (v4_ordinal2(A) -> v1_finseq_1(k1_finseq_2(A)) & v1_funct_1(k1_finseq_2(A)) & v1_relat_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4094 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_2(D,k5_numbers,B) & m2_relset_1(D,k5_numbers,B) & v1_funct_1(D) -> (k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) = C -> k3_finseq_1(C) = A))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4095 (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]. 23.27/22.39 4096 (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) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k5_relat_1(D,B) = C & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C)))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4097 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> k6_finseq_1(B) = k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4098 (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]. 23.27/22.39 4099 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4100 (all A all B (v4_ordinal2(A) -> v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) & v1_relat_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4101 (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]. 23.27/22.39 4102 (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) -> (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_finseq_1(k3_funcop_1(C,A,B)) & v1_funct_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4103 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (exists C m2_finseq_2(C,A,B)))) # label(existence_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4104 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (m1_subset_1(C,A) & B = k12_finseq_1(A,C))))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4105 (all A k2_finseq_2(np__2,A) = k10_finseq_1(A,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4106 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> C = k5_relat_1(k1_finseq_2(A),C))))))) # label(t138_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4107 (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_relat_1(E) & v1_finseq_1(E) & v1_funct_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,B) -> (k5_funcop_1(F,D,G) = E -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4108 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k5_funcop_1(E,D,F),C))))))))))))) # label(t91_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4109 (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) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_2(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]. 23.27/22.39 4110 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (C = k5_funcop_1(D,A,B) & r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4111 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k2_finseq_1(A) = k4_finseq_1(C))))))) # label(t144_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4112 (all A all B (-v1_xboole_0(B) -> ((exists C exists D (m1_subset_1(D,B) & A = k10_finseq_1(C,D) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_finseq_2(B))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4113 (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]. 23.27/22.39 4114 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4115 (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)) -> k1_funct_1(k2_finseq_2(A,C),D) = C))))))))) # label(t71_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4116 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (all H (m2_finseq_1(H,B) -> (k12_finseq_1(B,E) = H & k12_finseq_1(A,D) = G -> k3_funcop_1(F,G,H) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.39 4117 (exists A (m2_finseq_1(A,f2_s1_finseq_2) & f1_s1_finseq_2 = k3_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_2)) -> f3_s1_finseq_2(B) = k1_funct_1(A,B)))))) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4118 (all A (v1_finseq_1(A) & v1_funct_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]. 23.27/22.40 4119 (all A (v4_ordinal2(A) -> (all B k4_finseq_1(k2_finseq_2(A,B)) = k2_finseq_1(A)))) # label(t68_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4120 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_finseq_2(B)) <-> (exists C (k4_finseq_2(C,B) = A & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4121 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & (exists E (k11_finseq_1(C,D,E) = B & m1_subset_1(E,A))))))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4122 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4123 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k7_relat_1(B,k2_finseq_1(A)) = k5_relat_1(k1_finseq_2(A),B))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4124 (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]. 23.27/22.40 4125 (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_2(F,k2_zfmisc_1(B,C),D) & m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_1(F) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k5_funcop_1(F,E,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t141_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4126 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> (all D (v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (r1_xreal_0(A,k3_finseq_1(C)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B)))))))))) # label(t50_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4127 (all A all B k2_relat_1(k10_finseq_1(A,B)) = k2_tarski(A,B)) # label(t147_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4128 (all A k11_finseq_1(A,A,A) = k2_finseq_2(np__3,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4129 (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]. 23.27/22.40 4130 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4131 (all A (v4_ordinal2(A) -> v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(k1_finseq_2(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4132 (all A k9_finseq_1(A) = k2_finseq_2(np__1,A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4133 (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]. 23.27/22.40 4134 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & A = k12_finseq_1(B,C))) <-> r2_hidden(A,a_1_0_finseq_2(B))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4135 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (k9_finseq_1(A) = D -> 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]. 23.27/22.40 4136 (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]. 23.27/22.40 4137 (all A exists B (-v1_xboole_0(B) & m1_finseq_2(B,A))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4138 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4139 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(D,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]. 23.27/22.40 4140 (all A (m2_finseq_1(A,f1_s2_finseq_2) -> (all B (m1_subset_1(B,f1_s2_finseq_2) -> (p1_s2_finseq_2(A) -> p1_s2_finseq_2(k8_finseq_1(f1_s2_finseq_2,A,k12_finseq_1(f1_s2_finseq_2,B)))))))) & p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2)) -> (all A (m2_finseq_1(A,f1_s2_finseq_2) -> p1_s2_finseq_2(A))) # label(s2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4141 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_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]. 23.27/22.40 4142 (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)))) -> C = D))))))))) # label(t139_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4143 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> (all J (v1_funct_1(J) & m2_relset_1(J,k2_zfmisc_1(A,B),C) & v1_funct_2(J,k2_zfmisc_1(A,B),C) -> (all K (m2_finseq_1(K,A) -> (all L (m2_finseq_1(L,B) -> (L = k11_finseq_1(G,H,I) & k11_finseq_1(D,E,F) = K -> k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I)) = k3_funcop_1(J,K,L)))))))))))))))))))))))))) # label(t90_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4144 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (k2_finseq_1(A) = B -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_relat_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4145 (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]. 23.27/22.40 4146 (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]. 23.27/22.40 4147 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)))))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4148 (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]. 23.27/22.40 4149 (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]. 23.27/22.40 4150 (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]. 23.27/22.40 4151 (all A all B (-v1_xboole_0(B) -> ((exists C exists D exists E (k11_finseq_1(C,D,E) = A & m1_subset_1(E,B) & m1_subset_1(D,B) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_2_finseq_2(B))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4152 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C ((exists D (m1_subset_1(D,A) & k10_finseq_1(C,D) = B)) & m1_subset_1(C,A))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4153 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> k6_finseq_1(A) = B)) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4154 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,B) -> (k11_finseq_1(E,F,G) = I -> k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G))))))))))))))))))))) # label(t96_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4155 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4156 (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]. 23.27/22.40 4157 (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]. 23.27/22.40 4158 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_finseq_1(E,C) -> (all F (v1_funct_1(F) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> (k10_finseq_1(A,B) = E -> 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]. 23.27/22.40 4159 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_finseq_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_finseq_1(G) = k3_finseq_1(F) & k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_finseq_1(F) & k3_finseq_1(D) = k3_finseq_1(G)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4160 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> k6_finseq_1(C) = k5_funcop_1(E,D,k6_finseq_1(B)))))))))))) # label(t93_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4161 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (k2_relat_1(D) = k2_finseq_1(A) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B))))))))))) # label(t134_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4162 (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]. 23.27/22.40 4163 (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]. 23.27/22.40 4164 (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)) -> D = C & A = B))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4165 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> k3_funcop_1(D,k6_finseq_1(A),F) = k6_finseq_1(C) & k6_finseq_1(C) = k3_funcop_1(D,E,k6_finseq_1(B)))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4166 (all A (v4_ordinal2(A) -> (all B k2_finseq_2(A,B) = k2_funcop_1(k2_finseq_1(A),B)))) # label(d2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4167 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G))))))))))))))))) # label(t85_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4168 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_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]. 23.27/22.40 4169 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,A) -> (G = k12_finseq_1(A,D) -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k4_funcop_1(F,G,E)))))))))))))))) # label(t100_finseq_2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4170 (all A all B r1_tarski(k5_classes1(k3_xboole_0(A,B)),k3_xboole_0(k5_classes1(A),k5_classes1(B)))) # label(t68_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4171 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r2_hidden(A,k4_classes1(C)) <-> r2_hidden(k4_tarski(A,B),k4_classes1(k1_ordinal1(k1_ordinal1(C))))))) # label(t51_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4172 (all A all B (r2_hidden(A,B) -> r2_hidden(k6_classes1(A),k6_classes1(B)))) # label(t76_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4173 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))))) # label(t28_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4174 (all A all B (v3_ordinal1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k6_classes1(C),B))) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t77_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4175 (all A exists B (k3_classes1(A,B) = k1_classes1(A) & v3_ordinal1(B))) # label(t22_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4176 (all A v1_ordinal1(k5_classes1(A))) # label(t58_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4177 (all A (v3_ordinal1(A) -> k6_classes1(A) = A)) # label(t81_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4178 (all A (v1_ordinal1(A) -> A = k5_classes1(A))) # label(t62_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4179 (all A all B (v3_ordinal1(B) -> k2_xboole_0(k2_xboole_0(a_2_0_classes1(A,B),a_2_1_classes1(A,B)),k3_xboole_0(k1_zfmisc_1(k3_classes1(A,B)),k1_classes1(A))) = k3_classes1(A,k1_ordinal1(B)))) # label(t11_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4180 (all A all B (r1_tarski(A,B) & v1_ordinal1(B) -> r1_tarski(k5_classes1(A),B))) # label(t60_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4181 $T # label(t57_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4182 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_zfmisc_1(A),k1_classes1(B)))) # label(t7_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4183 (all A all B all C all D (v3_ordinal1(D) -> (r1_tarski(A,B) & r2_hidden(B,k3_classes1(C,D)) -> r2_hidden(A,k3_classes1(C,k1_ordinal1(D)))))) # label(t14_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4184 (all A -(v1_ordinal1(A) & (all B (v3_ordinal1(B) -> -r1_tarski(k1_classes1(A),k4_classes1(B)))))) # label(t53_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4185 (all A r2_hidden(A,k1_classes1(A))) # label(t5_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4186 (all A exists B (v3_ordinal1(B) & k1_classes1(A) = k3_classes1(A,B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & k3_classes1(A,C) = k1_classes1(A)))))) # label(t23_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4187 (all A (v2_classes1(A) <-> (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) & (all B -(r1_tarski(B,A) & -r2_hidden(B,A) & -r2_tarski(B,A))) & v1_classes1(A))) # label(d2_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4188 (all A all B all C all D (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v3_ordinal1(D) -> (r2_hidden(A,a_3_0_classes1(B,C,D)) <-> (exists E (E = A & (exists F (m1_subset_1(F,k1_classes1(B)) & r2_hidden(F,k1_funct_1(C,D)) & r1_tarski(E,F))) & m1_subset_1(E,k1_classes1(B))))))) # label(fraenkel_a_3_0_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4189 (all A (k6_classes1(A) = k1_xboole_0 <-> A = k1_xboole_0)) # label(t79_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4190 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k2_xboole_0(A,B)))) # label(t55_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4191 (all A all B -(r2_tarski(A,k1_classes1(B)) & r2_hidden(A,k1_classes1(B)))) # label(t29_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4192 (all A all B ((all C (r1_tarski(A,C) & v1_ordinal1(C) -> r1_tarski(B,C))) & v1_ordinal1(B) & r1_tarski(A,B) -> k5_classes1(A) = B)) # label(t61_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4193 (all A all B all C (v3_ordinal1(C) -> (v4_ordinal1(C) -> k1_xboole_0 = C | ((exists D (v3_ordinal1(D) & r2_hidden(D,C) & r2_hidden(B,k3_classes1(A,D)))) <-> r2_hidden(B,k3_classes1(A,C)))))) # label(t16_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4194 (all A all B all C (r2_hidden(C,k1_classes1(A)) & r2_hidden(B,k1_classes1(A)) -> r2_hidden(k4_tarski(B,C),k1_classes1(A)))) # label(t31_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4195 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k6_classes1(A),k6_classes1(B)))) # label(t75_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4196 (all A all B all C (v3_ordinal1(C) -> ((exists D (m1_subset_1(D,k1_classes1(B)) & (exists E (r1_tarski(D,E) & r2_hidden(E,k3_classes1(B,C)) & m1_subset_1(E,k1_classes1(B)))) & D = A)) <-> r2_hidden(A,a_2_0_classes1(B,C))))) # label(fraenkel_a_2_0_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4197 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k3_classes1(B,k1_ordinal1(C))) <-> -((all D -(r2_hidden(D,k3_classes1(B,C)) & (r1_tarski(A,D) | k1_zfmisc_1(D) = A))) & -(r1_tarski(A,k3_classes1(B,C)) & r2_hidden(A,k1_classes1(B))))))) # label(t13_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4198 $T # label(dt_k2_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4199 (all A all B (r1_classes1(A,B) & (all C (r1_classes1(A,C) -> r1_tarski(B,C))) <-> B = k1_classes1(A))) # label(d4_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4200 (all A (v1_classes1(A) & (all B (r2_hidden(B,A) -> r2_hidden(k1_zfmisc_1(B),A))) & (all B (r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A)) -> r2_hidden(B,A))) <-> v2_classes1(A))) # label(t2_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4201 (all A all B all C (r2_hidden(B,k1_classes1(A)) & r2_hidden(C,k1_classes1(A)) -> r2_hidden(k2_tarski(B,C),k1_classes1(A)) & r2_hidden(k1_tarski(B),k1_classes1(A)))) # label(t30_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4202 (all A all B all C (r1_tarski(C,k1_classes1(B)) & r1_tarski(A,k1_classes1(B)) -> r1_tarski(k2_zfmisc_1(A,C),k1_classes1(B)))) # label(t32_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4203 $T # label(t1_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4204 (all A all B (v3_ordinal1(B) -> (v4_ordinal1(B) -> k1_xboole_0 = B | a_2_2_classes1(A,B) = k3_classes1(A,B)))) # label(t12_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4205 (all A all B all C (r2_hidden(A,k1_classes1(B)) & r1_tarski(C,A) -> r2_hidden(C,k1_classes1(B)))) # label(t6_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4206 $T # label(dt_k1_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4207 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k4_classes1(A),k4_classes1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4208 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(B,k4_classes1(C)) & r1_tarski(A,B) -> r2_hidden(A,k4_classes1(C))))) # label(t47_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4209 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k4_classes1(C)) & r2_hidden(B,k4_classes1(C)) <-> r2_hidden(k2_tarski(A,B),k4_classes1(k1_ordinal1(C)))))) # label(t50_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4210 (all A v3_ordinal1(k6_classes1(A))) # label(dt_k6_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4211 (all A all B all C all D (v3_ordinal1(D) -> (r2_hidden(A,k3_classes1(B,D)) & v4_ordinal1(D) -> -r1_tarski(C,A) & C != k1_zfmisc_1(A) | r2_hidden(C,k3_classes1(B,D)) | D = k1_xboole_0))) # label(t17_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4212 (all A all B -(r2_hidden(A,k1_classes1(B)) & (all C (v3_ordinal1(C) -> -(-r2_hidden(A,k3_classes1(B,C)) & r2_hidden(A,k3_classes1(B,k1_ordinal1(C)))))) & A != B)) # label(t24_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4213 (all A all B (v1_ordinal1(A) & v1_ordinal1(B) -> v1_ordinal1(k3_xboole_0(A,B)))) # label(t56_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4214 (all A all B (v3_ordinal1(B) -> (all C (C = k2_classes1(A,B) <-> (exists D (v1_funct_1(D) & v5_ordinal1(D) & k1_relat_1(D) = k1_ordinal1(B) & k1_funct_1(D,k1_xboole_0) = k1_tarski(A) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k2_xboole_0(k2_xboole_0(a_3_0_classes1(A,D,E),a_3_1_classes1(A,D,E)),k3_xboole_0(k1_zfmisc_1(k1_funct_1(D,E)),k1_classes1(A)))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> E = k1_xboole_0 | k1_funct_1(D,E) = k3_xboole_0(k3_tarski(k2_relat_1(k2_ordinal1(D,E))),k1_classes1(A))))) & k1_ordinal2(D) = C & v1_relat_1(D))))))) # label(d5_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4215 (all A all B (r2_hidden(A,B) & v2_classes1(B) <-> r1_classes1(A,B))) # label(d3_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4216 (all A all B (B = k5_classes1(A) <-> (all C (r2_hidden(C,B) <-> (exists D ((exists E (m2_subset_1(E,k1_numbers,k5_numbers) & k1_funct_1(D,np__0) = A & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> k1_funct_1(D,k1_nat_1(F,np__1)) = k3_tarski(k1_funct_1(D,F)))) & k1_relat_1(D) = k5_numbers & r2_hidden(C,k1_funct_1(D,E)))) & v1_funct_1(D) & v1_relat_1(D))))))) # label(d7_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4217 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) <-> r2_hidden(k1_tarski(A),k4_classes1(k1_ordinal1(B)))))) # label(t49_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4218 (all A -v1_xboole_0(k1_classes1(A))) # label(fc1_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4219 (all A (v3_ordinal1(A) -> r1_tarski(k3_tarski(k4_classes1(A)),k4_classes1(A)))) # label(t40_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4220 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k1_xboole_0 != B -> v1_ordinal1(k3_classes1(A,B))))))) # label(t25_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4221 (all A (v1_ordinal1(A) -> v1_ordinal1(k1_classes1(A)))) # label(t27_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4222 (all A (v1_ordinal1(A) -> r1_tarski(k3_tarski(A),A))) # label(t54_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4223 (all A all B all C all D (v1_relat_1(C) & v5_ordinal1(C) & v3_ordinal1(D) & v1_funct_1(C) -> (r2_hidden(A,a_3_1_classes1(B,C,D)) <-> (exists E (m1_subset_1(E,k1_classes1(B)) & r2_hidden(E,k1_funct_1(C,D)) & A = k1_zfmisc_1(E)))))) # label(fraenkel_a_3_1_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4224 (all A all B (v3_ordinal1(B) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,k1_ordinal1(B))))) # label(t18_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4225 (all A all B (v3_ordinal1(B) -> m1_subset_1(k3_classes1(A,B),k1_zfmisc_1(k1_classes1(A))))) # label(dt_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4226 (all A (v3_ordinal1(A) -> A = k6_classes1(k4_classes1(A)))) # label(t72_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4227 $T # label(t4_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4228 (all A all B (v3_ordinal1(B) -> (r1_tarski(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B))) <-> r1_tarski(A,k4_classes1(B))))) # label(t46_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4229 (all A all B (v3_ordinal1(B) -> -(k6_classes1(A) = k1_ordinal1(B) & (all C -(k6_classes1(C) = B & r2_hidden(C,A)))))) # label(t80_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4230 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r1_tarski(A,k4_classes1(B))))) # label(t38_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4231 (all A exists B (k3_classes1(A,B) = k3_classes1(A,k1_ordinal1(B)) & v3_ordinal1(B))) # label(t20_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4232 $T # label(dt_k4_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4233 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k4_classes1(A),k4_classes1(B))))))) # label(t42_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4234 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_classes1(A),k5_classes1(B)))) # label(t65_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4235 $T # label(t3_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4236 (all A all B all C (v3_ordinal1(C) -> ((exists D (m1_subset_1(D,k1_classes1(B)) & (exists E (r2_hidden(E,C) & r2_hidden(D,k3_classes1(B,E)) & v3_ordinal1(E))) & D = A)) <-> r2_hidden(A,a_2_2_classes1(B,C))))) # label(fraenkel_a_2_2_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4237 (all A all B (v3_ordinal1(B) -> (k3_classes1(A,k1_ordinal1(B)) = k3_classes1(A,B) -> k1_classes1(A) = k3_classes1(A,B)))) # label(t21_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4238 (all A (v3_ordinal1(A) -> A = k5_classes1(A))) # label(t64_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4239 (all A (v3_ordinal1(A) -> (all B (r2_hidden(B,k4_classes1(A)) -> r2_hidden(k1_card_1(B),k1_card_1(k4_classes1(A))) & -r2_tarski(B,k4_classes1(A)))))) # label(t45_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4240 (all A all B (v3_ordinal1(B) -> (v1_ordinal1(A) & k3_xboole_0(k4_classes1(k1_ordinal1(B)),k1_classes1(A)) = k3_xboole_0(k4_classes1(B),k1_classes1(A)) -> r1_tarski(k1_classes1(A),k4_classes1(B))))) # label(t52_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4241 $T # label(dt_k5_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4242 $T # label(t70_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4243 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) <-> r2_hidden(k6_classes1(A),B)))) # label(t74_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4244 (all A (v3_ordinal1(A) -> (all B (B = k4_classes1(A) <-> (exists C ((all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_zfmisc_1(k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | k3_tarski(k2_relat_1(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = k1_xboole_0 & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) # label(d6_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4245 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> (all B ((exists C (v3_ordinal1(C) & r2_hidden(C,A) & r2_hidden(B,k4_classes1(C)))) <-> r2_hidden(B,k4_classes1(A)))) | A = k1_xboole_0))) # label(t35_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4246 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(k1_ordinal1(B))) <-> r1_tarski(A,k4_classes1(B))))) # label(t36_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4247 (all A (v3_ordinal1(A) -> k1_zfmisc_1(k4_classes1(A)) = k4_classes1(k1_ordinal1(A)))) # label(t34_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4248 (all A exists B (v3_ordinal1(B) & r1_tarski(A,k4_classes1(B)))) # label(t69_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4249 (all A (v3_ordinal1(A) -> r1_tarski(A,k4_classes1(A)))) # label(t44_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4250 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,k4_classes1(B)) -> r2_hidden(k3_tarski(A),k4_classes1(B))))) # label(t41_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4251 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(t37_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4252 (all A (v3_ordinal1(A) -> r1_tarski(k4_classes1(A),k4_classes1(k1_ordinal1(A))))) # label(t39_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4253 (all A all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(B,C) -> r1_tarski(k3_classes1(A,B),k3_classes1(A,C))))))) # label(t19_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4254 (all A r1_tarski(A,k5_classes1(A))) # label(t59_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4255 (all A all B k5_classes1(k2_xboole_0(A,B)) = k2_xboole_0(k5_classes1(A),k5_classes1(B))) # label(t67_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4256 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,k4_classes1(B)) <-> r1_ordinal1(k6_classes1(A),B)))) # label(t73_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4257 (all A all B all C (v3_ordinal1(C) -> (r2_hidden(A,k3_classes1(B,C)) -> r2_hidden(k1_zfmisc_1(A),k3_classes1(B,k1_ordinal1(C)))))) # label(t15_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4258 (all A all B (r1_tarski(A,k1_classes1(B)) & r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))) # label(t9_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4259 (all A all B (v3_ordinal1(B) -> (r2_hidden(k1_zfmisc_1(A),k4_classes1(k1_ordinal1(B))) <-> r2_hidden(A,k4_classes1(B))))) # label(t48_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4260 (all A k1_ordinal1(k6_classes1(A)) = k6_classes1(k1_zfmisc_1(A))) # label(t71_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4261 (all A all B (v3_ordinal1(B) -> (r1_ordinal1(B,k6_classes1(A)) <-> (all C (v3_ordinal1(C) -> -(r2_hidden(C,B) & (all D -(r2_hidden(D,A) & r1_ordinal1(C,k6_classes1(D)))))))))) # label(t78_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4262 (all A k5_classes1(k5_classes1(A)) = k5_classes1(A)) # label(t66_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4263 (all A (v1_classes1(A) <-> (all B all C (r1_tarski(C,B) & r2_hidden(B,A) -> r2_hidden(C,A))))) # label(d1_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4264 (all A all B all C (v3_ordinal1(C) -> ((exists D (m1_subset_1(D,k1_classes1(B)) & A = k1_zfmisc_1(D) & r2_hidden(D,k3_classes1(B,C)))) <-> r2_hidden(A,a_2_1_classes1(B,C))))) # label(fraenkel_a_2_1_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4265 (all A k1_tarski(A) = k3_classes1(A,k1_xboole_0)) # label(t10_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4266 (all A all B -(r1_tarski(A,k1_classes1(B)) & -r2_hidden(A,k1_classes1(B)) & -r2_tarski(A,k1_classes1(B)))) # label(t8_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4267 (all A (v4_ordinal1(k6_classes1(k1_classes1(A))) & k1_xboole_0 != k6_classes1(k1_classes1(A)))) # label(t82_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4268 (all A all B (v3_ordinal1(B) -> k3_classes1(A,B) = k2_classes1(A,B))) # label(redefinition_k3_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4269 (all A (r2_hidden(k3_classes1(A,k1_xboole_0),k3_classes1(A,k4_ordinal2)) & k3_classes1(A,k1_xboole_0) != k3_classes1(A,k4_ordinal2))) # label(t26_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4270 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(A,k4_classes1(C)) -> r1_ordinal1(B,C)))) & r1_tarski(A,k4_classes1(B)) <-> k6_classes1(A) = B))) # label(d8_classes1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4271 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4272 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4273 (all A all B all C (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) & v1_setfam_1(B) -> v1_fraenkel(k4_card_3(C)) & -v1_xboole_0(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4274 (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]. 23.27/22.40 4275 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & D = k1_funct_1(E,A) & v1_funct_1(E) & v1_relat_1(E))))) <-> k5_card_3(A,B) = C)) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4276 (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]. 23.27/22.40 4277 (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]. 23.27/22.40 4278 (all A all B k1_card_3(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_card_1(B))) # label(t10_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4279 (all A -(v6_ordinal1(A) & (all B -((all C -(r1_tarski(C,B) & (all D -((all E (r2_hidden(E,C) -> r1_tarski(D,E))) & r2_hidden(D,C))) & k1_xboole_0 != C)) & k3_tarski(A) = k3_tarski(B) & r1_tarski(B,A))))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4280 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s4_card_3 & (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_relat_1(A))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4281 (all A all B all C k5_card_3(C,k2_xboole_0(A,B)) = k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B))) # label(t27_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4282 (all A all B all C (p1_s3_card_3(B,C) & p1_s3_card_3(A,B) -> p1_s3_card_3(A,C))) & (all A all B (p1_s3_card_3(A,B) | p1_s3_card_3(B,A))) & f1_s3_card_3 != k1_xboole_0 -> (exists A ((all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))) & r2_hidden(A,f1_s3_card_3))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4283 (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)) -> r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B)) | A = B))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4284 (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]. 23.27/22.40 4285 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4286 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4287 (all A all B k1_funct_2(A,B) = k4_card_3(k2_funcop_1(A,B))) # label(t20_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4288 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4289 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> (all B (v1_card_3(B) & v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t46_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4290 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(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]. 23.27/22.40 4291 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4292 (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]. 23.27/22.40 4293 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_card_3(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(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]. 23.27/22.40 4294 (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]. 23.27/22.40 4295 (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]. 23.27/22.40 4296 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4297 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (k7_card_3(A) = np__0 <-> r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4298 (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]. 23.27/22.40 4299 (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]. 23.27/22.40 4300 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> -(r2_hidden(A,k3_card_3(k2_card_3(B))) & (all C all D A != k4_tarski(C,D))))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4301 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k4_card_3(B)) <-> (all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(t18_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4302 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> v1_fraenkel(k4_card_3(A)) & -v1_xboole_0(k4_card_3(A)))) # label(fc5_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4303 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) & v1_relat_1(k1_card_3(A)))) # label(dt_k1_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4304 (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]. 23.27/22.40 4305 (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]. 23.27/22.40 4306 (all A all B (k1_xboole_0 != A -> B = k3_card_3(k2_funcop_1(A,B)))) # label(t16_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.40 4307 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r2_hidden(np__0,k2_relat_1(B)) | r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t47_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4308 (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]. 23.27/22.41 4309 (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]. 23.27/22.41 4310 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k4_card_3(A)))) # label(fc3_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4311 (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]. 23.27/22.41 4312 (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]. 23.27/22.41 4313 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k5_card_3(A,k2_tarski(B,C)))))) # label(t26_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4314 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))))) # label(t54_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4315 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4316 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_card_3(A),k2_card_3(B))))))) # label(t34_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4317 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4318 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_card_3(B) & v1_funct_1(B) -> (B = k1_card_3(A) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4319 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> k1_card_1(k3_card_3(k2_card_3(A))) = k6_card_3(A))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4320 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(A,B)))))) # label(t39_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4321 (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]. 23.27/22.41 4322 (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]. 23.27/22.41 4323 (all A k1_xboole_0 = k5_card_3(A,k1_xboole_0)) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4324 (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]. 23.27/22.41 4325 (all A (v1_card_1(A) -> (all B k6_card_3(k2_funcop_1(k1_tarski(B),A)) = A))) # label(t50_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4326 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4327 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4328 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_card_3(A,k4_card_3(B)) | k4_card_3(B) = k1_xboole_0))) # label(t22_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4329 (exists A (v1_funct_1(A) & f1_s1_card_3 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_card_3) -> k1_funct_1(A,B) = f2_s1_card_3(B))) & v1_card_3(A) & v1_relat_1(A))) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4330 (all A all B all C (p1_s2_card_3(A,B) & p1_s2_card_3(B,C) -> p1_s2_card_3(A,C))) & (all A all B (p1_s2_card_3(A,B) & p1_s2_card_3(B,A) -> B = A)) & k1_xboole_0 != f1_s2_card_3 -> (exists A ((all B -(p1_s2_card_3(B,A) & A != B & r2_hidden(B,f1_s2_card_3))) & r2_hidden(A,f1_s2_card_3))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4331 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k2_card_3(A) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4332 (all A all B k3_card_3(k2_card_3(k2_funcop_1(A,B))) = k2_zfmisc_1(B,A)) # label(t36_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4333 (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]. 23.27/22.41 4334 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4335 (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]. 23.27/22.41 4336 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_card_3(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t43_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4337 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k1_card_1(k4_card_3(A)) = k7_card_3(A))) # label(d8_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4338 (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]. 23.27/22.41 4339 (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]. 23.27/22.41 4340 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4341 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4342 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4343 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4344 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k4_card_3(A) <-> (all C (r2_hidden(C,B) <-> (exists D ((all E (r2_hidden(E,k1_relat_1(A)) -> r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)))) & k1_relat_1(A) = k1_relat_1(D) & C = D & v1_funct_1(D) & v1_relat_1(D))))))))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4345 (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]. 23.27/22.41 4346 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k3_card_3(k2_card_3(B))) <-> r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A))) & A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) & r2_hidden(k2_mcart_1(A),k1_relat_1(B))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4347 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_card_3(B) & v1_funct_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]. 23.27/22.41 4348 (all A all B B = k3_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t17_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4349 (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]. 23.27/22.41 4350 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> k1_xboole_0 = k4_card_3(A)))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4351 (all A all B (v1_card_1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4352 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k1_card_1(k1_funct_1(k2_card_3(A),B)))))) # label(t40_card_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4353 (all A all B (v2_classes1(A) -> r1_tarski(k1_funct_2(B,A),A) | -(r2_hidden(B,A) & r1_tarski(B,A)) & -(r2_hidden(k1_card_1(B),k1_card_1(A)) & r1_tarski(B,A)) & -(r2_hidden(B,A) & v1_ordinal1(A)))) # label(t23_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4354 (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]. 23.27/22.41 4355 (all A (v1_ordinal1(A) -> k1_classes1(A) = k4_classes1(k1_card_1(k1_classes1(A))))) # label(t46_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4356 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))) & r2_hidden(k4_classes1(A),k1_classes1(B)))))) # label(t27_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4357 (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]. 23.27/22.41 4358 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (v4_ordinal1(k1_relat_1(A)) & (all B (v3_ordinal1(B) -> (r2_hidden(B,k1_relat_1(A)) -> k4_classes1(B) = k1_funct_1(A,B)))) -> k3_card_3(A) = k4_classes1(k1_relat_1(A))))) # label(t25_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4359 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4360 (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(k12_classes2(A,B,C),A))) # label(dt_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4361 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k11_classes2(A,B,C),A))) # label(dt_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4362 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,B) -> r1_tarski(A,B) & r2_hidden(k1_ordinal1(A),B))))) # label(t6_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4363 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k16_classes2(B) = k16_classes2(A) -> B = A))))) # label(t81_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4364 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k8_classes2(A,C,B) = k8_classes2(A,B,C))) # label(commutativity_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4365 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_tarski(k16_classes2(A),k16_classes2(B))))))) # label(t82_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4366 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc2_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4367 (exists A (-v1_xboole_0(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) & v1_ordinal1(A))) # label(rc1_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4368 (all A all B (r2_hidden(B,A) & v1_classes1(A) -> r2_hidden(k1_card_1(B),k1_card_1(A)) & -r2_wellord2(B,A))) # label(t1_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4369 (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]. 23.27/22.41 4370 (all A (v1_classes2(k15_classes2(A)) & -v1_xboole_0(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4371 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k2_ordinal2(B)) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(B)))))) # label(t33_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4372 (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]. 23.27/22.41 4373 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k5_classes2(A,B,C) = k2_tarski(B,C))) # label(redefinition_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4374 (all A (v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc1_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4375 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc3_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4376 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k1_classes2(A,B),A))) # label(dt_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4377 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_classes2(A,B) = k1_setfam_1(B))) # label(redefinition_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4378 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4379 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc4_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4380 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k2_ordinal2(B)) -> r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(B)) & r2_hidden(k4_classes1(A),B))))) # label(t26_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4381 (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]. 23.27/22.41 4382 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> r2_hidden(k1_setfam_1(A),B) & r2_hidden(k3_tarski(A),B) & r2_hidden(k1_zfmisc_1(A),B)))) # label(t65_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4383 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)) & k1_xboole_0 != k1_card_1(A) & k1_card_1(A) != np__0 | A = k1_xboole_0)) # label(t21_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4384 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k4_tarski(B,C) = k6_classes2(A,B,C))) # label(redefinition_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4385 (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]. 23.27/22.41 4386 (all A all B (r2_hidden(A,k1_classes1(B)) & v1_ordinal1(A) -> r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t44_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4387 (all A (v2_classes1(A) -> k1_card_1(k4_classes1(k1_card_1(A))) = k1_card_1(A))) # label(t35_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4388 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k2_classes2(A,B) = k1_zfmisc_1(B))) # label(redefinition_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4389 (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]. 23.27/22.41 4390 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4391 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4392 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k4_xboole_0(B,C) = k9_classes2(A,B,C))) # label(redefinition_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4393 (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]. 23.27/22.41 4394 (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]. 23.27/22.41 4395 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4396 (all A all B all C (v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k12_classes2(A,B,C) = k1_funct_2(B,C))) # label(redefinition_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4397 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4398 (all A (v1_ordinal1(A) -> v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc6_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4399 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k1_classes2(A,B) = k1_tarski(B))) # label(redefinition_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4400 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r3_xboole_0(A,B))))) # label(t58_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4401 (all A (v1_classes2(A) -> v2_classes1(A) & v1_classes1(A) & v1_ordinal1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4402 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k3_xboole_0(A,B),C) & r2_hidden(k5_xboole_0(A,B),C) & r2_hidden(k4_xboole_0(A,B),C) & r2_hidden(k2_xboole_0(A,B),C)))) # label(t66_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4403 (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(k9_classes2(A,B,C),A))) # label(dt_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4404 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k7_classes2(A,B,C),A))) # label(dt_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4405 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k4_classes2(A,B),A))) # label(dt_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4406 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r1_tarski(k13_classes2,A) & r1_tarski(k16_classes2(k1_xboole_0),A) & r1_tarski(k1_classes1(k1_xboole_0),A))) # label(t79_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4407 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4408 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> (v4_ordinal1(A) & (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k16_classes2(C)))) & k1_relat_1(B) = A -> k16_classes2(A) = k15_classes2(k3_card_3(B)) | k1_xboole_0 = A))))) # label(t78_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4409 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,B) -> r2_hidden(k1_tarski(A),B)))) # label(t63_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4410 (all A (v4_ordinal1(k1_card_1(k1_classes1(A))) & k1_card_1(k1_classes1(A)) != k1_xboole_0 & k1_card_1(k1_classes1(A)) != np__0)) # label(t22_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4411 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k5_classes2(A,B,C) = k5_classes2(A,C,B))) # label(commutativity_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4412 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4413 (all A (v1_ordinal1(A) & v2_classes1(A) -> k4_classes1(k1_card_1(A)) = A)) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4414 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4415 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4416 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> -v1_xboole_0(k2_classes2(A,B)) & m1_subset_1(k2_classes2(A,B),A))) # label(dt_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4417 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r2_hidden(B,A) | r1_tarski(A,B))))) # label(t57_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4418 (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]. 23.27/22.41 4419 (all A k1_card_1(k4_classes1(k1_card_1(k1_classes1(A)))) = k1_card_1(k1_classes1(A))) # label(t36_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4420 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k6_classes2(A,B,C),A))) # label(dt_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4421 (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]. 23.27/22.41 4422 (all A all B (r2_hidden(B,A) & v1_ordinal1(B) & v1_classes1(A) -> r1_tarski(B,A))) # label(t8_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4423 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k8_classes2(A,B,B) = B)) # label(idempotence_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4424 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4425 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k7_classes2(A,C,B) = k7_classes2(A,B,C))) # label(commutativity_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4426 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k8_classes2(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4427 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k10_classes2(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4428 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k8_classes2(A,B,C),A))) # label(dt_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4429 (all A (v1_classes2(A) <-> v2_classes1(A) & v1_ordinal1(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4430 (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]. 23.27/22.41 4431 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> -v1_xboole_0(k2_xboole_0(A,B)) & v1_classes2(k2_xboole_0(A,B)) & v1_classes2(k3_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)))))) # label(t61_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4432 (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]. 23.27/22.41 4433 (all A all B all C (v1_classes2(C) & -v1_xboole_0(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]. 23.27/22.41 4434 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_tarski(B) = k3_classes2(A,B))) # label(redefinition_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4435 (all A (v1_classes2(A) & -v1_xboole_0(A) -> A = k4_classes1(k2_ordinal2(A)))) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4436 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4437 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k10_classes2(A,C,B) = k10_classes2(A,B,C))) # label(commutativity_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4438 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k5_classes2(A,B,C),A))) # label(dt_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4439 (all A all B (r2_hidden(A,k1_classes1(B)) & v1_ordinal1(A) -> r1_tarski(A,k1_classes1(B)))) # label(t9_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4440 (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]. 23.27/22.41 4441 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4442 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v4_ordinal1(k2_ordinal2(A)) & k2_ordinal2(A) != k1_xboole_0)) # label(t55_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4443 (all A (v3_ordinal1(A) -> k1_classes1(k16_classes2(A)) = k16_classes2(k1_ordinal1(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4444 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_ordinal1(k2_ordinal2(A)) & v3_ordinal1(k2_ordinal2(A)) & v2_ordinal1(k2_ordinal2(A)))) # label(fc2_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4445 (all A all 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))) & -(v1_ordinal1(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]. 23.27/22.41 4446 (all A (v3_ordinal1(A) -> (all B -((all C -(A = k6_classes1(C) & r2_hidden(C,B))) & r2_hidden(A,k6_classes1(B)) & v1_ordinal1(B))))) # label(t41_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4447 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4448 (all A (v2_classes1(A) -> k2_ordinal2(A) = k1_card_1(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4449 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (k15_classes2(A) = B <-> 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]. 23.27/22.41 4450 (all A all B (v2_classes1(A) & v1_ordinal1(A) & r2_hidden(B,A) -> r2_hidden(k6_classes1(B),A))) # label(t30_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4451 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4452 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> -(-r2_hidden(B,A) & B != A & -r2_hidden(A,B)))))) # label(t56_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4453 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4454 (all A all B (r2_hidden(B,A) & v1_ordinal1(B) & v2_classes1(A) -> r2_hidden(B,k4_classes1(k1_card_1(A))))) # label(t43_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4455 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k7_classes2(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4456 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4457 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4458 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4459 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_classes1(A)) & v1_classes2(k1_classes1(A)))) # label(t52_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4460 (all A all B all C (r2_hidden(C,A) & r2_hidden(B,A) & v2_classes1(A) -> r2_hidden(k4_tarski(B,C),A))) # label(t4_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4461 (all A all B -(-r2_wellord2(B,k4_classes1(k1_card_1(A))) & -r2_hidden(B,k4_classes1(k1_card_1(A))) & r1_tarski(B,k4_classes1(k1_card_1(A))) & v2_classes1(A))) # label(t37_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4462 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4463 (all A (v3_ordinal1(A) -> v1_classes2(k16_classes2(A)) & v2_classes1(k16_classes2(A)) & v1_classes1(k16_classes2(A)) & -v1_xboole_0(k16_classes2(A)) & v1_ordinal1(k16_classes2(A)))) # label(fc8_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4464 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4465 (all A all B -(-r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))) & -r2_wellord2(A,k4_classes1(k1_card_1(k1_classes1(B)))) & r1_tarski(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t38_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4466 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4467 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k10_classes2(A,B,C),A))) # label(dt_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4468 (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]. 23.27/22.41 4469 (all A all B (r2_hidden(B,A) & v2_classes1(A) -> r1_tarski(k1_classes1(B),A))) # label(t5_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4470 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k7_classes2(A,B,B) = B)) # label(idempotence_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4471 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k16_classes2(A),k16_classes2(B)) <-> r2_hidden(A,B)))))) # label(t80_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4472 (all A all B all C (r2_hidden(B,A) & r2_hidden(C,A) & v2_classes1(A) -> r2_hidden(k2_tarski(B,C),A) & r2_hidden(k1_tarski(B),A))) # label(t3_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4473 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k2_zfmisc_1(B,C) = k11_classes2(A,B,C))) # label(redefinition_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4474 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_ordinal1(A),k1_classes1(B)) & r1_tarski(A,k1_classes1(B)))))) # label(t7_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4475 (all A k1_card_1(k1_classes1(A)) = k2_ordinal2(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4476 (all A (v1_ordinal1(A) & v2_classes1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4477 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & k1_funct_1(C,k1_xboole_0) = k13_classes2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k1_classes1(k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | k15_classes2(k3_card_3(k2_ordinal1(C,D))) = k1_funct_1(C,D)))) & v5_ordinal1(C) & v1_funct_1(C))) <-> B = k16_classes2(A))))) # label(d5_classes2) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4478 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k2_finseq_3(A,B)),k2_relat_1(B)))))) # label(t115_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4479 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (-r2_hidden(B,k2_relat_1(A)) <-> k1_finseq_3(A,k1_tarski(B)) = A)))) # label(t77_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4480 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k2_relat_1(A)) & v2_funct_1(A) -> k6_xcmplx_0(k3_finseq_1(A),np__1) = k3_finseq_1(k1_finseq_3(A,k1_tarski(B))))))) # label(t97_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4481 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v4_ordinal2(A) -> v1_funct_1(k2_finseq_3(A,B)) & v1_finseq_1(k2_finseq_3(A,B)) & v1_relat_1(k2_finseq_3(A,B)))) # label(dt_k2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4482 (all A (v4_ordinal2(A) -> (all B all C (m2_finseq_1(C,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(D,A) -> k1_funct_1(k16_finseq_1(B,C,A),D) = k1_funct_1(C,D)))))))) # label(t121_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4483 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> k1_finseq_3(k10_finseq_1(A,B),C) = k1_xboole_0)) # label(t84_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4484 (all A (v4_ordinal2(A) -> k1_finseq_2(A) = k14_finseq_1(k2_finseq_1(A)))) # label(t54_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4485 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (r1_xboole_0(B,k2_relat_1(A)) <-> k1_finseq_3(A,B) = A)))) # label(t76_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4486 $T # label(t37_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4487 (all A k1_finseq_3(k1_xboole_0,A) = k1_xboole_0) # label(t81_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4488 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(B,k3_finseq_1(A)) & r1_xreal_0(np__1,B) <-> r2_hidden(B,k4_finseq_1(A))))))) # label(t27_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4489 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (B = k7_relat_1(A,k2_finseq_1(C)) & k3_finseq_1(A) = k2_xcmplx_0(C,D) -> C = k3_finseq_1(B)))))))))) # label(t59_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4490 (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) -> (k2_xcmplx_0(C,np__1) = k3_finseq_1(A) & k7_relat_1(A,k2_finseq_1(C)) = B -> k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,np__1)))) = A))))))) # label(t61_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4491 (all A all B (v2_funct_1(k10_finseq_1(A,B)) <-> B != A)) # label(t103_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4492 (all A (v4_ordinal2(A) -> (k1_xboole_0 = k2_finseq_1(A) <-> -r2_hidden(A,k2_finseq_1(A))))) # label(t7_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4493 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B r1_tarski(k4_finseq_1(k1_finseq_3(A,B)),k4_finseq_1(A))))) # label(t70_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4494 (all A all B all C (B != A & C != A & C != B <-> v2_funct_1(k11_finseq_1(A,B,C)))) # label(t104_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4495 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (r2_hidden(A,k4_finseq_1(B)) -> k1_funct_1(B,A) = k1_funct_1(k7_finseq_1(k9_finseq_1(C),B),k2_xcmplx_0(A,np__1)))))))) # label(t112_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4496 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k2_relat_1(B)) & v2_funct_1(B) & v2_funct_1(A) <-> v2_funct_1(k7_finseq_1(A,B))))))) # label(t98_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4497 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C (v4_ordinal2(C) -> (k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) = C -> k4_finseq_1(k1_finseq_3(A,B)) = k2_finseq_1(C)))))) # label(t69_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4498 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(B,A) <-> k1_finseq_2(B) = k7_relat_1(k1_finseq_2(A),k2_finseq_1(B))))))) # label(t57_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4499 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k2_xcmplx_0(A,B),k2_finseq_1(A)) -> B = np__0))))) # label(t11_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4500 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(v2_funct_1(A) & k2_tarski(B,C) = k2_relat_1(A) & C != B & A != k10_finseq_1(C,B) & k10_finseq_1(B,C) != A)))) # label(t108_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4501 $T # label(t8_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4502 (all A all B (v4_ordinal2(B) -> (k1_tarski(A) = k2_finseq_1(B) -> A = np__1 & B = np__1))) # label(t22_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4503 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(B),k1_tarski(A))),B) = k2_finseq_3(A,B))))) # label(d2_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4504 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(-v1_xboole_0(B) & (all C (m1_subset_1(C,A) -> (all D (m2_finseq_1(D,A) -> -(C = k1_funct_1(B,np__1) & B = k8_finseq_1(A,k12_finseq_1(A,C),D))))))))))) # label(t111_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4505 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> k1_funct_1(A,k1_nat_1(k3_finseq_1(B),D)) = k1_funct_1(C,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(A,D) = k1_funct_1(B,D)))) & k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) = k3_finseq_1(A) -> A = k7_finseq_1(B,C)))))))) # label(t43_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4506 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(B,k4_finseq_1(A)) & k3_finseq_1(A) = k2_xcmplx_0(C,np__1) -> C = k3_finseq_1(k2_finseq_3(B,A))))))))) # label(t118_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4507 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(k2_xcmplx_0(A,B)) -> B = np__0))))) # label(t18_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4508 (all A (v4_ordinal2(A) -> r1_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t15_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4509 $T # label(t101_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4510 (all A all B all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (r1_tarski(B,k2_finseq_1(D)) & r1_tarski(A,k2_finseq_1(C)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> -(r1_xreal_0(F,E) & r2_hidden(F,B) & r2_hidden(E,A)))))) <-> k8_finseq_1(k5_numbers,k14_finseq_1(A),k14_finseq_1(B)) = k14_finseq_1(k2_xboole_0(A,B)))))))) # label(t48_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4511 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (k2_relat_1(A) = k2_relat_1(k1_finseq_3(A,B)) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t74_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4512 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k7_relat_1(k1_finseq_2(k2_xcmplx_0(A,B)),k2_finseq_1(A)) = k1_finseq_2(A))))) # label(t56_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4513 (all A (v4_ordinal2(A) -> k3_finseq_1(k14_finseq_1(k2_finseq_1(A))) = A)) # label(t52_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4514 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r3_xboole_0(k2_finseq_1(A),k2_finseq_1(B)))))) # label(t20_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4515 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B)) <-> r1_tarski(k4_finseq_1(A),k4_finseq_1(B))))))) # label(t32_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4516 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> -(-r1_xreal_0(B,A) & k10_finseq_1(A,B) != k14_finseq_1(k2_tarski(A,B)) & -r1_xreal_0(A,np__0)))))) # label(t51_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4517 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(k7_relat_1(A,B)) & v1_finseq_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)) <-> (exists C (k2_finseq_1(C) = k3_xboole_0(B,k4_finseq_1(A)) & m2_subset_1(C,k1_numbers,k5_numbers))))))) # label(t62_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4518 (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 (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))))))))) # label(t24_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4519 (all A (v4_ordinal2(A) -> v2_funct_1(k1_finseq_2(A)))) # label(t100_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4520 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B -(r2_hidden(B,k4_finseq_1(A)) & np__0 = B)))) # label(t26_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4521 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k10_relat_1(A,B))) = k3_finseq_1(k1_finseq_3(A,B))))) # label(t66_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4522 (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 all D (v4_ordinal2(D) -> (k3_finseq_1(A) = k2_xcmplx_0(D,np__1) & B = k7_relat_1(A,k2_finseq_1(D)) -> (k1_finseq_3(A,C) = k1_finseq_3(B,C) <-> r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C))))))))) # label(t90_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4523 (all A all B all C (r2_hidden(A,B) -> k1_finseq_3(k10_finseq_1(A,C),B) = k9_finseq_1(C) | r2_hidden(C,B))) # label(t85_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4524 (all A v2_funct_1(k9_finseq_1(A))) # label(t102_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4525 (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 k7_finseq_1(k1_finseq_3(A,C),k1_finseq_3(B,C)) = k1_finseq_3(k7_finseq_1(A,B),C)))))) # label(t80_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4526 (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 all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(D)) = B & k2_xcmplx_0(D,np__1) = k3_finseq_1(A) -> (-r2_hidden(k1_funct_1(A,k2_xcmplx_0(D,np__1)),C) <-> k7_finseq_1(k1_finseq_3(B,C),k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(D,np__1)))) = k1_finseq_3(A,C))))))))) # label(t91_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4527 (all A all B all C (k9_finseq_1(B) = k1_finseq_3(k10_finseq_1(A,B),C) -> -r2_hidden(B,C) & r2_hidden(A,C) | A = B)) # label(t86_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4528 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(C,k2_finseq_1(A)) & k2_xcmplx_0(B,np__1) = A -> k3_finseq_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(A),k1_tarski(C)))) = B))))))) # label(t116_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.41 4529 (all A all B k10_finseq_1(A,B) != k1_xboole_0) # label(t38_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4530 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> k1_xboole_0 = k1_finseq_3(A,k2_relat_1(A)))) # label(t79_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4531 (all A (v4_ordinal2(A) -> k6_subset_1(k5_numbers,k2_finseq_1(k2_xcmplx_0(A,np__1)),k2_finseq_1(A)) = k1_tarski(k2_xcmplx_0(A,np__1)))) # label(t16_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4532 (all A (v4_ordinal2(A) -> (A != np__0 -> k14_finseq_1(k1_tarski(A)) = k9_finseq_1(A)))) # label(t50_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4533 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (k7_relat_1(A,k2_finseq_1(C)) = B & k3_finseq_1(A) = k2_xcmplx_0(C,D) -> k4_finseq_1(B) = k2_finseq_1(C)))))))))) # label(t60_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4534 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B k2_relat_1(k1_finseq_3(A,B)) = k4_xboole_0(k2_relat_1(A),B)))) # label(t72_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4535 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> k14_finseq_1(k2_finseq_1(A)) = k7_relat_1(k14_finseq_1(k2_finseq_1(k2_xcmplx_0(A,B))),k2_finseq_1(A)))))) # label(t53_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4536 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(D)) & k1_nat_1(C,np__1) = D -> (r1_xreal_0(B,A) & r1_xreal_0(A,C) -> k1_nat_1(A,np__1) = k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A)) & (r1_xreal_0(np__1,A) -> A = k1_funct_1(k14_finseq_1(k4_xboole_0(k2_finseq_1(D),k1_tarski(B))),A) | r1_xreal_0(B,A))))))))))) # label(t117_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4537 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B r1_tarski(k2_relat_1(k1_finseq_3(A,B)),k2_relat_1(A))))) # label(t73_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4538 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) -> v2_funct_1(k1_finseq_3(A,B)))))) # label(t94_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4539 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k2_relat_1(A)) -> r2_hidden(np__1,k4_finseq_1(A)))))) # label(t33_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4540 $T # label(t47_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4541 (all A all B k4_finseq_1(k10_finseq_1(A,B)) = k2_finseq_1(np__2)) # label(t29_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4542 (all A all B all C (k9_finseq_1(A) = k1_finseq_3(k10_finseq_1(A,B),C) -> r2_hidden(B,C) & -r2_hidden(A,C) | B = A)) # label(t88_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4543 (all A all B all C all D (v1_relat_1(B) & v4_ordinal2(D) & v1_finseq_1(B) & v1_funct_1(B) -> ((exists E (m2_subset_1(E,k1_numbers,k5_numbers) & A = E & r2_hidden(E,k4_finseq_1(B)) & r1_xreal_0(E,D) & r2_hidden(k1_funct_1(B,E),C))) <-> r2_hidden(A,a_3_0_finseq_3(B,C,D))))) # label(fraenkel_a_3_0_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4544 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B r1_xreal_0(k3_finseq_1(k1_finseq_3(A,B)),k3_finseq_1(A))))) # label(t67_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4545 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (k7_relat_1(A,k2_finseq_1(B)) = A <-> r1_xreal_0(k3_finseq_1(A),B)))))) # label(t55_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4546 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(k2_finseq_3(A,C),B))))))) # label(t114_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4547 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_nat_1(C,np__1) = k3_finseq_1(A) -> r1_xreal_0(B,D) | k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,D)))))))))) # label(t119_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4548 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) & v2_funct_1(A) -> A = k9_finseq_1(B))))) # label(t106_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4549 (all A all B all C all D k11_finseq_1(B,C,D) != k9_finseq_1(A)) # label(t41_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4550 (all A all B all C k1_xboole_0 != k11_finseq_1(A,B,C)) # label(t39_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4551 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(A,k2_finseq_1(B)) -> r2_hidden(k6_xcmplx_0(A,C),k2_finseq_1(B)) | r1_xreal_0(A,C)))))))) # label(t13_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4552 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) -> k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(k3_xboole_0(B,k2_relat_1(A)))))))) # label(t95_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4553 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_tarski(k2_finseq_1(A),k2_finseq_1(k2_xcmplx_0(A,B))))))) # label(t19_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4554 (all A all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(r1_tarski(A,k2_finseq_1(B)) & -r1_xreal_0(D,C) & r1_xreal_0(F,k3_finseq_1(k14_finseq_1(A))) & k1_funct_1(k14_finseq_1(A),F) = C & r1_xreal_0(E,F) & k1_funct_1(k14_finseq_1(A),E) = D & r1_xreal_0(np__1,E)))))))))))) # label(t46_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4555 $T # label(t35_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4556 (all A all B (v4_ordinal2(B) -> (r1_tarski(A,k2_finseq_1(B)) -> v2_funct_1(k14_finseq_1(A))))) # label(t99_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4557 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (A != np__0 -> r2_hidden(A,k2_finseq_1(k2_xcmplx_0(A,B)))))))) # label(t10_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4558 $T # label(t21_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4559 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k4_finseq_1(A)) -> m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t25_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4560 (all A all B all C k4_finseq_1(k11_finseq_1(A,B,C)) = k2_finseq_1(np__3)) # label(t30_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4561 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B all C all D (k2_relat_1(A) = k1_enumset1(B,C,D) & v2_funct_1(A) -> C = B | D = C | k3_finseq_1(A) = np__3 | D = B)))) # label(t110_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4562 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B all C (v4_ordinal2(C) -> (r2_hidden(C,k4_finseq_1(A)) -> (all D (v1_finset_1(D) -> -(k1_funct_1(A,C) != k1_funct_1(k1_finseq_3(A,B),k6_xcmplx_0(C,k4_card_1(D))) & -r2_hidden(k1_funct_1(A,C),B) & a_3_0_finseq_3(A,B,C) = D)))))))) # label(t92_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4563 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k4_finseq_1(A) = k4_finseq_1(k1_finseq_3(A,B)) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t71_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4564 (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) -> (k4_finseq_1(A) = k4_finseq_1(B) <-> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t31_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4565 (all A all B all C (v4_ordinal2(C) -> (k2_tarski(A,B) = k2_finseq_1(C) -> B = A | k2_tarski(np__1,np__2) = k2_tarski(A,B) & C = np__2))) # label(t23_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4566 (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 r1_tarski(k10_relat_1(A,C),k10_relat_1(k7_finseq_1(A,B),C))))))) # label(t64_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4567 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -(r2_hidden(A,k4_finseq_1(B)) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(k3_finseq_1(B) = k1_nat_1(C,np__1) & k3_finseq_1(k2_finseq_3(A,B)) = C)))) & (-r2_hidden(A,k4_finseq_1(B)) -> B = k2_finseq_3(A,B)))))) # label(t113_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4568 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B k5_relat_1(k14_finseq_1(k4_xboole_0(k4_finseq_1(A),k10_relat_1(A,B))),A) = k1_finseq_3(A,B)))) # label(d1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4569 $T # label(t36_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4570 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_relat_1(A)) & v2_funct_1(A) -> k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k4_card_1(B))))))) # label(t96_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4571 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k2_tarski(B,C) = k2_relat_1(A) & v2_funct_1(A) -> k3_finseq_1(A) = np__2 | B = C)))) # label(t107_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4572 (all A all B all C k9_finseq_1(A) != k10_finseq_1(B,C)) # label(t40_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4573 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (-r1_xreal_0(B,A) -> r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(B))))))) # label(t12_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4574 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B all C (m2_finseq_1(A,B) -> m2_finseq_1(k1_finseq_3(A,C),B))))) # label(t93_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4575 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_nat_1(C,np__1) = k3_finseq_1(A) & r1_xreal_0(D,C) & r1_xreal_0(B,D) & r2_hidden(B,k4_finseq_1(A)) -> k1_funct_1(k2_finseq_3(B,A),D) = k1_funct_1(A,k1_nat_1(D,np__1))))))))))) # label(t120_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4576 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(k6_xcmplx_0(A,B),k2_finseq_1(A)) <-> -r1_xreal_0(A,B)))))) # label(t14_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4577 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> A = k1_finseq_3(A,k1_xboole_0))) # label(t78_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4578 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k4_finseq_1(k14_finseq_1(B)) = k2_finseq_1(k4_card_1(B))))))) # label(t45_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4579 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(B,k4_finseq_1(A)) <-> m2_subset_1(k6_xcmplx_0(k3_finseq_1(A),B),k1_numbers,k5_numbers) & m2_subset_1(k6_xcmplx_0(B,np__1),k1_numbers,k5_numbers)))))) # label(t28_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4580 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (r1_tarski(k2_relat_1(A),B) <-> k1_xboole_0 = k1_finseq_3(A,B))))) # label(t75_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4581 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k1_finseq_3(A,B)) & v1_finseq_1(k1_finseq_3(A,B)) & v1_funct_1(k1_finseq_3(A,B)))) # label(dt_k1_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4582 (all A (v4_ordinal2(A) -> -r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(A)))) # label(t9_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4583 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (k2_relat_1(A) = k1_enumset1(B,C,D) & v2_funct_1(k11_finseq_1(B,C,D)) & v2_funct_1(A) -> k3_finseq_1(A) = np__3)))) # label(t109_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4584 $T # label(t65_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4585 (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 k4_card_1(k10_relat_1(k7_finseq_1(A,B),C)) = k1_nat_1(k4_card_1(k10_relat_1(A,C)),k4_card_1(k10_relat_1(B,C)))))))) # label(t63_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4586 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (k3_finseq_1(k1_finseq_3(A,B)) = k3_finseq_1(A) -> r1_xboole_0(B,k2_relat_1(A)))))) # label(t68_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4587 (all A all B all C (k10_finseq_1(A,B) = k1_finseq_3(k10_finseq_1(A,B),C) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t89_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4588 (all A all B (k1_finseq_3(k9_finseq_1(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t83_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4589 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k1_finseq_2(A) = k7_relat_1(k1_finseq_2(A),k2_finseq_1(B)) <-> r1_xreal_0(A,B)))))) # label(t58_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4590 (all A all B all C all D all E k10_finseq_1(A,B) != k11_finseq_1(C,D,E)) # label(t42_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4591 (all A all B (k9_finseq_1(A) = k1_finseq_3(k9_finseq_1(A),B) <-> -r2_hidden(A,B))) # label(t82_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4592 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) != k2_finseq_1(A))) # label(t17_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4593 (all A all B all C (r2_hidden(C,B) -> r2_hidden(A,B) | k9_finseq_1(A) = k1_finseq_3(k10_finseq_1(A,C),B))) # label(t87_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4594 (all A (v4_ordinal2(A) -> (all B (v1_finset_1(B) -> (r1_tarski(B,k2_finseq_1(A)) -> k3_finseq_1(k14_finseq_1(B)) = k4_card_1(B)))))) # label(t44_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4595 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (k2_relat_1(A) != k1_xboole_0 -> r2_hidden(np__1,k4_finseq_1(A))))) # label(t34_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4596 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) & k2_relat_1(A) = k1_tarski(B) -> np__1 = k3_finseq_1(A))))) # label(t105_finseq_3) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4597 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> (v4_ordinal1(A) <-> v4_ordinal1(B))))))) # label(t27_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4598 (all A (v3_ordinal1(A) -> (r4_zfrefle1(A,k1_xboole_0) -> A = k1_xboole_0))) # label(t28_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4599 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -(r2_hidden(k5_ordinal2,A) & (all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r4_zfrefle1(B,k5_ordinal2) & v1_zf_model(C) & C = k4_classes1(B))))))))) # label(t42_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4600 (all A (m2_finseq_1(A,k5_numbers) & v1_zf_lang(A) -> (exists B (v1_zf_lang(B) & (all C (-v1_xboole_0(C) -> (r2_zf_model(C,A) <-> r2_zf_model(C,B)))) & k2_zf_model(B) = k1_xboole_0 & m2_finseq_1(B,k5_numbers))))) # label(t6_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4601 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -((all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(r2_hidden(B,C) & r3_zfrefle1(D,A) & k4_classes1(C) = D))))) & r2_hidden(k5_ordinal2,A)))))) # label(t36_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4602 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> -(r2_hidden(k5_ordinal2,A) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> -(r2_hidden(B,C) & D = k4_classes1(C) & r2_zfrefle1(D,A))))))))))) # label(t40_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4603 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,B) -> r2_zfrefle1(A,B)))))) # label(t9_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4604 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> r3_zfrefle1(A,A))) # label(reflexivity_r3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4605 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (k1_xboole_0 = k2_zf_model(C) -> (r2_zf_model(A,C) <-> r2_zf_model(B,C))))) <-> r2_zfrefle1(A,B)))))) # label(d2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4606 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_zfrefle1(A,B) & r4_zfrefle1(B,C) -> r4_zfrefle1(A,C)))))))) # label(t21_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4607 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r3_zfrefle1(C,A) & C = k4_classes1(B) & r4_zfrefle1(B,k5_ordinal2)))))) & r2_hidden(k5_ordinal2,A)))) # label(t37_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4608 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) -> (v4_ordinal1(k1_relat_1(B)) & v2_ordinal2(B) & r1_ordinal2(A,B) -> k1_xboole_0 = k1_relat_1(B) | r4_zfrefle1(A,k1_relat_1(B))))))) # label(t24_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4609 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> ((all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_zf_model(A,C) <-> r2_zf_model(B,C)))) <-> r2_zfrefle1(A,B)))))) # label(t7_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4610 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -((all D (m1_ordinal4(D,A) -> -(r2_hidden(B,D) & D = k4_ordinal4(A,C,D)))) & v3_ordinal2(C) & v2_ordinal2(C) & r2_hidden(k5_ordinal2,A)))))))) # label(t30_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4611 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> r2_hidden(k4_classes1(B),A))))) # label(t33_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4612 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m2_ordinal4(B,A) -> -(v2_ordinal2(B) & v3_ordinal2(B) & (all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (C = k4_ordinal4(A,B,C) & D = k4_classes1(C) -> k1_xboole_0 = C | r3_zfrefle1(D,A))))))))) & r2_hidden(k5_ordinal2,A)))) # label(t35_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4613 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (all C (m2_ordinal4(C,A) -> -(r2_hidden(k5_ordinal2,A) & (all D (m1_ordinal4(D,A) -> -(D = k4_ordinal4(A,C,D) & r4_zfrefle1(D,k5_ordinal2) & r2_hidden(B,D)))) & v3_ordinal2(C) & v2_ordinal2(C)))))))) # label(t31_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4614 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> -(r2_hidden(k5_ordinal2,B) & r2_hidden(A,B) & (all C (-v1_xboole_0(C) -> -(v1_zf_model(C) & r2_hidden(C,B) & r2_hidden(A,C))))))) # label(t43_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4615 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r3_zfrefle1(A,B) <-> (all C (v1_zf_lang(C) & m2_finseq_1(C,k5_numbers) -> (all D (v1_funct_1(D) & v1_funct_2(D,k1_zf_lang,A) & m2_relset_1(D,k1_zf_lang,A) -> (r1_zf_model(A,D,C) <-> r1_zf_model(B,k2_zf_lang1(k1_zf_lang,A,B,D),C)))))) & r1_tarski(A,B)))))) # label(d3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4616 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_zfrefle1(A,B) <-> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(B,C) <-> r1_zfrefle1(A,C))))))))) # label(t8_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.27/22.42 4617 (all A (-v1_xboole_0(A) -> r1_zfrefle1(A,k1_subset_1(k9_zf_lang)))) # label(t1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4618 (all A (-v1_xboole_0(A) -> (v1_zf_model(A) -> r1_zfrefle1(A,k2_zfrefle1)))) # label(t4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4619 (all A all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) -> v3_ordinal1(A)))) # label(t19_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4620 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) & r4_zfrefle1(B,A) -> A = B))))) # label(t23_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4621 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & m2_relset_1(C,B,k1_funct_2(k2_ordinal2(A),k2_ordinal2(A))) & v1_funct_1(C) -> -(r2_hidden(k1_card_1(B),k1_card_1(A)) & (all D (m2_ordinal4(D,A) -> -(v2_ordinal2(D) & (all E (m1_ordinal4(E,A) -> (v4_ordinal1(E) -> k2_ordinal4(A) = E | k4_ordinal4(A,D,E) = k8_ordinal2(k2_ordinal1(D,E))))) & (all E (m1_ordinal4(E,A) -> k4_ordinal4(A,D,k6_ordinal4(A,E)) = k7_ordinal2(k2_xboole_0(k1_tarski(k4_ordinal4(A,D,E)),k9_relat_1(k4_funct_5(C),k2_zfmisc_1(B,k1_tarski(k6_ordinal4(A,E)))))))) & k2_ordinal4(A) = k4_ordinal4(A,D,k2_ordinal4(A)) & v3_ordinal2(D))))))))))) # label(t14_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4622 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_zfrefle1(A,B) -> r2_zfrefle1(B,A)))) # label(symmetry_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4623 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k8_ordinal2(A)))) # label(t20_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4624 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -((all B (m2_ordinal4(B,A) -> -((all C (m1_ordinal4(C,A) -> (all D (-v1_xboole_0(D) -> (k4_classes1(C) = D & k4_ordinal4(A,B,C) = C -> r2_zfrefle1(D,A) | k1_xboole_0 = C))))) & v3_ordinal2(B) & v2_ordinal2(B)))) & r2_hidden(k5_ordinal2,A)))) # label(t39_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4625 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(k1_relat_1(A),B) & r1_tarski(k2_relat_1(A),B) -> r2_hidden(k2_relat_1(A),B)))))) # label(t12_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4626 $T # label(dt_k1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4627 (all A -(r2_hidden(A,f1_s1_zfrefle1) & (all B -p1_s1_zfrefle1(A,B)))) -> (exists A (f1_s1_zfrefle1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s1_zfrefle1) -> p1_s1_zfrefle1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4628 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (v1_ordinal1(B) & r2_zfrefle1(A,B) & v1_zf_model(A) -> v1_zf_model(B)))))) # label(t10_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4629 (all A (-v1_xboole_0(A) -> (r1_zfrefle1(A,k2_zfrefle1) & v1_ordinal1(A) -> v1_zf_model(A)))) # label(t5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4630 (all A all B (k1_card_1(A) = k1_card_1(B) | r2_wellord2(A,B) -> k1_card_1(k1_zfmisc_1(A)) = k1_card_1(k1_zfmisc_1(B)) & r2_wellord2(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t13_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4631 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,B) <-> (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> (r2_hidden(C,B) -> r2_zf_model(A,C))))))))) # label(d1_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4632 $T # label(t11_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4633 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> k1_ordinal3(A,k2_ordinal1(C,B)) = k2_ordinal1(k1_ordinal3(A,C),B))))))) # label(t16_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4634 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> r2_zfrefle1(A,A))) # label(reflexivity_r2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4635 (all A (k1_zfrefle1 = A <-> (all B (r2_hidden(B,A) <-> -(B != k8_zf_model & B != k9_zf_model & (all C (m2_finseq_1(C,k5_numbers) & v1_zf_lang(C) -> -(r1_xboole_0(k1_enumset1(k2_zf_lang(np__0),k2_zf_lang(np__1),k2_zf_lang(np__2)),k2_zf_model(C)) & k11_zf_model(C) = B))) & B != k10_zf_model & B != k7_zf_model & k6_zf_model != B) & r2_hidden(B,k9_zf_lang))))) # label(d4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4636 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_zf_refle(B,A) & m1_ordinal1(B,A) & v2_relat_1(B) -> -((all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> k3_card_3(k2_ordinal1(B,C)) = k5_zf_refle(A,B,C) | C = k1_xboole_0))) & (all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & (all D (m1_ordinal4(D,A) -> (D = k4_ordinal4(A,C,D) -> r2_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B)) | k1_xboole_0 = D))) & v3_ordinal2(C)))) & (all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & r2_hidden(k5_ordinal2,A)))))) # label(t38_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4637 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (v2_ordinal2(B) & v3_ordinal2(B) -> v3_ordinal2(k1_ordinal3(A,B))))))) # label(t17_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4638 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_tarski(B,C) & r1_zfrefle1(A,C) -> r1_zfrefle1(A,B)))))))) # label(t2_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4639 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> (k1_xboole_0 != B -> m1_subset_1(k4_classes1(B),A) & -v1_xboole_0(k4_classes1(B))))))) # label(t34_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4640 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_relat_1(B) -> (v2_ordinal2(B) -> v2_ordinal2(k1_ordinal3(A,B))))))) # label(t15_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4641 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_ordinal4(B,A) -> -r4_zfrefle1(k2_ordinal2(A),B))))) # label(t29_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4642 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r4_zfrefle1(A,A))) # label(reflexivity_r4_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4643 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v2_relat_1(B) & v1_zf_refle(B,A) & m1_ordinal1(B,A) -> -((all C (m1_ordinal4(C,A) -> (all D (m1_ordinal4(D,A) -> (r2_hidden(C,D) -> r1_tarski(k5_zf_refle(A,B,C),k5_zf_refle(A,B,D))))))) & (all C (m1_ordinal4(C,A) -> (v4_ordinal1(C) -> k5_zf_refle(A,B,C) = k3_card_3(k2_ordinal1(B,C)) | C = k1_xboole_0))) & (all C (m2_ordinal4(C,A) -> -(v2_ordinal2(C) & v3_ordinal2(C) & (all D (m1_ordinal4(D,A) -> (D = k4_ordinal4(A,C,D) -> r3_zfrefle1(k5_zf_refle(A,B,D),k4_zf_refle(A,B)) | D = k1_xboole_0)))))) & r2_hidden(k5_ordinal2,A)))))) # label(t32_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4644 (all A (v3_ordinal1(A) -> r4_zfrefle1(k1_ordinal1(A),k4_ordinal2))) # label(t25_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4645 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -((all B (m1_ordinal4(B,A) -> (all C (-v1_xboole_0(C) -> -(r4_zfrefle1(B,k5_ordinal2) & k4_classes1(B) = C & r2_zfrefle1(C,A)))))) & r2_hidden(k5_ordinal2,A)))) # label(t41_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4646 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) -> (r1_zfrefle1(A,C) & r1_zfrefle1(A,B) -> r1_zfrefle1(A,k4_subset_1(k9_zf_lang,B,C))))))))) # label(t3_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4647 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> A != k1_ordinal1(C))) & r4_zfrefle1(A,k1_ordinal1(B))))))) # label(t26_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4648 $T # label(t18_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4649 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) -> r1_tarski(B,A)))))) # label(t22_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4650 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_zfrefle1(A,B) <-> (exists C (v1_relat_1(C) & v1_ordinal2(C) & r1_tarski(k2_relat_1(C),A) & v2_ordinal2(C) & A = k8_ordinal2(C) & k1_relat_1(C) = B & v5_ordinal1(C) & v1_funct_1(C)))))))) # label(d5_zfrefle1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4651 (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]. 23.37/22.42 4652 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4653 (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]. 23.37/22.42 4654 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4655 (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]. 23.37/22.42 4656 (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]. 23.37/22.42 4657 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__0 -> A = k11_qc_lang1) & ((exists B (m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> v2_qc_lang1(A)) & (np__3 = 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__2 -> v4_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]. 23.37/22.42 4658 (all A all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (k1_funct_1(k16_qc_lang1(B),C) = A & r1_xreal_0(np__1,C) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_2_qc_lang1(B))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4659 (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]. 23.37/22.42 4660 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4661 (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]. 23.37/22.42 4662 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4663 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = k12_qc_lang1(B) <-> k17_qc_lang1(A) = B)))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4664 (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]. 23.37/22.42 4665 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.42 4666 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (A = k13_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))))) <-> v4_qc_lang1(A)))) # label(d19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4667 (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]. 23.37/22.43 4668 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4669 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v3_qc_lang1(A) & v2_qc_lang1(A)) & -(v5_qc_lang1(A) & v2_qc_lang1(A)) & -(v3_qc_lang1(A) & v5_qc_lang1(A)) & -(v4_qc_lang1(A) & v5_qc_lang1(A)) & -(v4_qc_lang1(A) & v3_qc_lang1(A)) & -(v2_qc_lang1(A) & v4_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4670 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) <-> (exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (k14_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1)))))))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4671 (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]. 23.37/22.43 4672 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4673 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> (r2_hidden(A,a_1_1_qc_lang1(B)) <-> (exists C (r2_hidden(k1_funct_1(B,C),k2_qc_lang1) & r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) & A = k1_funct_1(B,C) & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4674 (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]. 23.37/22.43 4675 (exists A (v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & m2_relset_1(A,k8_qc_lang1,f1_s3_qc_lang1) & (all B (m1_subset_1(B,k8_qc_lang1) -> (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)))) & (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)))) & (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)) & (v2_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f3_s3_qc_lang1(B)))) & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) = f2_s3_qc_lang1 & v1_funct_1(A))) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4676 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k18_qc_lang1(A)))) & -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k19_qc_lang1(A))))))) # label(t46_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4677 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_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(k18_qc_lang1(A)) & p1_s2_qc_lang1(k19_qc_lang1(A)) -> p1_s2_qc_lang1(A)) & (p1_s2_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A) -> p1_s2_qc_lang1(A)) & p1_s2_qc_lang1(k11_qc_lang1))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(A))) # label(s2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4678 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4679 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4680 (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]. 23.37/22.43 4681 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4682 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k18_qc_lang1(A) = B <-> (exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))))))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4683 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4684 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4685 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) & (exists D (k9_qc_lang1(C,D) = A & m1_qc_lang1(D,B))))) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> v2_qc_lang1(A)))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4686 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k7_qc_lang1(A) = a_1_0_qc_lang1(A))) # label(d7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4687 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4688 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4689 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (A = k14_qc_lang1(C,B) & m2_subset_1(C,k1_qc_lang1,k2_qc_lang1))) <-> B = k21_qc_lang1(A))))))) # label(d27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4690 (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]. 23.37/22.43 4691 (all A (m1_subset_1(A,k8_qc_lang1) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(k11_qc_lang1),np__1)) = np__0 & (v3_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1) & (v4_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__2) & (v5_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__3) & -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) & v2_qc_lang1(A)))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4692 (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]. 23.37/22.43 4693 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4694 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4695 (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) -> (k7_finseq_1(k10_qc_lang1(B),C) = k10_qc_lang1(A) -> k10_qc_lang1(A) = k10_qc_lang1(B)))))))) # label(t37_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4696 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (C = A & k6_qc_lang1(C) = B & m1_subset_1(C,k5_qc_lang1))) <-> r2_hidden(A,a_1_0_qc_lang1(B))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4697 (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]. 23.37/22.43 4698 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4699 (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]. 23.37/22.43 4700 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4701 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> ((exists C (m2_relset_1(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & (all D (m1_subset_1(D,k8_qc_lang1) -> (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) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = k6_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k21_qc_lang1(D)),k23_qc_lang1(k20_qc_lang1(D)))) & (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)) & (v2_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = a_1_2_qc_lang1(D)) & k1_xboole_0 = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k11_qc_lang1))) & B = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,A) & v1_funct_2(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & v1_funct_1(C))) <-> B = k24_qc_lang1(A)))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4702 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4703 (all A (m1_subset_1(A,k8_qc_lang1) -> k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),k10_qc_lang1(A)) = k12_qc_lang1(A))) # label(d14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4704 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4705 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4706 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4707 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (A = k3_finseq_1(B) <-> m1_qc_lang1(B,A)))))) # label(d8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4708 (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]. 23.37/22.43 4709 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4710 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4711 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> A = k6_qc_lang1(B))))) # label(t35_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4712 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4713 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4714 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4715 (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]. 23.37/22.43 4716 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> (k15_qc_lang1(A) = B <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D ((exists E (E = B & k9_qc_lang1(E,D) = A & m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)))) & m1_qc_lang1(D,C))))))))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4717 (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]. 23.37/22.43 4718 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4719 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4720 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4721 (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]. 23.37/22.43 4722 (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]. 23.37/22.43 4723 (all A (m1_subset_1(A,k2_qc_lang1) -> k23_qc_lang1(A) = k1_tarski(A))) # label(redefinition_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4724 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> np__1 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__2 & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__3 & np__0 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4725 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_mcart_1(A) = k1_nat_1(np__7,B) <-> B = k6_qc_lang1(A)))))) # label(d6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.43 4726 (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]. 23.37/22.44 4727 (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]. 23.37/22.44 4728 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B = k19_qc_lang1(A) <-> (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]. 23.37/22.44 4729 (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]. 23.37/22.44 4730 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4731 (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 (A = k14_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))) <-> k20_qc_lang1(A) = B)))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4732 (all 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))))))) & (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,B)),C),A)))))) & (all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),B),C),A)))))) & (all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),B),A)))) & r2_hidden(k9_finseq_1(k4_tarski(np__0,np__0)),A) & m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) <-> v1_qc_lang1(A))) # label(d9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4733 (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]. 23.37/22.44 4734 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4735 (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]. 23.37/22.44 4736 (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]. 23.37/22.44 4737 (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]. 23.37/22.44 4738 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4739 p1_s1_qc_lang1(k11_qc_lang1) & (all A (m1_subset_1(A,k8_qc_lang1) -> (p1_s1_qc_lang1(A) -> p1_s1_qc_lang1(k12_qc_lang1(A))))) & (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(A) & p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k13_qc_lang1(A,B))))))) & (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k14_qc_lang1(A,B))))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> p1_s1_qc_lang1(k9_qc_lang1(B,C)))))))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s1_qc_lang1(A))) # label(s1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4740 (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) & B = E & k9_qc_lang1(D,E) = A)) & 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]. 23.37/22.44 4741 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k3_finseq_1(B) = k6_qc_lang1(A) -> k7_finseq_1(k12_finseq_1(k5_qc_lang1,A),B) = k9_qc_lang1(A,B)))))) # label(d11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4742 (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]. 23.37/22.44 4743 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v5_qc_lang1(A) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k21_qc_lang1(A))))))) # label(t47_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4744 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4745 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4746 (all A (m1_subset_1(A,k8_qc_lang1) -> (k24_qc_lang1(A) = k1_xboole_0 <-> v6_qc_lang1(A)))) # label(d30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4747 (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]. 23.37/22.44 4748 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4749 (all A (m1_subset_1(A,k8_qc_lang1) -> -(-v4_qc_lang1(A) & -v5_qc_lang1(A) & -v3_qc_lang1(A) & -v2_qc_lang1(A) & k11_qc_lang1 != A))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4750 (all A (r2_hidden(A,a_0_0_qc_lang1) <-> (exists B exists C (m2_subset_1(B,k1_numbers,k5_numbers) & r1_xreal_0(np__7,B) & k4_tarski(B,C) = A & m2_subset_1(C,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4751 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4752 (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]. 23.37/22.44 4753 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k6_qc_lang2(C,E,A) = k6_qc_lang2(D,F,B) -> B = A & F = E & C = D))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4754 (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]. 23.37/22.44 4755 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k13_qc_lang1(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_tarski(k13_qc_lang1(A,B))))))) # label(t111_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4756 (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]. 23.37/22.44 4757 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(B,C) & r3_qc_lang2(A,B) -> r3_qc_lang2(A,C)))))))) # label(t76_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4758 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (B = k15_qc_lang2(A) <-> (all C ((exists D (m1_subset_1(D,k8_qc_lang1) & C = D & r2_qc_lang2(D,A))) <-> r2_hidden(C,B))))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4759 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> v4_qc_lang2(k7_qc_lang2(A,B,D)) & v4_qc_lang2(k9_qc_lang2(A,B,C,D)))))))))) # label(t38_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4760 (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]. 23.37/22.44 4761 (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]. 23.37/22.44 4762 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(A,B,C,D) = k14_qc_lang1(F,E) -> k6_qc_lang2(B,C,D) = E & A = F))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4763 (all A all B all C (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(C,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4764 (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]. 23.37/22.44 4765 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k2_qc_lang2(C,D) = k2_qc_lang2(A,B) -> C = A & B = D))))))))) # label(t17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4766 (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]. 23.37/22.44 4767 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(D,F,H,B) = k8_qc_lang2(C,E,G,A) -> D = C & F = E & H = G & B = A))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4768 (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]. 23.37/22.44 4769 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k7_qc_lang2(D,F,B) = k7_qc_lang2(C,E,A) -> C = D & B = A & F = E))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4770 (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]. 23.37/22.44 4771 (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]. 23.37/22.44 4772 (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]. 23.37/22.44 4773 (all A (m1_subset_1(A,k8_qc_lang1) -> k10_qc_lang2(A) = k17_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))))) # label(d14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4774 (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]. 23.37/22.44 4775 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_hidden(B,k15_qc_lang2(C)) -> r2_hidden(A,k15_qc_lang2(C)) | -r2_qc_lang2(A,B) & -r3_qc_lang2(A,B) & -r1_qc_lang2(A,B)))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4776 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4777 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A))))) # label(t118_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4778 (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]. 23.37/22.44 4779 (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]. 23.37/22.44 4780 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> A = k3_qc_lang2(k10_qc_lang2(A),k11_qc_lang2(A))))) # label(t53_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4781 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k13_qc_lang1(A,B) = k13_qc_lang1(C,D) -> A = C & B = D))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4782 (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]. 23.37/22.44 4783 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k15_qc_lang2(k9_qc_lang1(B,C)) = k1_tarski(k9_qc_lang1(B,C)))))))) # label(t108_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4784 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(A,k3_qc_lang2(A,B)) & r3_qc_lang2(B,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B)))))) # label(t94_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4785 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k11_qc_lang1) <-> r3_qc_lang2(A,k1_qc_lang2)))) # label(t88_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4786 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4787 (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]. 23.37/22.44 4788 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4789 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(A,k13_qc_lang1(B,C)) <-> r2_qc_lang2(A,C) | r2_qc_lang2(A,B)))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4790 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4791 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4792 (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]. 23.37/22.44 4793 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k12_qc_lang1(B))))))) # label(t86_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4794 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4795 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.44 4796 (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]. 23.37/22.44 4797 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k4_qc_lang2(C,D) = k4_qc_lang2(A,B) -> C = A & D = B))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4798 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_qc_lang2(A,B) = k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)))))) # label(d4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4799 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) & r2_qc_lang2(B,A) -> B = A))))) # label(t78_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4800 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k5_qc_lang2(A,k5_qc_lang2(B,C)) = k7_qc_lang2(A,B,C) & k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4801 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(A,k2_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k2_qc_lang2(A,B)) & r3_qc_lang2(B,k2_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B)))))) # label(t93_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4802 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k18_qc_lang1(k13_qc_lang1(A,B)) = A & k19_qc_lang1(k13_qc_lang1(A,B)) = B)))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4803 (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]. 23.37/22.45 4804 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang2(k18_qc_lang1(A)) = k13_qc_lang2(A))) # label(d18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4805 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (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]. 23.37/22.45 4806 (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]. 23.37/22.45 4807 (all A (m1_subset_1(A,k8_qc_lang1) -> (A = k11_qc_lang1 <-> r1_qc_lang2(A,k1_qc_lang2)))) # label(t61_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4808 (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]. 23.37/22.45 4809 (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) -> C = D & B = A))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4810 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4811 (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]. 23.37/22.45 4812 (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]. 23.37/22.45 4813 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(C,E,G,A) = k9_qc_lang2(D,F,H,B) -> C = D & G = H & B = A & E = F))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4814 (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]. 23.37/22.45 4815 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (k21_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4816 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4817 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(A,B) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A)))))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4818 (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]. 23.37/22.45 4819 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (A = k2_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1))) <-> v2_qc_lang2(A)))) # label(d11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4820 (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]. 23.37/22.45 4821 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k2_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4822 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k2_enumset1(k12_qc_lang1(B),k12_qc_lang1(A),k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))) = k15_qc_lang2(k3_qc_lang2(A,B)))))) # label(t114_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4823 (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]. 23.37/22.45 4824 (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]. 23.37/22.45 4825 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> r2_qc_lang2(A,A))) # label(reflexivity_r2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4826 (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]. 23.37/22.45 4827 (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]. 23.37/22.45 4828 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k4_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))))))) # label(t115_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4829 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4830 (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]. 23.37/22.45 4831 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k5_qc_lang2(A,k7_qc_lang2(B,C,D)) = k9_qc_lang2(A,B,C,D) & k14_qc_lang1(A,k6_qc_lang2(B,C,D)) = k8_qc_lang2(A,B,C,D))))))))) # label(t26_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4832 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k7_qc_lang2(A,B,D) = k5_qc_lang2(C,E) -> E = k5_qc_lang2(B,D) & A = C))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4833 (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]. 23.37/22.45 4834 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4835 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k5_qc_lang2(A,C) = k5_qc_lang2(B,D) -> A = B & C = D))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4836 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v5_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(A)))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4837 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (A = B | C = A <-> r1_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4838 (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]. 23.37/22.45 4839 (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) & r2_qc_lang2(B,C)) & -(r2_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r3_qc_lang2(B,C)) & -(r3_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r2_qc_lang2(B,C)) & -(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]. 23.37/22.45 4840 (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]. 23.37/22.45 4841 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t91_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4842 (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]. 23.37/22.45 4843 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4844 (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]. 23.37/22.45 4845 (all A all B all C all D (m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4846 (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 & k11_qc_lang2(k2_qc_lang2(A,B)) = B & k13_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k2_qc_lang2(A,B)))))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4847 (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]. 23.37/22.45 4848 (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]. 23.37/22.45 4849 (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]. 23.37/22.45 4850 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4851 (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]. 23.37/22.45 4852 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4853 (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]. 23.37/22.45 4854 (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]. 23.37/22.45 4855 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> 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]. 23.37/22.45 4856 (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]. 23.37/22.45 4857 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (A = k3_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1))) <-> v1_qc_lang2(A)))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4858 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k1_qc_lang2) <-> k11_qc_lang1 = A | A = k1_qc_lang2))) # label(t101_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4859 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B != A & r2_qc_lang2(A,B) <-> r3_qc_lang2(A,B)))))) # label(d22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4860 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (-((all C (m1_subset_1(C,k8_qc_lang1) -> B != k13_qc_lang1(C,A) & k13_qc_lang1(A,C) != B)) & (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> k14_qc_lang1(C,A) != B)) & k12_qc_lang1(A) != B) <-> r1_qc_lang2(A,B)))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4861 (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]. 23.37/22.45 4862 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k4_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4863 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> r3_qc_lang2(k18_qc_lang1(A),A) & r3_qc_lang2(k19_qc_lang1(A),A)))) # label(t97_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4864 (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]. 23.37/22.45 4865 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4866 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4867 (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]. 23.37/22.45 4868 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k10_qc_lang2(k3_qc_lang2(A,B)) & k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) = k17_qc_lang1(k3_qc_lang2(A,B)) & B = k11_qc_lang2(k3_qc_lang2(A,B)))))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4869 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4870 (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]. 23.37/22.45 4871 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k12_qc_lang1(B) = k12_qc_lang1(A) -> A = B))))) # label(t1_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4872 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) <-> (exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & k4_qc_lang2(B,C) = A)) & m1_subset_1(B,k8_qc_lang1)))))) # label(d12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4873 (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)) & k18_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(A,B) & k19_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(B,A) & B = k14_qc_lang2(k4_qc_lang2(A,B)))))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4874 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A)) = A))) # label(t55_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4875 (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]. 23.37/22.45 4876 (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]. 23.37/22.45 4877 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (A = k5_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))))) <-> v4_qc_lang2(A)))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4878 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_tarski(A) = k15_qc_lang2(A) <-> A = k11_qc_lang1 | v2_qc_lang1(A)))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4879 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v2_qc_lang2(A) & v3_qc_lang1(A) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v4_qc_lang1(k17_qc_lang1(A))))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4880 (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]. 23.37/22.45 4881 (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]. 23.37/22.45 4882 (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]. 23.37/22.45 4883 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (k18_qc_lang1(A) = B | k19_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4884 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> v5_qc_lang1(k8_qc_lang2(A,B,C,D)) & 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)))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4885 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) <-> (exists C ((exists D (v1_relat_1(D) & v1_funct_1(D) & C = k3_finseq_1(D) & A = k1_funct_1(D,np__1) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(-r1_xreal_0(C,E) & (all F (m1_subset_1(F,k8_qc_lang1) -> (all G (m1_subset_1(G,k8_qc_lang1) -> -(r1_qc_lang2(F,G) & k1_funct_1(D,k1_nat_1(E,np__1)) = G & F = k1_funct_1(D,E)))))) & r1_xreal_0(np__1,E)))) & B = k1_funct_1(D,C) & r1_xreal_0(np__1,C) & v1_finseq_1(D))) & m2_subset_1(C,k1_numbers,k5_numbers)))))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4886 (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) -> k21_qc_lang1(k6_qc_lang2(A,B,C)) = k14_qc_lang1(B,C) & k20_qc_lang1(k6_qc_lang2(A,B,C)) = A & v5_qc_lang1(k6_qc_lang2(A,B,C)))))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4887 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k3_qc_lang2(A,B) = k3_qc_lang2(C,D) -> B = D & A = C))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4888 (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]. 23.37/22.45 4889 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (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) -> A = F & B = G & E = k5_qc_lang2(C,D)))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4890 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4891 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k5_qc_lang2(A,B) = k12_qc_lang1(k14_qc_lang1(A,k12_qc_lang1(B))))))) # label(d5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4892 (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]. 23.37/22.45 4893 (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]. 23.37/22.45 4894 (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]. 23.37/22.45 4895 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4896 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(A,B,C,D) = k6_qc_lang2(F,G,E) -> A = F & B = G & E = k14_qc_lang1(C,D)))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4897 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4898 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k5_qc_lang2(A,k5_qc_lang2(B,C)) = k7_qc_lang2(A,B,C))))))) # label(d7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4899 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4900 (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]. 23.37/22.45 4901 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k14_qc_lang1(C,E) = k6_qc_lang2(A,B,D) -> A = C & E = k14_qc_lang1(B,D)))))))))))) # label(t22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4902 (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]. 23.37/22.45 4903 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4904 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4905 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4906 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t82_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4907 (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]. 23.37/22.45 4908 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4909 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> p1_s1_cqc_lang(k9_cqc_lang) & p1_s1_cqc_lang(k8_cqc_lang(D,F,E)) & (p1_s1_cqc_lang(B) & p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k11_cqc_lang(A,B))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k15_cqc_lang(C,A))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k10_cqc_lang(A))))))))))))))) -> (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]. 23.37/22.45 4910 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang)) # label(t28_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4911 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> k17_cqc_lang(B,A) = k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A)))))))) # label(t29_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4912 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k12_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4913 (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_2(C,k7_cqc_lang,f1_s8_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s8_cqc_lang(G,I,H) & f5_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k10_cqc_lang(D)) & 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)) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) = 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)))))))))))))) & f3_s8_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A) = B & v1_funct_1(C))) <-> 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]. 23.37/22.45 4914 (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) -> 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]. 23.37/22.45 4915 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> B = k17_cqc_lang(B,A))))) # label(t40_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4916 (all A all B k2_funcop_1(k1_tarski(A),B) = k3_cqc_lang(A,B)) # label(d2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4917 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)) = k17_cqc_lang(k13_qc_lang1(B,C),A))))))) # label(t34_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4918 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> k16_cqc_lang(A,B) = k5_qc_lang2(A,B))) # label(redefinition_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4919 (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]. 23.37/22.45 4920 (all A (m1_subset_1(A,k5_numbers) -> (exists B (m1_qc_lang1(B,A) & v1_funct_1(B) & v1_cqc_lang(B,A) & v1_finseq_1(B) & v1_relat_1(B))))) # label(rc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4921 (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) -> B = k17_cqc_lang(B,A)))))) # label(t39_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4922 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4923 (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]. 23.37/22.45 4924 (all A (r2_hidden(A,k1_qc_lang1) <-> -(-r2_hidden(A,k2_qc_lang1) & -r2_hidden(A,k4_qc_lang1) & -r2_hidden(A,k3_qc_lang1)))) # label(t7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4925 (all A all B (m1_finseq_1(A,k1_qc_lang1) & m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(B) -> m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1))) # label(dt_k4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4926 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k3_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t21_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4927 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (r1_tarski(k2_relat_1(B),k2_qc_lang1) <-> v1_cqc_lang(B,A)))))) # label(d5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4928 (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]. 23.37/22.45 4929 (all A all B B = k1_funct_1(k3_cqc_lang(A,B),A)) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4930 (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_1(D) & v1_funct_2(D,k8_qc_lang1,k8_qc_lang1) & (all E (m1_subset_1(E,k8_qc_lang1) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang) = k9_cqc_lang & (v2_qc_lang1(E) -> k9_qc_lang1(k15_qc_lang1(E),k4_cqc_lang(k16_qc_lang1(E),k6_cqc_lang(k3_qc_lang3(np__0),B))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v3_qc_lang1(E) -> k12_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k17_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v4_qc_lang1(E) -> k13_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k18_qc_lang1(E)),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k19_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v5_qc_lang1(E) -> k2_cqc_lang(k8_qc_lang1,k20_qc_lang1(E),B,E,k14_qc_lang1(k20_qc_lang1(E),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k21_qc_lang1(E)))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)))) & C = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A) & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1)))))))))) # label(d6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4931 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s9_cqc_lang) -> ((exists C (B = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) & 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)) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s9_cqc_lang(G,I,H))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) = f3_s9_cqc_lang & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang) & v1_funct_1(C))) <-> f2_s9_cqc_lang(A) = B))))) -> f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) = f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) # label(s9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4932 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4933 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4934 (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]. 23.37/22.45 4935 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(B) = k6_qc_lang3(k17_cqc_lang(B,A)))))) # label(t41_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4936 (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]. 23.37/22.45 4937 (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]. 23.37/22.45 4938 (exists A (v1_funct_1(A) & v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang) & (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_cqc_lang(F,E) & m1_qc_lang1(F,E) -> (all G (m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) -> k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)) = f5_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B),k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,C)) & f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) & f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) & f3_s2_cqc_lang(E,G,F) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)))))))))))))) & 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))) # label(s2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4939 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4940 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(B) -> k17_cqc_lang(B,A) = k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A))))))) # label(t31_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4941 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4942 (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]. 23.37/22.45 4943 (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]. 23.37/22.45 4944 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> ((exists D (m2_subset_1(D,k1_numbers,k5_numbers) & k1_funct_1(C,D) = A & r1_xreal_0(np__1,D) & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)))) <-> r2_hidden(A,a_2_0_cqc_lang(B,C))))) # label(fraenkel_a_2_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4945 (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]. 23.37/22.45 4946 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4947 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4948 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1) & v1_funct_1(k6_cqc_lang(A,B)))) # label(dt_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.45 4949 f4_s3_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_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)) -> f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)) & 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)) & 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)) & 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)))))))))))))) & (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)) -> f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k11_cqc_lang(A,B)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang -> f2_s3_cqc_lang = f3_s3_cqc_lang # label(s3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4950 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s7_cqc_lang) -> ((exists C (v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A) = B & 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)) -> k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) = f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) = f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) & f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)))))))))))))) & v1_funct_1(C))) <-> B = f2_s7_cqc_lang(A)))))) -> 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]. 23.37/22.46 4951 (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]. 23.37/22.46 4952 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4953 (all A (m1_subset_1(A,k7_cqc_lang) -> k12_qc_lang1(A) = k10_cqc_lang(A))) # label(redefinition_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4954 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A)) -> (all D (m1_qc_lang1(D,A) -> k17_cqc_lang(k9_qc_lang1(C,D),B) = k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))))))))))) # label(t30_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4955 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4956 (all A all B all C all D ((B = A -> k1_cqc_lang(A,B,C,D) = C) & (B != A -> D = k1_cqc_lang(A,B,C,D)))) # label(d1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4957 (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 -> k14_qc_lang1(A,k17_cqc_lang(C,B)) = k17_cqc_lang(k14_qc_lang1(A,C),B)))))))) # label(t38_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4958 (all A (r2_hidden(A,a_0_0_cqc_lang) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & A = B & k5_qc_lang3(B) = k1_xboole_0 & k1_xboole_0 = k6_qc_lang3(B))))) # label(fraenkel_a_0_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4959 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k15_cqc_lang(A,B) = k14_qc_lang1(A,B))) # label(redefinition_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4960 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,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]. 23.37/22.46 4961 (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) -> k17_cqc_lang(B,A) = k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A)) | A = k20_qc_lang1(B)))))) # label(t36_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4962 (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]. 23.37/22.46 4963 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4964 (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]. 23.37/22.46 4965 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4966 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = k20_qc_lang1(B) & v5_qc_lang1(B) -> k17_cqc_lang(B,A) = B))))) # label(t35_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4967 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s5_cqc_lang) -> ((exists C (v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A) = B & f3_s5_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s5_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_s5_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E)) & 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)))))))))))))) & m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang) & v1_funct_1(C))) <-> f2_s5_cqc_lang(A) = B))))) -> f3_s5_cqc_lang = f2_s5_cqc_lang(k9_cqc_lang) # label(s5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4968 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k4_qc_lang2(A,B) = k14_cqc_lang(A,B))) # label(redefinition_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4969 (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]. 23.37/22.46 4970 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) & m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)))))) # label(t19_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4971 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1) & v1_funct_1(k3_cqc_lang(B,A)))))) # label(t10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4972 (all A all B all C (m1_qc_lang1(B,A) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(C) & m1_subset_1(A,k5_numbers) -> m1_qc_lang1(k5_cqc_lang(A,B,C),A))) # label(dt_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4973 (all A all B (k1_tarski(B) = k2_relat_1(k3_cqc_lang(A,B)) & k1_tarski(A) = k1_relat_1(k3_cqc_lang(A,B)))) # label(t5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4974 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4975 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> (k1_xboole_0 = a_2_0_cqc_lang(A,C) & k1_xboole_0 = a_2_1_cqc_lang(A,C) <-> m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)))))))) # label(t17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4976 (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]. 23.37/22.46 4977 (all A all B all C (v1_cqc_lang(C,A) & m1_qc_lang1(C,A) & m1_subset_1(B,k7_qc_lang1(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]. 23.37/22.46 4978 (all A (m2_finseq_1(A,k1_qc_lang1) -> (all B (v1_funct_1(B) & m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) -> (all C (m2_finseq_1(C,k1_qc_lang1) -> (k3_finseq_1(C) = k3_finseq_1(A) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) & r1_xreal_0(D,k3_finseq_1(A)) -> (-r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(A,D)) & (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(B,k1_funct_1(A,D)) = k1_funct_1(C,D))))) <-> C = k4_cqc_lang(A,B)))))))) # label(d3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4979 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_qc_lang1(B,A) & v1_funct_1(C) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) -> k5_cqc_lang(A,B,C) = k4_cqc_lang(B,C))) # label(redefinition_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4980 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4981 (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]. 23.37/22.46 4982 (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]. 23.37/22.46 4983 (all A all B all C k1_binop_1(k9_funct_2(A,B,C),A,B) = C) # label(t43_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4984 (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) & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)) & f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) = f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s6_cqc_lang(G,I,H))))))))))))) & 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))) <-> f3_s6_cqc_lang(A) = B))))) -> 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]. 23.37/22.46 4985 (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) & (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)) -> f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) & f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & f4_s4_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = A)) & B != A & (exists C (v1_funct_1(C) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> 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,k11_cqc_lang(D,E)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = B & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang)))))))) # label(s4_cqc_lang_AndLHS) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4986 (exists A (m1_subset_1(A,f1_s4_cqc_lang) & (exists B (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)) -> f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k10_cqc_lang(C)) & f7_s4_cqc_lang(E,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,C)) & f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k11_cqc_lang(C,D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) = f4_s4_cqc_lang(F,H,G))))))))))))) & m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(B))))) # label(s4_cqc_lang_AndRHS) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4987 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> m1_subset_1(k2_cqc_lang(A,B,C,D,E),A))) # label(dt_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4988 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k2_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t20_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4989 (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]. 23.37/22.46 4990 (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) -> (k6_cqc_lang(C,B) = F & k4_cqc_lang(E,F) = D & r1_xreal_0(A,k3_finseq_1(E)) & r1_xreal_0(np__1,A) -> (C != k1_funct_1(E,A) -> k1_funct_1(D,A) = k1_funct_1(E,A)) & (k1_funct_1(E,A) = C -> B = k1_funct_1(D,A))))))))))))))) # label(t11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4991 (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(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & r1_xreal_0(np__1,D) & k1_funct_1(C,D) = A))))) # label(fraenkel_a_2_1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4992 (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]. 23.37/22.46 4993 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4994 (all A (m1_subset_1(A,k8_qc_lang1) -> (k6_qc_lang3(A) = k1_xboole_0 & k1_xboole_0 = k5_qc_lang3(A) <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)))) # label(t13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4995 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (v1_cqc_lang(B,A) & m1_qc_lang1(B,A) <-> a_2_0_cqc_lang(A,B) = k1_xboole_0 & a_2_1_cqc_lang(A,B) = k1_xboole_0))))) # label(t15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 4996 (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]. 23.37/22.46 4997 (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]. 23.37/22.46 4998 (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]. 23.37/22.46 4999 (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]. 23.37/22.46 5000 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k11_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> 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]. 23.37/22.46 5001 (all A all B all C (-v1_xboole_0(A) & v2_relat_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5002 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> v1_pboole(B,A)))) # label(redefinition_v1_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5003 (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]. 23.37/22.46 5004 (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]. 23.37/22.46 5005 (all A -(r2_hidden(A,f1_s3_pboole) & (all B -p1_s3_pboole(A,B)))) -> (exists A (m1_pboole(A,f1_s3_pboole) & (all B (r2_hidden(B,f1_s3_pboole) -> p1_s3_pboole(B,k1_funct_1(A,B)))))) # label(s3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5006 (all A exists B (m1_pboole(B,A) & v2_relat_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5007 (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]. 23.37/22.46 5008 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5009 (exists A ((all B (m1_subset_1(B,f1_s5_pboole) -> f2_s5_pboole(B) = k1_funct_1(A,B))) & m1_pboole(A,f1_s5_pboole))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5010 (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]. 23.37/22.46 5011 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5012 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,B,C) -> m1_pboole(D,A))))) # label(dt_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5013 (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,D),C) & r2_pboole(A,k4_pboole(A,B,C),D)))))))) # label(t82_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5014 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,C),B) & r6_pboole(A,k3_pboole(A,C,B),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5015 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C all D (m1_pboole(D,k1_tarski(C)) -> (D = k2_funcop_1(k1_tarski(C),A) -> k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B) = k1_funct_2(k2_finseq_1(B),A)))))))) # label(t153_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5016 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k3_pboole(A,C,D)) <-> 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))))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5017 (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]. 23.37/22.46 5018 (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]. 23.37/22.46 5019 (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]. 23.37/22.46 5020 (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]. 23.37/22.46 5021 (all A all B (m1_pboole(B,A) -> v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5022 (all A all B all C all D (v1_funct_2(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> m1_pboole(k8_pboole(A,B,C,D),A) & v2_relat_1(k8_pboole(A,B,C,D)))) # label(dt_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5023 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r6_pboole(A,B,C) <-> C = B))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5024 (all A all B k1_funct_1(k1_pboole(B),A) = k1_xboole_0) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5025 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) & r5_pboole(A,D,B) & r5_pboole(A,E,C) -> r6_pboole(A,D,C) & r6_pboole(A,E,B)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5026 (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]. 23.37/22.46 5027 (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]. 23.37/22.46 5028 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) -> (all C (v1_funcop_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)))) <-> k13_pboole(A,B) = C))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5029 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5030 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5031 (all A (v1_funct_2(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(k9_pboole(A)))) # label(dt_k9_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5032 (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]. 23.37/22.46 5033 (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]. 23.37/22.46 5034 (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]. 23.37/22.46 5035 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D)) & r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C))))))))) # label(t20_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5036 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d11_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5037 (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]. 23.37/22.46 5038 (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]. 23.37/22.46 5039 (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]. 23.37/22.46 5040 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D)))) <-> m2_pboole(C,A,B)))))) # label(d17_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5041 (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]. 23.37/22.46 5042 (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]. 23.37/22.46 5043 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k4_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d9_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5044 (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]. 23.37/22.46 5045 (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]. 23.37/22.46 5046 (all A -(r2_hidden(A,f1_s1_pboole) & f2_s1_pboole(A) = k1_xboole_0)) -> (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]. 23.37/22.46 5047 (exists A ((all B (r2_hidden(B,f1_s2_pboole) -> (all C (r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) & p1_s2_pboole(B,C) <-> r2_hidden(C,k1_funct_1(A,B)))))) & m1_pboole(A,f1_s2_pboole))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5048 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) <-> (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r1_pboole(A,D,C))))))))) # label(d14_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5049 (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,k3_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) & 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))))))))) # label(t46_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5050 (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]. 23.37/22.46 5051 (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]. 23.37/22.46 5052 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> r6_pboole(A,B,k1_pboole(A))))) # label(t141_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5053 (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]. 23.37/22.46 5054 (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]. 23.37/22.46 5055 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) & r4_pboole(A,B,C)))))))) # label(t139_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5056 (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]. 23.37/22.46 5057 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r3_pboole(A,B,D) & k1_pboole(A) = k3_pboole(A,C,D) & r3_pboole(A,B,C)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5058 (all A k1_pboole(A) = k2_funcop_1(A,k1_xboole_0)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5059 (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]. 23.37/22.46 5060 (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]. 23.37/22.46 5061 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5062 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5063 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5064 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) <-> r1_pboole(A,E,C) & r1_pboole(A,E,B)))) -> r6_pboole(A,D,k3_pboole(A,B,C))))))))) # label(t148_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5065 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5066 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,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]. 23.37/22.46 5067 (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]. 23.37/22.46 5068 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r2_pboole(A,B,C) -> r2_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t19_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5069 (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]. 23.37/22.46 5070 (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]. 23.37/22.46 5071 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) <-> r1_pboole(A,D,B)))) -> r6_pboole(A,C,B)))))) # label(t147_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5072 (all A exists B (m1_pboole(B,A) & v1_funcop_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(rc4_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5073 (all A (v1_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5074 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k2_pboole(A,C,D)) <-> r2_pboole(A,C,B) & r2_pboole(A,D,B) & (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,C,E) -> r2_pboole(A,B,E))))))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5075 (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]. 23.37/22.46 5076 (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]. 23.37/22.46 5077 (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]. 23.37/22.46 5078 (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_funcop_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)) & v1_relat_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5079 (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]. 23.37/22.46 5080 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k3_pboole(A,C,D)) -> r2_pboole(A,B,C) & r2_pboole(A,B,D)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5081 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5082 (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]. 23.37/22.46 5083 (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]. 23.37/22.46 5084 (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]. 23.37/22.46 5085 (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]. 23.37/22.46 5086 (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]. 23.37/22.46 5087 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k2_relat_1(B)) -> (exists D (r2_hidden(D,A) & k1_funct_1(B,D) = C)))))))) # label(t150_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5088 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5089 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)))) <-> k2_pboole(A,B,C) = D))))))) # label(d7_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5090 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D))))))))))) # label(t61_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5091 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> (all C (r2_hidden(C,A) -> v1_xboole_0(k1_funct_1(B,C))))))) # label(d15_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5092 (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]. 23.37/22.46 5093 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B) & r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B))))) # label(t71_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5094 (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]. 23.37/22.46 5095 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5096 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,D) | r4_pboole(A,B,C) -> r4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t106_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5097 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r7_pboole(A,C,D) & r7_pboole(A,B,C) -> r7_pboole(A,B,D)))))))) # label(t132_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5098 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5099 (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]. 23.37/22.46 5100 (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]. 23.37/22.46 5101 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -((all D (m1_pboole(D,A) -> -(r1_pboole(A,D,C) & r1_pboole(A,D,B)))) & r4_pboole(A,B,C)))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5102 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (A = k1_relat_1(B) <-> m1_pboole(B,A)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5103 (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]. 23.37/22.46 5104 (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]. 23.37/22.46 5105 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,B)),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B))))) # label(t36_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.46 5106 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))) & r6_pboole(A,k2_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))))))))) # label(t45_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5107 (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]. 23.37/22.47 5108 (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]. 23.37/22.47 5109 (exists A (m1_pboole(A,f1_s4_pboole) & (all B (r2_hidden(B,f1_s4_pboole) -> f2_s4_pboole(B) = k1_funct_1(A,B))))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5110 (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]. 23.37/22.47 5111 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5112 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5113 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5114 (all A all B all C all D (m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5115 (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]. 23.37/22.47 5116 (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]. 23.37/22.47 5117 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) & r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5118 (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]. 23.37/22.47 5119 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5120 (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]. 23.37/22.47 5121 (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]. 23.37/22.47 5122 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5123 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k5_pboole(A,B,C),k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t95_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5124 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5125 (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]. 23.37/22.47 5126 (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]. 23.37/22.47 5127 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,B,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]. 23.37/22.47 5128 (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]. 23.37/22.47 5129 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5130 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r7_pboole(A,B,C) -> r2_pboole(A,B,C)))))) # label(t144_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5131 (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]. 23.37/22.47 5132 (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]. 23.37/22.47 5133 (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]. 23.37/22.47 5134 (all A all B (m1_pboole(B,A) -> (v2_relat_1(B) <-> (all C -(v1_xboole_0(k1_funct_1(B,C)) & r2_hidden(C,A)))))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5135 (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]. 23.37/22.47 5136 (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]. 23.37/22.47 5137 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5138 (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]. 23.37/22.47 5139 (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]. 23.37/22.47 5140 (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]. 23.37/22.47 5141 (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]. 23.37/22.47 5142 (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]. 23.37/22.47 5143 (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]. 23.37/22.47 5144 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,B,C),C) & r6_pboole(A,k2_pboole(A,C,B),C)))))) # label(t24_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5145 (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]. 23.37/22.47 5146 (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]. 23.37/22.47 5147 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,C,D) -> r2_pboole(A,B,D)))))))) # label(t15_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5148 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k3_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5149 (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]. 23.37/22.47 5150 (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]. 23.37/22.47 5151 (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]. 23.37/22.47 5152 (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]. 23.37/22.47 5153 (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]. 23.37/22.47 5154 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A)) & r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)))))) # label(t67_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5155 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & -v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)))) # label(fc1_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5156 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_funct_1(B,D))) -> B = C))))) # label(t3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5157 (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]. 23.37/22.47 5158 (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]. 23.37/22.47 5159 (all A all B (m1_pboole(B,A) -> -(B != k1_pboole(A) & r5_pboole(A,B,B)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5160 (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]. 23.37/22.47 5161 (all A all B (m1_pboole(B,A) -> (v2_relat_1(B) <-> v2_pboole(B,A)))) # label(redefinition_v2_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5162 (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]. 23.37/22.47 5163 (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]. 23.37/22.47 5164 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r5_pboole(A,B,C) & r4_pboole(A,B,C)))))))) # label(t135_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5165 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))))))))) # label(t39_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5166 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k2_pboole(A,B,C),D) -> r2_pboole(A,B,D) & r2_pboole(A,C,D)))))))) # label(t43_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5167 (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]. 23.37/22.47 5168 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,B,D) & r5_pboole(A,C,D) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t123_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5169 (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]. 23.37/22.47 5170 (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]. 23.37/22.47 5171 (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]. 23.37/22.47 5172 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k12_pboole(A,B,C) <-> (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]. 23.37/22.47 5173 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (m4_pboole(C,A,B) & v2_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5174 (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]. 23.37/22.47 5175 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k5_pboole(A,B,C),A))) # label(dt_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5176 (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]. 23.37/22.47 5177 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v1_funcop_1(C) -> (all D (m1_pboole(D,A) -> (D = k14_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E))))))))))) # label(d25_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5178 (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,D) & r1_pboole(A,B,C)))))))) # label(t8_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5179 (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]. 23.37/22.47 5180 (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]. 23.37/22.47 5181 (all A all B all C (-v1_xboole_0(A) & m1_pboole(C,A) & m1_pboole(B,A) -> (r3_pboole(A,B,C) -> -r3_pboole(A,C,B)))) # label(antisymmetry_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5182 (all A (v1_funct_1(A) & v1_relat_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]. 23.37/22.47 5183 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(B = k1_pboole(A) & r4_pboole(A,B,B)))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5184 (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]. 23.37/22.47 5185 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k3_pboole(A,B,C) = k3_pboole(A,C,B))) # label(commutativity_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5186 (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]. 23.37/22.47 5187 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> ((all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k4_card_3(k5_relat_1(D,B)) = k1_funct_1(C,D))) <-> C = k6_pboole(A,B)))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5188 (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]. 23.37/22.47 5189 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,C,B) & v3_relat_1(B) -> v3_relat_1(C)))))) # label(t142_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5190 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(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]. 23.37/22.47 5191 (all A all B (v1_funct_1(k10_pboole(A,B)) & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5192 (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]. 23.37/22.47 5193 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> (r1_pboole(A,B,C) <-> r3_pboole(A,B,C)))) # label(redefinition_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5194 (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]. 23.37/22.47 5195 (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]. 23.37/22.47 5196 (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]. 23.37/22.47 5197 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,C,B),D) & r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5198 (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]. 23.37/22.47 5199 (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]. 23.37/22.47 5200 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5201 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),k1_pboole(A)) <-> r2_pboole(A,B,C)))))) # label(t58_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5202 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r4_pboole(A,B,D) & r2_pboole(A,D,E) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5203 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5204 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5205 (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]. 23.37/22.47 5206 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k3_pboole(A,B,k1_pboole(A)),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,k1_pboole(A),B),k1_pboole(A)))) # label(t55_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5207 (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]. 23.37/22.47 5208 (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]. 23.37/22.47 5209 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (r1_pboole(A,C,B) & m1_pboole(C,A))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5210 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k5_pboole(A,C,B) = k5_pboole(A,B,C))) # label(commutativity_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5211 (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]. 23.37/22.47 5212 (all A all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_2(B,k5_numbers,k3_finseq_2(k1_tarski(A))) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),B,C) = k2_finseq_2(C,A))) <-> k9_pboole(A) = B))) # label(d20_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5213 (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) & r5_pboole(A,B,D) & r2_pboole(A,C,D)))))))) # label(t116_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5214 (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]. 23.37/22.47 5215 (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]. 23.37/22.47 5216 (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]. 23.37/22.47 5217 (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]. 23.37/22.47 5218 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_xboole_0 = k1_funct_1(B,C))) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5219 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)) & r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C)))))) # label(t73_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5220 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5221 (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]. 23.37/22.47 5222 (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]. 23.37/22.47 5223 (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]. 23.37/22.47 5224 (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]. 23.37/22.47 5225 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D -(r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) & r2_hidden(D,A))) <-> r4_pboole(A,B,C)))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5226 (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]. 23.37/22.47 5227 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> r7_pboole(A,B,B))) # label(reflexivity_r7_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5228 (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]. 23.37/22.47 5229 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,D) & r1_pboole(A,B,C) -> r4_pboole(A,C,D)))))))) # label(t10_pboole) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5230 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v4_seq_2(k22_seq_1(A)) & k2_seq_2(k22_seq_1(A)) = np__0 -> k2_seq_2(A) = np__0 & v4_seq_2(A)))) # label(t28_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5231 $T # label(t11_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5232 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(B,C)))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) -> B = k2_seq_4(A)))))) # label(t63_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5233 $T # label(t13_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5234 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v2_seq_2(A) & v4_seqm_3(A) -> v4_seq_2(A)))) # label(t52_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5235 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> v4_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_seqm_3(B,C) != A))))))) # label(t35_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5236 $T # label(t6_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5237 (all A (v1_xreal_0(A) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,B,C) = k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)))) -> r1_xreal_0(A,np__0) | v4_seq_2(B)))))) # label(t47_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5238 (all A (v2_membered(A) -> ((exists B ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) & v1_xreal_0(B))) <-> v2_seq_4(A)))) # label(d2_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5239 (all A (v1_xreal_0(A) -> -(all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(B,A))))) # label(t10_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5240 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(A,D)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(k2_xcmplx_0(B,D),E)))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(B,D)))) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,np__0) & (all E (v1_xreal_0(E) -> -(-r1_xreal_0(k2_xcmplx_0(A,D),E) & r2_hidden(E,C))))))) -> B = A))))))) # label(t19_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5241 (all A (v1_xreal_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r2_hidden(k2_xcmplx_0(C,A),B)))) -> (all C (v1_xreal_0(C) -> -r2_hidden(C,B))) | (all C (v1_xreal_0(C) -> (exists D (v1_xreal_0(D) & r2_hidden(D,B) & -r1_xreal_0(D,C))))) | r1_xreal_0(A,np__0)))))) # label(t9_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5242 $T # label(t7_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5243 $T # label(t4_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5244 (all A (v2_membered(A) -> -(-v1_xboole_0(A) & (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(-r1_xreal_0(k2_xcmplx_0(B,C),D) & r2_hidden(D,A))))))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C))))))) & v2_seq_4(A)))) # label(t18_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5245 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v1_seq_2(A) & v3_seqm_3(A) -> v4_seq_2(A)))) # label(t51_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5246 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,A) -> r1_xreal_0(D,C)))) -> r1_xreal_0(k2_seq_4(A),C)))))))) # label(t62_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5247 $T # label(t20_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5248 (all A (v2_membered(A) -> -(-v1_xboole_0(A) & v1_seq_4(A) & (all B (v1_xreal_0(B) -> -((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & (all C (v1_xreal_0(C) -> -((all D (v1_xreal_0(D) -> -(r2_hidden(D,A) & -r1_xreal_0(D,k6_xcmplx_0(B,C))))) & -r1_xreal_0(C,np__0)))))))))) # label(t16_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5249 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -(v4_seq_2(A) & (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> -(v2_relat_1(B) & m1_seqm_3(B,A)))) & k2_seq_2(A) != np__0))) # label(t38_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5250 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k5_seq_4(A),k1_numbers))) # label(dt_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5251 (all A (v1_xreal_0(A) -> k5_seq_4(k1_seq_4(A)) = k4_seq_4(k1_seq_4(A)))) # label(t23_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5252 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v2_relat_1(B) & m1_seqm_3(B,A) -> k2_real_1(k2_seq_2(A)) = k2_seq_2(k18_seq_1(B))))) | np__0 = k2_seq_2(A)))) # label(t42_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5253 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> (m1_seqm_3(A,B) & v4_seq_2(B) -> k2_seq_2(B) = k2_seq_2(A)))))) # label(t30_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5254 (all A (v2_membered(A) -> (v1_seq_4(A) <-> (exists B (v1_xreal_0(B) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B))))))))) # label(d1_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5255 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v2_membered(B) -> (v1_seq_4(B) & r1_tarski(A,B) -> r1_xreal_0(k2_seq_4(A),k2_seq_4(B))))))) # label(t65_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5256 $T # label(t12_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5257 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> k2_seq_2(k22_seq_1(A)) = k18_complex1(k2_seq_2(A))))) # label(t27_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5258 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v5_seqm_3(A) -> v4_seq_2(A)))) # label(t39_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5259 (all A (v1_xreal_0(A) -> (all B (-v1_xboole_0(B) & v2_membered(B) -> ((all C (v1_xreal_0(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,B) -> r1_xreal_0(C,D)))) -> r1_xreal_0(C,A)))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,B) -> r1_xreal_0(A,C)))) -> k3_seq_4(B) = A))))) # label(t61_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5260 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) <-> (exists B (v1_xreal_0(B) & (all C (v1_xreal_0(C) -> -(r1_xreal_0(B,k18_complex1(C)) & r2_hidden(C,A)))) & -r1_xreal_0(B,np__0)))))) # label(t14_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5261 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> r1_xreal_0(k5_seq_4(A),k4_seq_4(A)) | v1_xboole_0(A)))) # label(t24_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5262 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> v4_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(C,D) & k8_funct_2(k5_numbers,k1_numbers,B,D) != k8_funct_2(k5_numbers,k1_numbers,A,D)))))))))) # label(t31_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5263 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k5_numbers,k1_numbers) & m2_relset_1(C,k5_numbers,k1_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(D,A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> r1_xreal_0(A,np__0) | v4_seq_2(C) & np__0 = k2_seq_2(C)))))))) # label(t46_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5264 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> -(v4_seq_2(A) & np__0 != k2_seq_2(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -v2_relat_1(k1_seqm_3(A,B))))))) # label(t37_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5265 $T # label(t5_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5266 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k3_seq_4(A) = k5_seq_4(A))) # label(redefinition_k5_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5267 (all A (v2_membered(A) -> (v2_seq_4(A) -> v1_xboole_0(A) | (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> -(-r1_xreal_0(C,np__0) & (all D (v1_xreal_0(D) -> -(r2_hidden(D,A) & -r1_xreal_0(k2_xcmplx_0(B,C),D))))))) & (all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) <-> k3_seq_4(A) = B)))))) # label(d5_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5268 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v5_seqm_3(B) & (exists C (k8_funct_2(k5_numbers,k1_numbers,B,C) = A & m2_subset_1(C,k1_numbers,k5_numbers))) | r2_hidden(A,k2_relat_1(B)) & v5_seqm_3(B) -> k2_seq_2(B) = A))))) # label(t40_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5269 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v6_seqm_3(A) & v3_seq_2(A) -> v4_seq_2(A)))) # label(t53_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5270 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_numbers)) -> -((all C (v1_xreal_0(C) -> (exists D ((exists E (v1_xreal_0(E) & r2_hidden(D,A) & -(r1_xreal_0(D,C) & r1_xreal_0(C,E)) & r2_hidden(E,B))) & v1_xreal_0(D))))) & (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> -(r2_hidden(C,A) & r1_xreal_0(D,C) & r2_hidden(D,B))))))))))) # label(t8_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5271 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> v4_seq_2(k22_seq_1(A))))) # label(t26_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5272 (all A (v2_membered(A) -> v1_xreal_0(k2_seq_4(A)))) # label(dt_k2_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5273 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v3_seq_4(A) -> -(r1_xreal_0(k4_seq_4(A),k5_seq_4(A)) & (exists B (v1_xreal_0(B) & (exists C (v1_xreal_0(C) & r2_hidden(B,A) & r2_hidden(C,A) & B != C))))) & -((all B (v1_xreal_0(B) -> (all C (v1_xreal_0(C) -> -(r2_hidden(B,A) & r2_hidden(C,A) & B != C))))) & -r1_xreal_0(k4_seq_4(A),k5_seq_4(A))) | v1_xboole_0(A)))) # label(t25_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5274 (all A (v1_xreal_0(A) -> v3_seq_4(k1_seq_4(A)))) # label(t15_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5275 (all A (v2_membered(A) & -v1_xboole_0(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(B,C)))) -> r1_xreal_0(B,k3_seq_4(A))))))) # label(t60_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5276 (all A (v1_xreal_0(A) -> m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)))) # label(dt_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5277 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> v4_seq_2(B) | r1_xreal_0(A,np__0)))))) # label(t43_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5278 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> -(v3_seq_2(A) & (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> -(m1_seqm_3(B,A) & v4_seq_2(B))))))) # label(t57_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5279 (all A (v1_xreal_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(C,A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> r1_xreal_0(A,np__0) | k2_seq_2(B) = np__0))))) # label(t44_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5280 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> m1_subset_1(k4_seq_4(A),k1_numbers))) # label(dt_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5281 $T # label(t2_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5282 (all A (v1_xreal_0(A) -> k5_seq_4(k1_seq_4(A)) = A & A = k4_seq_4(k1_seq_4(A)))) # label(t22_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5283 (all A (v1_xreal_0(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k7_xcmplx_0(np__1,k2_xcmplx_0(k2_nat_1(C,C),A)) = k8_funct_2(k5_numbers,k1_numbers,B,C))) -> np__0 = k2_seq_2(B) | r1_xreal_0(A,np__0)))))) # label(t48_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5284 $T # label(t1_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5285 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (v2_seq_2(A) & v4_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k2_seq_2(A),k8_funct_2(k5_numbers,k1_numbers,A,B))))))) # label(t55_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5286 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k5_numbers,k1_numbers) & v1_funct_2(C,k5_numbers,k1_numbers) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k7_xcmplx_0(B,k2_xcmplx_0(k2_nat_1(D,D),A)) = k8_funct_2(k5_numbers,k1_numbers,C,D))) -> r1_xreal_0(A,np__0) | v4_seq_2(C) & np__0 = k2_seq_2(C)))))))) # label(t50_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5287 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> k4_seq_4(A) = k2_seq_4(A))) # label(redefinition_k4_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5288 (all A (-v1_xboole_0(A) & v2_membered(A) -> (all B (v2_membered(B) -> (v2_seq_4(B) & r1_tarski(A,B) -> r1_xreal_0(k3_seq_4(B),k3_seq_4(A))))))) # label(t64_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.47 5289 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (all B (m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(A) -> k2_seq_2(A) = k2_seq_2(B) | (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (k8_funct_2(k5_numbers,k1_numbers,B,D) != k8_funct_2(k5_numbers,k1_numbers,A,D) & r1_xreal_0(C,D) & m2_subset_1(D,k1_numbers,k5_numbers)))))))))) # label(t32_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5290 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (all C (v2_membered(C) -> ((all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,A)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(E,k6_xcmplx_0(B,D))))) & -r1_xreal_0(D,np__0)))) & (all D (v1_xreal_0(D) -> (r2_hidden(D,C) -> r1_xreal_0(D,B)))) & (all D (v1_xreal_0(D) -> -((all E (v1_xreal_0(E) -> -(r2_hidden(E,C) & -r1_xreal_0(E,k6_xcmplx_0(A,D))))) & -r1_xreal_0(D,np__0)))) -> A = B))))))) # label(t17_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5291 (all A (m1_relset_1(A,k5_numbers,k1_numbers) -> (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & v5_seqm_3(A) -> v1_seq_1(A) & v4_seq_2(A) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A)))) # label(cc1_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5292 $T # label(t21_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5293 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v1_seq_2(A) & v3_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_xreal_0(k8_funct_2(k5_numbers,k1_numbers,A,B),k2_seq_2(A))))))) # label(t54_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5294 $T # label(t34_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5295 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) -> (v4_seq_2(B) -> v4_seq_2(k1_seqm_3(B,A)) & k2_seq_2(B) = k2_seq_2(k1_seqm_3(B,A))))))) # label(t33_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5296 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> (v5_seqm_3(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k2_seq_2(A) = k8_funct_2(k5_numbers,k1_numbers,A,B)))))) # label(t41_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5297 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_2(B,k5_numbers,k1_numbers) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_1(B) -> (v4_seq_2(B) & v5_seqm_3(A) -> k2_seq_2(k9_seq_1(A,B)) = k3_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) & k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B)) = k2_seq_2(k10_seq_1(A,B)) & k5_real_1(k2_seq_2(B),k8_funct_2(k5_numbers,k1_numbers,A,np__0)) = k2_seq_2(k10_seq_1(B,A)) & k2_seq_2(k11_seq_1(A,B)) = k4_real_1(k8_funct_2(k5_numbers,k1_numbers,A,np__0),k2_seq_2(B))))))) # label(t59_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5298 $T # label(t3_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5299 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (exists B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v6_seqm_3(k3_seqm_3(B,A)) & v7_seqm_3(B) & v1_seqm_3(B) & v1_funct_2(B,k5_numbers,k1_numbers))))) # label(t56_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5300 (all A (v2_membered(A) -> v1_xreal_0(k3_seq_4(A)))) # label(dt_k3_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5301 (all A (v1_funct_1(A) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k1_numbers,A,B) = k6_real_1(np__1,k1_nat_1(k2_nat_1(B,B),np__1)))) -> v4_seq_2(A) & np__0 = k2_seq_2(A)))) # label(t49_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5302 (all A (v2_membered(A) -> (v1_seq_4(A) -> v1_xboole_0(A) | (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & (all C (v1_xreal_0(C) -> -((all D (v1_xreal_0(D) -> -(-r1_xreal_0(D,k6_xcmplx_0(B,C)) & r2_hidden(D,A)))) & -r1_xreal_0(C,np__0)))) <-> k2_seq_4(A) = B)))))) # label(d4_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5303 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> (v2_seq_4(A) & v1_seq_4(A) <-> v3_seq_4(A)))) # label(d3_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5304 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> ((all B (v1_xreal_0(B) -> -(-r1_xreal_0(B,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (exists D (r1_xreal_0(C,D) & r1_xreal_0(B,k18_complex1(k5_real_1(k8_funct_2(k5_numbers,k1_numbers,A,D),k8_funct_2(k5_numbers,k1_numbers,A,C)))) & m2_subset_1(D,k1_numbers,k5_numbers)))))))) <-> v4_seq_2(A)))) # label(t58_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5305 (all A (v1_funct_1(A) & v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k6_real_1(np__1,k1_nat_1(B,np__1)) = k8_funct_2(k5_numbers,k1_numbers,A,B))) -> np__0 = k2_seq_2(A) & v4_seq_2(A)))) # label(t45_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5306 (all A (m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_2(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (v4_seq_2(A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k1_seqm_3(B,C) != A)) | k2_seq_2(A) = k2_seq_2(B)))))) # label(t36_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5307 (all A (v1_xreal_0(A) -> k1_tarski(A) = k1_seq_4(A))) # label(redefinition_k1_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5308 (all A (v1_funct_2(A,k5_numbers,k1_numbers) & m2_relset_1(A,k5_numbers,k1_numbers) & v1_funct_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k5_numbers,k1_numbers) & v1_funct_2(B,k5_numbers,k1_numbers) -> (m1_seqm_3(A,B) & v4_seq_2(B) -> v4_seq_2(A)))))) # label(t29_seq_4) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5309 (all A (m1_subset_1(A,f1_s1_multop_1) -> (all B (m1_subset_1(B,f2_s1_multop_1) -> (all C (m1_subset_1(C,f3_s1_multop_1) -> (exists D (m1_subset_1(D,f4_s1_multop_1) & p1_s1_multop_1(A,B,C,D))))))))) -> (exists A (v1_funct_2(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & m2_relset_1(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & (all B (m1_subset_1(B,f1_s1_multop_1) -> (all C (m1_subset_1(C,f2_s1_multop_1) -> (all D (m1_subset_1(D,f3_s1_multop_1) -> p1_s1_multop_1(B,C,D,k8_funct_2(k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1,A,k4_domain_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1,B,C,D))))))))) & v1_funct_1(A))) # label(s1_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5310 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) -> (all F (v1_funct_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) -> k2_multop_1(A,B,C,D,E,G,H,I) = k2_multop_1(A,B,C,D,F,G,H,I))))))) -> E = F))))))))))))) # label(t4_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5311 (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]. 23.37/22.48 5312 $T # label(dt_k3_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5313 (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(C) & v1_funct_1(F) & m1_subset_1(I,C) & m1_subset_1(J,D) & m1_subset_1(H,B) & m1_subset_1(G,A) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(A) -> 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]. 23.37/22.48 5314 (all A (-v1_xboole_0(A) -> (all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(B,C,D,E),A) & m2_relset_1(F,k4_zfmisc_1(B,C,D,E),A) -> (all G (v1_funct_1(G) & m2_relset_1(G,k4_zfmisc_1(B,C,D,E),A) & v1_funct_2(G,k4_zfmisc_1(B,C,D,E),A) -> ((all H all I all J all K (r2_hidden(K,E) & r2_hidden(J,D) & r2_hidden(I,C) & r2_hidden(H,B) -> k1_funct_1(F,k4_mcart_1(H,I,J,K)) = k1_funct_1(G,k4_mcart_1(H,I,J,K)))) -> F = G))))))) # label(t6_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5315 $T # label(dt_k1_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5316 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_1(E) -> (all F (v1_funct_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,F,k4_domain_1(A,B,C,G,H,I)) = k8_funct_2(k3_zfmisc_1(A,B,C),D,E,k4_domain_1(A,B,C,G,H,I)))))))) -> F = E))))))))))))) # label(t3_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5317 (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 ((all B (m1_subset_1(B,f1_s2_multop_1) -> (all C (m1_subset_1(C,f1_s2_multop_1) -> (all D (m1_subset_1(D,f1_s2_multop_1) -> p1_s2_multop_1(B,C,D,k2_multop_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,A,B,C,D)))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & v1_funct_2(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & v1_funct_1(A))) # label(s2_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5318 (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]. 23.37/22.48 5319 (exists 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) & (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)))))))))) & 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) & v1_funct_1(A))) # label(s7_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5320 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(E) & 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_funct_2(E,k3_zfmisc_1(A,B,C),D) & -v1_xboole_0(B) -> k1_multop_1(E,F,G,H) = k2_multop_1(A,B,C,D,E,F,G,H))) # label(redefinition_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5321 (all A (v1_funct_1(A) & v1_relat_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]. 23.37/22.48 5322 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) -> (all G (v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(G) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k8_funct_2(k4_zfmisc_1(A,B,C,D),E,F,k5_domain_1(A,B,C,D,H,I,J,K)) = k8_funct_2(k4_zfmisc_1(A,B,C,D),E,G,k5_domain_1(A,B,C,D,H,I,J,K)))))))))) -> G = F))))))))))))))) # label(t7_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5323 $T # label(t1_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5324 (all A (-v1_xboole_0(A) -> (all B all C all D all E (m2_relset_1(E,k3_zfmisc_1(B,C,D),A) & v1_funct_2(E,k3_zfmisc_1(B,C,D),A) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k3_zfmisc_1(B,C,D),A) & m2_relset_1(F,k3_zfmisc_1(B,C,D),A) -> ((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]. 23.37/22.48 5325 (exists A (v1_funct_2(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1) & m2_relset_1(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1) & (all B (m1_subset_1(B,f1_s3_multop_1) -> (all C (m1_subset_1(C,f2_s3_multop_1) -> (all D (m1_subset_1(D,f3_s3_multop_1) -> 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))))))) & v1_funct_1(A))) # label(s3_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5326 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_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) & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k4_multop_1(A,B,C,D,E,F,H,I,J,K) = k4_multop_1(A,B,C,D,E,G,H,I,J,K))))))))) -> F = G))))))))))))))) # label(t8_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5327 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D all E k1_funct_1(A,k4_mcart_1(B,C,D,E)) = k3_multop_1(A,B,C,D,E)))) # label(d2_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5328 (exists A (v1_funct_1(A) & v1_funct_2(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1) & m2_relset_1(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1) & (all B (m1_subset_1(B,f1_s4_multop_1) -> (all C (m1_subset_1(C,f2_s4_multop_1) -> (all D (m1_subset_1(D,f3_s4_multop_1) -> k2_multop_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1,f4_s4_multop_1,A,B,C,D) = f5_s4_multop_1(B,C,D))))))))) # label(s4_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5329 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(C) & v1_funct_1(F) & m1_subset_1(G,A) & m1_subset_1(H,B) & m1_subset_1(I,C) & m1_subset_1(J,D) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k4_multop_1(A,B,C,D,E,F,G,H,I,J),E))) # label(dt_k4_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5330 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(H,C) & m1_subset_1(G,B) & m1_subset_1(F,A) & -v1_xboole_0(B) -> 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]. 23.37/22.48 5331 $T # label(t5_multop_1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5332 (all A (m1_subset_1(A,f1_s5_multop_1) -> (all B (m1_subset_1(B,f2_s5_multop_1) -> (all C (m1_subset_1(C,f3_s5_multop_1) -> (all D (m1_subset_1(D,f4_s5_multop_1) -> (exists E (m1_subset_1(E,f5_s5_multop_1) & p1_s5_multop_1(A,B,C,D,E))))))))))) -> (exists A (m2_relset_1(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & (all B (m1_subset_1(B,f1_s5_multop_1) -> (all C (m1_subset_1(C,f2_s5_multop_1) -> (all D (m1_subset_1(D,f3_s5_multop_1) -> (all E (m1_subset_1(E,f4_s5_multop_1) -> p1_s5_multop_1(B,C,D,E,k8_funct_2(k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1,A,k5_domain_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1,B,C,D,E))))))))))) & v1_funct_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]. 23.37/22.48 5333 (exists A (-v1_realset1(A) & -v1_xboole_0(A))) # label(rc2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5334 (all A all B all C (m1_realset1(C,A,B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> k1_realset1(B,C) = k2_realset1(A,B,C))) # label(redefinition_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5335 (all A all B (m1_subset_1(B,A) -> (exists C m3_realset1(C,A,B)))) # label(existence_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5336 (all A (-v1_realset1(A) -> (all B ((exists C (k1_tarski(C) = B & m1_subset_1(C,A))) <-> m4_realset1(B,A))))) # label(d10_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5337 (all A (-v1_xboole_0(A) -> ((all B -v1_xboole_0(k4_xboole_0(A,k1_tarski(B)))) <-> -v1_realset1(A)))) # label(t4_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5338 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B))) <-> m2_realset1(C,A,B)))))) # label(d6_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5339 $T # label(dt_k1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5340 (all A (-v1_realset1(A) -> (exists B (m4_realset1(B,A) & -v1_xboole_0(B))))) # label(rc3_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5341 (all A all B (m1_subset_1(B,A) -> (exists C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & (all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B))))) & v1_funct_1(C))))) # label(t10_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5342 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (exists C (m1_subset_1(C,k1_zfmisc_1(A)) & (all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))))))) # label(t2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5343 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_realset1(A,B)) & v1_funct_1(k1_realset1(A,B)))) # label(fc2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5344 (all A (v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc3_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5345 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> k4_realset1(A,B,C) = k1_realset1(C,k4_xboole_0(A,k1_tarski(B))))))))) # label(d9_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5346 (all A (-(-v1_realset1(A) & (all B all C -(C != B & r2_hidden(C,A) & r2_hidden(B,A)))) & -(v1_realset1(A) & (exists B exists C (r2_hidden(B,A) & r2_hidden(C,A) & B != C))))) # label(t14_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5347 (all A (-v1_realset1(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (r2_realset1(A,B,C) <-> v1_funct_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C))) & m2_relset_1(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C))) & v1_funct_2(k4_xboole_0(k1_realset1(B,A),k1_tarski(C)),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(A,k1_tarski(C))),k4_xboole_0(A,k1_tarski(C))) & m1_realset1(k4_xboole_0(A,k1_tarski(C)),A,B)))))))) # label(d5_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5348 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> v1_funct_1(k1_realset1(C,B)) & v1_funct_2(k1_realset1(C,B),k2_zfmisc_1(B,B),B) & m2_relset_1(k1_realset1(C,B),k2_zfmisc_1(B,B),B))))) # label(t9_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5349 (all A all B (m1_subset_1(B,A) & -v1_realset1(A) -> k1_tarski(B) = k5_realset1(A,B))) # label(redefinition_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5350 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (m3_realset1(C,A,B) <-> (all D (r2_hidden(D,k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B)))) -> r2_hidden(k1_funct_1(C,D),k4_xboole_0(A,k1_tarski(B)))))))))) # label(d8_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5351 (all A all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C))))) # label(dt_m3_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5352 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r2_hidden(B,k2_zfmisc_1(A,A)) -> r2_hidden(k1_funct_1(C,B),A)))) # label(t1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5353 (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) -> (exists C m1_realset1(C,A,B)))) # label(existence_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5354 (all A (-v1_realset1(A) -> -v1_xboole_0(A))) # label(cc1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5355 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))) <-> m1_realset1(C,A,B)))))) # label(d2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5356 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) -> -v1_realset1(A)))) # label(t7_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5357 (all A (v1_realset1(A) <-> -(-v1_xboole_0(A) & (all B k1_tarski(B) != A)))) # label(d4_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5358 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C m2_realset1(C,A,B)))) # label(existence_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5359 (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_realset1(C,A,B) -> v1_funct_1(k1_realset1(B,C)) & m2_relset_1(k1_realset1(B,C),k2_zfmisc_1(C,C),C) & v1_funct_2(k1_realset1(B,C),k2_zfmisc_1(C,C),C))))) # label(t3_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5360 (all A all B all C (m2_realset1(C,A,B) & m1_subset_1(B,k1_zfmisc_1(A)) -> v1_funct_1(k3_realset1(A,B,C)) & v1_funct_2(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B) & m2_relset_1(k3_realset1(A,B,C),k2_zfmisc_1(B,B),B))) # label(dt_k3_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5361 (exists A (v1_realset1(A) & -v1_xboole_0(A))) # label(rc1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5362 $T # label(dt_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5363 (all A (-v1_xboole_0(A) -> -(v1_realset1(A) & (all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B)))))))) # label(t6_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5364 (all A all B (m1_subset_1(B,A) & -v1_realset1(A) -> m4_realset1(k5_realset1(A,B),A))) # label(dt_k5_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5365 (all A (-v1_realset1(A) -> (all B (m4_realset1(B,A) -> -v1_xboole_0(k4_xboole_0(A,B)))))) # label(t12_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5366 (all A all B (v1_relat_1(A) -> v1_relat_1(k1_realset1(A,B)))) # label(fc1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5367 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (exists C (v1_funct_1(C) & (all D (r2_hidden(D,k2_zfmisc_1(B,B)) -> r2_hidden(k1_funct_1(C,D),B))) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A))))) # label(t8_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5368 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,k2_zfmisc_1(C,C)) -> r2_hidden(k1_funct_1(B,D),C))) <-> r1_realset1(A,B,C)))))) # label(d1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5369 (all A (-v1_realset1(A) -> (all B (m1_subset_1(B,A) -> (all C (m3_realset1(C,A,B) -> v1_funct_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B)))) & m2_relset_1(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & v1_funct_2(k1_realset1(C,k4_xboole_0(A,k1_tarski(B))),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))))))))) # label(t11_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5370 (all A all B all C (m1_subset_1(B,A) & m3_realset1(C,A,B) & -v1_realset1(A) -> v1_funct_1(k4_realset1(A,B,C)) & v1_funct_2(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))) & m2_relset_1(k4_realset1(A,B,C),k2_zfmisc_1(k4_xboole_0(A,k1_tarski(B)),k4_xboole_0(A,k1_tarski(B))),k4_xboole_0(A,k1_tarski(B))))) # label(dt_k4_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5371 (all A all B all C (v1_funct_1(B) & m1_realset1(C,A,B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> v1_funct_1(k2_realset1(A,B,C)) & v1_funct_2(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C) & m2_relset_1(k2_realset1(A,B,C),k2_zfmisc_1(C,C),C))) # label(dt_k2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5372 (all A (-v1_realset1(A) -> (exists B m4_realset1(B,A)))) # label(existence_m4_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5373 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(v1_realset1(B) & (exists C (m1_subset_1(C,A) & (exists D (r2_hidden(C,B) & C != D & r2_hidden(D,B) & m1_subset_1(D,A)))))) & -((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(C,B) & r2_hidden(D,B) & D != C))))) & -v1_realset1(B)))) # label(t15_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5374 (all A (v1_finset_1(A) -> (-r1_xreal_0(np__2,k4_card_1(A)) <-> v1_realset1(A)))) # label(t13_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5375 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_realset1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(A)))))) # label(dt_m1_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5376 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> k1_realset1(C,B) = k3_realset1(A,B,C))))) # label(d7_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5377 (exists A ((all B (m1_subset_1(B,A) -> -v1_xboole_0(k4_xboole_0(A,k1_tarski(B))))) & -v1_xboole_0(A))) # label(t5_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5378 (all A all B (-v1_realset1(A) & m4_realset1(B,A) -> -v1_xboole_0(k4_xboole_0(A,B)))) # label(fc4_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5379 (all A (v1_relat_1(A) -> (all B k7_relat_1(A,k2_zfmisc_1(B,B)) = k1_realset1(A,B)))) # label(d3_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5380 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_realset1(C,A,B) -> m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C))))) # label(dt_m2_realset1) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5381 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_funct_1(k6_funct_6(B),A) = C & r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(D,A),k1_relat_1(k4_funct_5(B))) & k1_funct_1(k4_funct_5(B),k4_tarski(D,A)) = k1_funct_1(C,D))) & k1_relat_1(C) = k10_relat_1(B,k1_funct_6(k2_relat_1(B)))))))) # label(t51_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5382 (all A (-v1_xboole_0(A) -> k4_card_3(k9_finseq_1(A)) = k4_finseq_2(np__1,A))) # label(t4_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5383 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> r2_hidden(k4_funct_5(D),k1_funct_2(k2_zfmisc_1(A,B),C)) & r2_hidden(k6_funct_5(D),k1_funct_2(k2_zfmisc_1(B,A),C))))) # label(t20_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5384 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_relat_1(k6_funct_5(k2_funcop_1(A,B))) = k2_zfmisc_1(k1_relat_1(B),A) & r1_tarski(k2_relat_1(k6_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)) & r1_tarski(k2_relat_1(k4_funct_5(k2_funcop_1(A,B))),k2_relat_1(B)) & k2_zfmisc_1(A,k1_relat_1(B)) = k1_relat_1(k4_funct_5(k2_funcop_1(A,B))))) # label(t17_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5385 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k10_funct_6(A)) & v1_funcop_1(k10_funct_6(A)) & v1_funct_1(k10_funct_6(A)))) # label(dt_k10_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5386 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> A = k1_xboole_0 | k10_funct_6(k10_funct_6(D)) = D | B = k1_xboole_0))) # label(t87_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5387 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> (r2_hidden(A,a_3_0_funct_6(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(E,B) & A = k11_finseq_1(E,F,G) & m1_subset_1(G,D) & m1_subset_1(F,C)))))) # label(fraenkel_a_3_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5388 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(D)) -> (all E all F (k1_funct_1(k7_funct_6(k10_finseq_1(C,D)),k10_finseq_1(A,B)) = k10_finseq_1(E,F) <-> k4_tarski(E,F) = k1_funct_1(k15_funct_3(C,D),k4_tarski(A,B))))))))) # label(t68_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5389 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(C,k1_relat_1(D)) -> k5_funct_6(k2_funcop_1(B,D),A,C) = k1_funct_1(D,C)))) # label(t48_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5390 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(k2_zfmisc_1(A,B),C)) -> k1_xboole_0 = k2_zfmisc_1(A,B) | r2_hidden(k3_funct_5(D),k1_funct_2(A,k1_funct_2(B,C))) & r2_hidden(k5_funct_5(D),k1_funct_2(B,k1_funct_2(A,C)))))) # label(t19_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5391 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k4_card_3(A),k1_funct_2(k1_relat_1(A),k3_card_3(A))))) # label(t10_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5392 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> k4_card_3(k11_finseq_1(A,B,C)) = a_3_0_funct_6(A,B,C))))))) # label(t7_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5393 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k1_relat_1(k7_funct_6(k10_finseq_1(A,B))) = k4_card_3(k10_finseq_1(k1_relat_1(A),k1_relat_1(B))) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(k7_funct_6(k10_finseq_1(A,B)),k10_finseq_1(C,D)) = k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,D)))) & k2_relat_1(k7_funct_6(k10_finseq_1(A,B))) = k4_card_3(k10_finseq_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t65_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5394 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_funct_1(B,A) & r2_hidden(A,k1_relat_1(B)) -> r2_hidden(A,k1_relat_1(k3_funct_6(B))) & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) & k1_relat_1(C) = k1_funct_1(k2_funct_6(B),A) & r2_hidden(A,k1_relat_1(k2_funct_6(B)))))))) # label(t31_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5395 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> v1_relat_1(k1_funct_1(k6_funct_6(B),A)) & v1_funct_1(k1_funct_1(k6_funct_6(B),A))))) # label(t50_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5396 (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(B) & k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_wellord2(k1_funct_1(B,D),k1_funct_1(C,D)))) -> r2_wellord2(k4_card_3(B),k4_card_3(C))))))) # label(t69_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5397 (all A all B all C ((exists D exists E (r2_hidden(D,B) & r2_hidden(E,C) & k10_finseq_1(D,E) = A)) <-> r2_hidden(A,k4_card_3(k10_finseq_1(B,C))))) # label(t2_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5398 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k3_funct_6(A) <-> (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k1_funct_1(B,C) = k2_funct_5(k1_funct_1(A,C)))) & k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A)))))))) # label(d3_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5399 (all A (k4_funct_6(k9_finseq_1(A)) = A & A = k3_card_3(k9_finseq_1(A)))) # label(t39_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5400 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k1_relat_1(B) = A -> r2_wellord2(k4_card_3(B),k4_card_3(k5_relat_1(C,B)))))))) # label(t71_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5401 (all A all B all C k2_funcop_1(B,k1_funct_2(A,C)) = k9_funct_6(A,k2_funcop_1(B,C))) # label(t82_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5402 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) & r2_hidden(A,k1_relat_1(C)) -> k5_funct_6(C,A,B) = k1_funct_1(D,B)))))) # label(t44_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5403 (all A all B all C all D (r2_hidden(A,k4_card_3(k11_finseq_1(B,C,D))) <-> (exists E exists F exists G (r2_hidden(G,D) & A = k11_finseq_1(E,F,G) & r2_hidden(F,C) & r2_hidden(E,B))))) # label(t3_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5404 (all A k1_xboole_0 = k8_funct_6(k1_xboole_0,A)) # label(t73_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5405 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k9_funct_6(A,B)) & v1_relat_1(k9_funct_6(A,B)))) # label(dt_k9_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5406 (all A all B k9_finseq_1(k1_funct_2(A,B)) = k8_funct_6(k9_finseq_1(A),B)) # label(t74_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5407 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_relat_1(k6_funct_6(A)) = k4_funct_6(k2_funct_6(A)) & r1_tarski(k2_relat_1(k6_funct_6(A)),k4_card_3(k3_funct_6(A))))) # label(t49_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5408 (all A (v1_funct_1(A) & v1_relat_1(A) -> k9_finseq_1(k2_relat_1(A)) = k3_funct_6(k9_finseq_1(A)) & k9_finseq_1(k1_relat_1(A)) = k2_funct_6(k9_finseq_1(A)))) # label(t33_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5409 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k4_card_3(k10_finseq_1(A,B)) = a_2_0_funct_6(A,B))))) # label(t5_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5410 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k6_funct_6(A)) & v1_relat_1(k6_funct_6(A)))) # label(dt_k6_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5411 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)))) # label(dt_k2_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5412 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_relat_1(k6_funct_6(k9_finseq_1(A))) = k1_relat_1(A) & (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(k6_funct_6(k9_finseq_1(A)),B) = k9_finseq_1(k1_funct_1(A,B)))))) # label(t61_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5413 (all A (v1_relat_1(A) & v1_funct_1(A) -> k6_funct_6(A) = k3_funct_5(k7_relat_1(k6_funct_5(A),k2_zfmisc_1(k4_funct_6(k2_funct_6(A)),k1_relat_1(A)))))) # label(d6_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5414 $T # label(dt_k1_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5415 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) & r1_tarski(k1_relat_1(F),A) -> -r2_hidden(k6_funct_5(F),k4_partfun1(k2_zfmisc_1(B,A),C)) & -r2_hidden(k4_funct_5(F),k4_partfun1(k2_zfmisc_1(A,B),C)) | r2_hidden(F,k4_partfun1(A,k4_partfun1(B,C)))))) # label(t26_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5416 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(k6_funct_6(k10_finseq_1(A,B)),C) = k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(k6_funct_6(k10_finseq_1(A,B))) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t62_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5417 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k5_funct_6(k11_finseq_1(C,B,D),np__2,A) = k1_funct_1(B,A) & k5_funct_6(k10_finseq_1(C,B),np__2,A) = k1_funct_1(B,A)))))))) # label(t46_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5418 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k2_funct_6(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_relat_1(B)) & k2_funcop_1(A,k2_relat_1(B)) = k3_funct_6(k2_funcop_1(A,B)))) # label(t36_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5419 (all A (v1_relat_1(A) & v1_funct_1(A) -> k4_funct_6(A) = k1_setfam_1(k2_relat_1(A)))) # label(d4_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5420 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (A = k1_relat_1(F) & r1_tarski(k2_relat_1(F),k4_partfun1(D,E)) -> -r2_hidden(k6_funct_5(F),k1_funct_2(k2_zfmisc_1(B,A),C)) & -r2_hidden(k4_funct_5(F),k1_funct_2(k2_zfmisc_1(A,B),C)) | r2_hidden(F,k1_funct_2(A,k1_funct_2(B,C)))))) # label(t22_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5421 (all A all B (k1_xboole_0 != A -> k3_card_3(k2_funcop_1(A,B)) = B & B = k4_funct_6(k2_funcop_1(A,B)))) # label(t43_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5422 $T # label(dt_k4_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5423 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_funct_1(C,A) = D & k1_funct_1(k6_funct_6(C),B) = E & r2_hidden(B,k1_relat_1(k6_funct_6(C))) & r2_hidden(A,k1_relat_1(C)) -> k1_funct_1(E,A) = k1_funct_1(D,B)))))))) # label(t54_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.48 5424 (all A (v1_funct_1(A) & v1_relat_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> k2_funcop_1(k1_relat_1(A),k1_xboole_0) = k8_funct_6(A,k1_xboole_0)))) # label(t72_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5425 (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) -> k11_finseq_1(k2_relat_1(A),k2_relat_1(B),k2_relat_1(C)) = k3_funct_6(k11_finseq_1(A,B,C)) & k2_funct_6(k11_finseq_1(A,B,C)) = k11_finseq_1(k1_relat_1(A),k1_relat_1(B),k1_relat_1(C)))))))) # label(t35_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5426 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (all G all H (r2_hidden(G,A) & F = k1_funct_1(k10_funct_6(D),H) & E = k1_funct_1(D,G) & r2_hidden(H,B) -> A = k1_relat_1(F) & k1_relat_1(E) = B & r1_tarski(k2_relat_1(F),C) & r1_tarski(k2_relat_1(E),C) & k1_funct_1(E,H) = k1_funct_1(F,G))))))) | B = k1_xboole_0 | k1_xboole_0 = A))) # label(t86_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5427 (all A k1_xboole_0 = k9_funct_6(A,k1_xboole_0)) # label(t79_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5428 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k4_partfun1(k2_zfmisc_1(A,B),C)) -> r2_hidden(k3_funct_5(D),k4_partfun1(A,k4_partfun1(B,C))) & r2_hidden(k5_funct_5(D),k4_partfun1(B,k4_partfun1(A,C)))))) # label(t23_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5429 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k4_partfun1(A,k4_partfun1(B,C))) -> r2_hidden(k4_funct_5(D),k4_partfun1(k2_zfmisc_1(A,B),C)) & r2_hidden(k6_funct_5(D),k4_partfun1(k2_zfmisc_1(B,A),C))))) # label(t24_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5430 (all A all B (r2_hidden(A,k4_card_3(k9_finseq_1(B))) <-> (exists C (A = k9_finseq_1(C) & r2_hidden(C,B))))) # label(t1_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5431 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(A) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(A)) -> k1_funct_2(k1_funct_1(A,D),B) = k1_funct_1(C,D))) <-> k8_funct_6(A,B) = C))))) # label(d8_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5432 (all A all B all C (k2_funcop_1(k2_zfmisc_1(B,A),C) = k6_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))) & k2_funcop_1(k2_zfmisc_1(A,B),C) = k4_funct_5(k2_funcop_1(A,k2_funcop_1(B,C))))) # label(t15_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5433 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_funct_6(A)) & v1_relat_1(k3_funct_6(A)))) # label(dt_k3_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5434 $T # label(d10_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5435 (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) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (C = k1_funct_1(B,A) & k1_funct_1(k7_funct_6(B),D) = E & r2_hidden(D,k4_card_3(k2_funct_6(B))) & r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(D,A),k1_relat_1(C)) & r2_hidden(E,k4_card_3(k3_funct_6(B))) & k1_funct_1(C,k1_funct_1(D,A)) = k1_funct_1(E,A)))))))))) # label(t57_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5436 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k1_funct_6(k1_xboole_0) = k1_xboole_0 & k1_enumset1(A,B,C) = k1_funct_6(k1_enumset1(A,B,C)) & k1_funct_6(k2_tarski(A,B)) = k2_tarski(A,B) & k1_funct_6(k1_tarski(A)) = k1_tarski(A))))))) # label(t29_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5437 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> (all C (r2_hidden(C,k1_relat_1(B)) -> k1_funct_1(k6_funct_6(k2_funcop_1(A,B)),C) = k2_funcop_1(A,k1_funct_1(B,C)))) & k1_relat_1(B) = k1_relat_1(k6_funct_6(k2_funcop_1(A,B)))))) # label(t63_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5438 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(k10_funct_6(A))) -> v1_relat_1(k1_funct_1(k10_funct_6(A),B)) & v1_funct_1(k1_funct_1(k10_funct_6(A),B)))))) # label(t84_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5439 (all A r1_tarski(k1_funct_6(A),A)) # label(t27_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5440 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k4_card_3(k2_funct_6(C))) & r2_hidden(A,k1_relat_1(B)) -> k5_funct_6(C,A,k1_funct_1(B,A)) = k5_funct_6(k7_funct_6(C),B,A)))))) # label(t56_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5441 (all A all B all C k10_finseq_1(k1_funct_2(A,B),k1_funct_2(A,C)) = k9_funct_6(A,k10_finseq_1(B,C))) # label(t81_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5442 (all A (k1_xboole_0 = k4_funct_6(k2_funcop_1(k1_xboole_0,A)) & k3_card_3(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t42_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5443 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (A != k1_xboole_0 -> k2_relat_1(B) = k2_relat_1(k6_funct_5(k2_funcop_1(A,B))) & k2_relat_1(k4_funct_5(k2_funcop_1(A,B))) = k2_relat_1(B)))) # label(t18_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5444 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k4_finseq_2(A,B) = k4_card_3(k2_finseq_2(A,B)))))) # label(t9_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5445 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_0_funct_6(B,C)) <-> (exists D exists E (m1_subset_1(D,B) & k10_finseq_1(D,E) = A & m1_subset_1(E,C)))))) # label(fraenkel_a_2_0_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5446 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(B)) -> (all D all E (k1_funct_1(k13_funct_3(B,C),A) = k4_tarski(D,E) <-> k10_finseq_1(D,E) = k1_funct_1(k6_funct_6(k10_finseq_1(B,C)),A)))))))) # label(t67_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5447 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k10_relat_1(A,k1_funct_6(k2_relat_1(A))) & (all C (r2_hidden(C,k10_relat_1(A,k1_funct_6(k2_relat_1(A)))) -> k1_funct_1(B,C) = k1_funct_5(k1_funct_1(A,C)))) <-> k2_funct_6(A) = B))))) # label(d2_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5448 (all A all B all C (k4_funct_6(k11_finseq_1(A,B,C)) = k3_xboole_0(k3_xboole_0(A,B),C) & k3_card_3(k11_finseq_1(A,B,C)) = k2_xboole_0(k2_xboole_0(A,B),C))) # label(t41_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5449 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> k1_relat_1(k2_funct_6(A)) = k1_relat_1(A))) # label(t89_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5450 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k10_relat_1(B,k1_funct_6(k2_relat_1(B)))) <-> v1_relat_1(k1_funct_1(B,A)) & v1_funct_1(k1_funct_1(B,A)) & r2_hidden(A,k1_relat_1(B))))) # label(t28_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5451 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_relat_1(k1_funct_1(C,A)) & v1_funct_1(k1_funct_1(C,A)) & r2_hidden(B,k1_relat_1(k6_funct_6(C))) & r2_hidden(A,k1_relat_1(C)) -> k5_funct_6(k6_funct_6(C),B,A) = k5_funct_6(C,A,B)))) # label(t55_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5452 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__2,A) = k4_card_3(k10_finseq_1(A,A)))) # label(t6_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5453 (all A all B k9_funct_6(A,k9_finseq_1(B)) = k9_finseq_1(k1_funct_2(A,B))) # label(t80_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5454 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r2_wellord2(k1_funct_2(k3_card_3(k2_card_3(B)),A),k4_card_3(k8_funct_6(B,A))))) # label(t77_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5455 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k9_funct_6(A,B) <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_2(A,k1_funct_1(B,D)))) & k1_relat_1(C) = k1_relat_1(B)))))) # label(d9_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5456 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k10_finseq_1(k1_relat_1(A),k1_relat_1(B)) = k2_funct_6(k10_finseq_1(A,B)) & k3_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k2_relat_1(A),k2_relat_1(B)))))) # label(t34_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5457 $T # label(d11_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5458 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_funct_2(A,k1_relat_1(B)) = k1_relat_1(k7_funct_6(k2_funcop_1(A,B))) & k1_funct_2(A,k2_relat_1(B)) = k2_relat_1(k7_funct_6(k2_funcop_1(A,B))) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,k1_relat_1(B))) -> k5_relat_1(C,B) = k1_funct_1(k7_funct_6(k2_funcop_1(A,B)),C)))))) # label(t66_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5459 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_funct_6(A)) & v1_funct_1(k7_funct_6(A)))) # label(dt_k7_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5460 $T # label(dt_k5_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5461 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k9_finseq_1(B),np__1,A) & k1_funct_1(B,A) = k5_funct_6(k11_finseq_1(B,C,D),np__1,A) & k5_funct_6(k10_finseq_1(B,C),np__1,A) = k1_funct_1(B,A)))))))) # label(t45_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5462 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_5(A) = k5_funct_5(k2_funct_4(A)) & k4_funct_5(A) = k2_funct_4(k6_funct_5(A)))) # label(t13_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5463 (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) -> -(r2_hidden(C,k4_card_3(k2_funct_6(A))) & (all D (v1_relat_1(D) & v1_funct_1(D) -> -(k1_funct_1(B,C) = D & k10_relat_1(A,k1_funct_6(k2_relat_1(A))) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(k4_funct_5(A),k4_tarski(E,k1_funct_1(C,E))) = k1_funct_1(D,E))))))))) & k4_card_3(k2_funct_6(A)) = k1_relat_1(B) <-> k7_funct_6(A) = B))))) # label(d7_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5464 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k8_funct_6(A,B)) & v1_relat_1(k8_funct_6(A,B)))) # label(dt_k8_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5465 (all A all B all C all D all E all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> r2_hidden(F,k1_funct_2(k2_zfmisc_1(A,B),C)) | -r2_hidden(k5_funct_5(F),k1_funct_2(B,k1_funct_2(A,C))) & -r2_hidden(k3_funct_5(F),k1_funct_2(A,k1_funct_2(B,C)))))) # label(t21_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5466 (all A (v1_funct_1(A) & v1_relat_1(A) -> k9_funct_6(k1_xboole_0,A) = k2_funcop_1(k1_relat_1(A),k1_tarski(k1_xboole_0)))) # label(t78_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5467 (all A (v1_funct_1(A) & v1_relat_1(A) -> (-r2_hidden(k1_xboole_0,k2_relat_1(A)) -> (v2_funct_1(k7_funct_6(A)) <-> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(B,k2_relat_1(A)) -> v2_funct_1(B)))))))) # label(t59_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5468 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k2_relat_1(C)) & (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k2_relat_1(C)) -> r2_hidden(A,k1_relat_1(D))))) -> r2_hidden(A,k1_relat_1(k6_funct_6(C)))))))) # label(t53_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5469 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__3,A) = k4_card_3(k11_finseq_1(A,A,A)))) # label(t8_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.37/22.49 5470 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k1_funct_2(A,k1_funct_2(B,C))) -> r2_hidden(k10_funct_6(D),k1_funct_2(B,k1_funct_2(A,C))) | k1_xboole_0 = B | k1_xboole_0 = A))) # label(t85_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5471 (all A all B (r1_tarski(A,k1_funct_6(B)) -> k1_funct_6(A) = A)) # label(t30_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5472 (all A all B all C k2_funcop_1(A,k1_funct_2(B,C)) = k8_funct_6(k2_funcop_1(A,B),C)) # label(t76_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5473 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (B != k1_xboole_0 -> ((all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(A,k1_funct_1(B,C)))) <-> r2_hidden(A,k4_funct_6(B)))))) # label(t37_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5474 (all A all B all C (k1_xboole_0 != k2_zfmisc_1(A,B) -> k2_funcop_1(A,k2_funcop_1(B,C)) = k3_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)) & k2_funcop_1(B,k2_funcop_1(A,C)) = k5_funct_5(k2_funcop_1(k2_zfmisc_1(A,B),C)))) # label(t14_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5475 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k5_funct_6(A,B,C) = k1_funct_1(k4_funct_5(A),k4_tarski(B,C))))) # label(d5_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5476 (all A (v1_funct_1(A) & v1_relat_1(A) -> k4_card_3(k9_finseq_1(k2_relat_1(A))) = k2_relat_1(k7_funct_6(k9_finseq_1(A))) & (all B (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(k7_funct_6(k9_finseq_1(A)),k9_finseq_1(B)) = k9_finseq_1(k1_funct_1(A,B)))) & k4_card_3(k9_finseq_1(k1_relat_1(A))) = k1_relat_1(k7_funct_6(k9_finseq_1(A))))) # label(t64_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5477 (all A (v1_funct_1(A) & v1_relat_1(A) -> k4_card_3(k3_funct_6(A)) = k2_relat_1(k7_funct_6(A)))) # label(t58_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5478 (all A all B all C k8_funct_6(k10_finseq_1(A,B),C) = k10_finseq_1(k1_funct_2(A,C),k1_funct_2(B,C))) # label(t75_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5479 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k6_funct_6(B))) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k2_relat_1(B)) -> r2_hidden(A,k1_relat_1(C)))))))) # label(t52_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5480 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_funct_5(k4_funct_5(A)) = k10_funct_6(A))) # label(d12_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5481 (all A all B all C all D all E all F (v1_relat_1(F) & v1_funct_1(F) -> (r1_tarski(k1_relat_1(F),k2_zfmisc_1(D,E)) -> -r2_hidden(k5_funct_5(F),k4_partfun1(B,k4_partfun1(A,C))) & -r2_hidden(k3_funct_5(F),k4_partfun1(A,k4_partfun1(B,C))) | r2_hidden(F,k4_partfun1(k2_zfmisc_1(A,B),C))))) # label(t25_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5482 (all A all B (k4_funct_6(k10_finseq_1(A,B)) = k3_xboole_0(A,B) & k3_card_3(k10_finseq_1(A,B)) = k2_xboole_0(A,B))) # label(t40_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5483 (all A all B all C k2_funcop_1(k2_zfmisc_1(B,A),C) = k2_funct_4(k2_funcop_1(k2_zfmisc_1(A,B),C))) # label(t12_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5484 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & C = k1_funct_1(B,A) -> r1_tarski(k2_relat_1(C),k2_relat_1(k4_funct_5(B))) & r1_tarski(k2_relat_1(C),k2_relat_1(k6_funct_5(B)))))))) # label(t16_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5485 (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) -> (v2_funct_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> r2_wellord2(k1_funct_1(A,D),k1_funct_1(C,k1_funct_1(B,D))))) & k2_relat_1(B) = k1_relat_1(C) & k1_relat_1(B) = k1_relat_1(A) -> r2_wellord2(k4_card_3(A),k4_card_3(C))))))))) # label(t70_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5486 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> k1_relat_1(A) = k1_relat_1(k3_funct_6(A)))) # label(t90_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5487 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(B,A) = k5_funct_6(k11_finseq_1(C,D,B),np__3,A)))))))) # label(t47_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5488 (all A all B (k1_funct_6(A) = B <-> (all C (r2_hidden(C,B) <-> v1_funct_1(C) & v1_relat_1(C) & r2_hidden(C,A))))) # label(d1_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5489 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r2_wellord2(k4_card_3(k9_funct_6(A,B)),k1_funct_2(A,k4_card_3(B))))) # label(t83_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5490 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C all D A != k4_tarski(C,D)) & r2_hidden(A,k1_relat_1(k2_funct_4(B)))))) # label(t11_funct_6) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5491 (all A all B k4_relat_1(k2_zfmisc_1(A,B)) = k2_zfmisc_1(B,A)) # label(t18_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5492 (all A all B all C all D all E (v1_relat_1(E) -> (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),E) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) -> r2_hidden(C,A) & -r2_hidden(C,B) & -r2_hidden(D,A)) & (r2_hidden(k4_tarski(C,D),E) & r2_hidden(C,B) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r1_xboole_0(A,B) -> -r2_hidden(D,B) & r2_hidden(D,A) & -r2_hidden(C,A)) & (r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),E) & r1_xboole_0(A,B) -> -r2_hidden(C,A) & -r2_hidden(D,B) & r2_hidden(C,B)) & (r1_xboole_0(A,B) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(C,A) -> r2_hidden(D,B) & -r2_hidden(D,A) & -r2_hidden(C,B)))) # label(t22_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5493 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) -> k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A))))) = k1_xboole_0) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) -> k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A)))),k6_relat_1(k1_relat_1(k1_sysrel(A)))) = k1_xboole_0))) # label(t56_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5494 (all A (v1_relat_1(A) -> v1_relat_1(k1_sysrel(A)))) # label(dt_k1_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5495 (all A (v1_relat_1(A) -> k2_relat_1(k1_sysrel(A)) = k1_relat_1(k1_sysrel(A)))) # label(t45_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5496 $T # label(t21_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5497 (all A all B all C (r2_hidden(k4_tarski(A,B),k6_relat_1(C)) <-> r2_hidden(k4_tarski(B,A),k6_relat_1(C)))) # label(t31_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5498 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k4_relat_1(A),k4_relat_1(B))))))) # label(t27_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5499 (all A (v1_relat_1(A) -> k3_xboole_0(A,k6_relat_1(k1_relat_1(A))) = k1_sysrel(A))) # label(d1_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5500 (all A (v1_relat_1(A) -> (r1_tarski(A,k6_relat_1(k1_relat_1(A))) -> A = k6_relat_1(k1_relat_1(A))))) # label(t35_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5501 (all A all B (v1_relat_1(B) -> (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) & r1_tarski(k6_relat_1(A),B) -> k6_relat_1(A) = k8_relat_1(A,B)) & (r1_tarski(k6_relat_1(A),B) & k1_xboole_0 = k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) -> k7_relat_1(B,A) = k6_relat_1(A)))) # label(t54_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5502 (all A all B (r1_tarski(A,B) -> r1_tarski(k6_relat_1(A),k6_relat_1(B)))) # label(t33_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5503 (all A all B all C (v1_relat_1(C) -> r1_tarski(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),A) & r1_tarski(k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),B))) # label(t13_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5504 $T # label(t6_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5505 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),B) -> r1_tarski(k6_relat_1(A),k4_relat_1(B))))) # label(t37_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5506 $T # label(t23_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5507 (all A all B (k2_xboole_0(k6_relat_1(A),k6_relat_1(B)) = k6_relat_1(k2_xboole_0(A,B)) & k6_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k6_relat_1(A),k6_relat_1(B)) & k6_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k6_relat_1(A),k6_relat_1(B)))) # label(t32_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5508 (all A all B all C (v1_relat_1(C) -> (r1_xboole_0(A,B) & r1_tarski(C,k2_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A))) -> r1_tarski(k7_relat_1(C,A),k2_zfmisc_1(A,B))))) # label(t26_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5509 (all A k1_tarski(k4_tarski(A,A)) = k6_relat_1(k1_tarski(A))) # label(t30_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5510 (all A all B all C all D (v1_relat_1(D) -> (r1_tarski(D,k2_zfmisc_1(A,B)) & r1_tarski(C,B) -> k3_xboole_0(D,k2_zfmisc_1(A,C)) = k8_relat_1(C,D)) & (r1_tarski(C,A) & r1_tarski(D,k2_zfmisc_1(A,B)) -> k3_xboole_0(D,k2_zfmisc_1(C,B)) = k7_relat_1(D,C)))) # label(t24_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5511 (all A k6_relat_1(A) = k5_relat_1(k6_relat_1(A),k6_relat_1(A))) # label(t29_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5512 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k1_relat_1(B))) & (r2_hidden(A,k1_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k2_relat_1(B)) -> r2_hidden(A,k1_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B) -> r2_hidden(A,k2_relat_1(k1_sysrel(B)))) & (r2_hidden(A,k2_relat_1(k1_sysrel(B))) -> r2_hidden(A,k2_relat_1(B)) & r2_hidden(k4_tarski(A,A),B)) & (r2_hidden(A,k1_relat_1(k1_sysrel(B))) -> r2_hidden(k4_tarski(A,A),B) & r2_hidden(A,k1_relat_1(B))))) # label(t46_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5513 (all A all B (v1_relat_1(B) -> (k5_relat_1(k6_relat_1(A),k4_xboole_0(B,k6_relat_1(A))) = k1_xboole_0 -> k1_relat_1(k4_xboole_0(B,k6_relat_1(A))) = k4_xboole_0(k1_relat_1(B),k1_relat_1(k6_relat_1(A)))) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),k6_relat_1(A)) -> k4_xboole_0(k2_relat_1(B),k2_relat_1(k6_relat_1(A))) = k2_relat_1(k4_xboole_0(B,k6_relat_1(A)))))) # label(t39_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5514 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(k1_sysrel(A)),k2_relat_1(A)) & r1_tarski(k2_relat_1(k1_sysrel(A)),k1_relat_1(A)) & r1_tarski(k2_relat_1(k1_sysrel(A)),k2_relat_1(A)) & r1_tarski(k1_relat_1(k1_sysrel(A)),k1_relat_1(A)))) # label(t51_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5515 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))) & r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),k6_relat_1(k1_relat_1(A))))) # label(t52_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5516 $T # label(t11_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5517 $T # label(t17_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5518 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) = k5_relat_1(A,k2_xboole_0(B,C)) & k5_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k5_relat_1(A,C),k5_relat_1(B,C)))))))) # label(t20_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5519 $T # label(t9_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5520 (all A (v1_relat_1(A) -> r1_tarski(k6_relat_1(k2_relat_1(k1_sysrel(A))),A) & r1_tarski(k6_relat_1(k1_relat_1(k1_sysrel(A))),A))) # label(t53_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5521 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k4_relat_1(C),k2_zfmisc_1(B,A))))) # label(t16_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5522 (all A all B (v1_relat_1(B) -> (r1_tarski(B,k2_zfmisc_1(A,A)) -> k4_xboole_0(B,k6_relat_1(k2_relat_1(B))) = k4_xboole_0(B,k6_relat_1(A)) & k4_xboole_0(B,k6_relat_1(k1_relat_1(B))) = k4_xboole_0(B,k6_relat_1(A))))) # label(t38_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5523 $T # label(t7_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5524 $T # label(t28_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5525 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(A,B) = A & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 -> k5_relat_1(A,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) & A = k5_relat_1(B,A) -> k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),A)))))) # label(t57_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5526 $T # label(t4_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5527 (all A all B all C (v1_relat_1(C) -> (r1_tarski(C,k2_zfmisc_1(A,B)) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A)))) # label(t15_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5528 (all A (v1_relat_1(A) -> (r1_tarski(A,k5_relat_1(A,A)) & k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) -> r1_tarski(k6_relat_1(k2_relat_1(A)),A)) & (r1_tarski(A,k5_relat_1(A,A)) & k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) -> r1_tarski(k6_relat_1(k1_relat_1(A)),A)))) # label(t40_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5529 (all A all B all C (v1_relat_1(C) -> (k5_relat_1(C,C) = C & k5_relat_1(C,k4_xboole_0(C,k6_relat_1(k1_relat_1(C)))) = k1_xboole_0 & r2_hidden(k4_tarski(A,B),C) -> B = A | r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(B,k1_relat_1(k1_sysrel(C)))) & (k5_relat_1(k4_xboole_0(C,k6_relat_1(k1_relat_1(C))),C) = k1_xboole_0 & r2_hidden(k4_tarski(A,B),C) & k5_relat_1(C,C) = C -> B = A | r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(A,k1_relat_1(k1_sysrel(C)))))) # label(t49_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5530 $T # label(t10_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5531 (all A (v1_relat_1(A) -> k6_relat_1(k1_relat_1(k1_sysrel(A))) = k1_sysrel(A))) # label(t47_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5532 $T # label(t19_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5533 $T # label(t5_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5534 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) & k5_relat_1(B,k4_xboole_0(B,k6_relat_1(A))) = k1_xboole_0 -> k1_xboole_0 = k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k2_relat_1(B))))) & (k1_xboole_0 = k5_relat_1(k4_xboole_0(B,k6_relat_1(A)),B) & r1_tarski(k1_relat_1(B),A) -> k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0))) # label(t42_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5535 (all A all B (v1_relat_1(B) -> (r1_tarski(k6_relat_1(A),k2_xboole_0(B,k4_relat_1(B))) -> r1_tarski(k6_relat_1(A),k4_relat_1(B)) & r1_tarski(k6_relat_1(A),B)))) # label(t36_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5536 (all A all B all C (v1_relat_1(C) -> (C = k5_relat_1(C,C) & k1_xboole_0 = k5_relat_1(C,k4_xboole_0(C,k1_sysrel(C))) & r2_hidden(k4_tarski(A,B),C) -> B = A | r2_hidden(A,k4_xboole_0(k1_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(B,k1_relat_1(k1_sysrel(C)))) & (k5_relat_1(C,C) = C & r2_hidden(k4_tarski(A,B),C) & k5_relat_1(k4_xboole_0(C,k1_sysrel(C)),C) = k1_xboole_0 -> A = B | r2_hidden(B,k4_xboole_0(k2_relat_1(C),k1_relat_1(k1_sysrel(C)))) & r2_hidden(A,k1_relat_1(k1_sysrel(C)))))) # label(t48_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5537 $T # label(t8_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5538 $T # label(t2_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5539 (all A all B -(k1_xboole_0 != A & -(k1_relat_1(k2_zfmisc_1(A,B)) = A & k2_relat_1(k2_zfmisc_1(A,B)) = B) & k1_xboole_0 != B)) # label(t12_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5540 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) = k1_xboole_0 & k5_relat_1(B,A) = B & k1_xboole_0 = k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) & k5_relat_1(A,B) = A -> k1_sysrel(A) = k1_sysrel(B)) & (A = k5_relat_1(B,A) & B = k5_relat_1(A,B) & k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) = k1_xboole_0 & k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 -> k1_sysrel(B) = k1_sysrel(A)))))) # label(t59_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5541 (all A all B k4_xboole_0(k6_relat_1(k4_xboole_0(A,B)),k6_relat_1(A)) = k1_xboole_0) # label(t34_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5542 $T # label(t3_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5543 (all A all B all C (v1_relat_1(C) -> (r1_xboole_0(A,B) -> r1_xboole_0(k1_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(C,k2_zfmisc_1(A,B)))) & r1_xboole_0(k1_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B))),k2_relat_1(k3_xboole_0(k4_relat_1(C),k2_zfmisc_1(A,B))))))) # label(t14_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5544 (all A (v1_relat_1(A) -> (r1_tarski(A,k5_relat_1(A,A)) & k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) -> k3_xboole_0(A,k6_relat_1(k1_relat_1(A))) = k6_relat_1(k1_relat_1(A))) & (r1_tarski(A,k5_relat_1(A,A)) & k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k2_relat_1(A)))) -> k3_xboole_0(A,k6_relat_1(k2_relat_1(A))) = k6_relat_1(k2_relat_1(A))))) # label(t41_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5545 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(fc1_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5546 (all A (v1_relat_1(A) -> r1_tarski(k1_sysrel(A),A) & r1_tarski(k1_sysrel(A),k6_relat_1(k1_relat_1(A))))) # label(t43_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5547 $T # label(t1_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5548 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (k5_relat_1(k4_xboole_0(B,k6_relat_1(k1_relat_1(B))),B) = k1_xboole_0 & k5_relat_1(B,A) = A -> r1_tarski(k1_sysrel(A),k1_sysrel(B))) & (k5_relat_1(B,k4_xboole_0(B,k6_relat_1(k1_relat_1(B)))) = k1_xboole_0 & A = k5_relat_1(A,B) -> r1_tarski(k1_sysrel(A),k1_sysrel(B))))))) # label(t58_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5549 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_sysrel(C)) -> B = A & r2_hidden(A,k1_relat_1(k1_sysrel(C)))))) # label(t44_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5550 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(k6_relat_1(k1_relat_1(k1_sysrel(A))),k4_xboole_0(A,k6_relat_1(k1_relat_1(k1_sysrel(A))))) -> k7_relat_1(A,k2_relat_1(k1_sysrel(A))) = k6_relat_1(k1_relat_1(k1_sysrel(A))) & k7_relat_1(A,k1_relat_1(k1_sysrel(A))) = k6_relat_1(k1_relat_1(k1_sysrel(A)))) & (k5_relat_1(k4_xboole_0(A,k6_relat_1(k2_relat_1(k1_sysrel(A)))),k6_relat_1(k2_relat_1(k1_sysrel(A)))) = k1_xboole_0 -> k6_relat_1(k1_relat_1(k1_sysrel(A))) = k8_relat_1(k1_relat_1(k1_sysrel(A)),A) & k8_relat_1(k2_relat_1(k1_sysrel(A)),A) = k6_relat_1(k2_relat_1(k1_sysrel(A)))))) # label(t55_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5551 (all A all B all C all D all E (v1_relat_1(E) -> (r1_tarski(E,k2_zfmisc_1(A,B)) & A = k2_xboole_0(C,D) -> E = k2_xboole_0(k7_relat_1(E,C),k7_relat_1(E,D))))) # label(t25_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5552 (all A (v1_relat_1(A) -> (k1_xboole_0 = k5_relat_1(A,k4_xboole_0(A,k6_relat_1(k1_relat_1(A)))) & A = k5_relat_1(A,A) -> k2_relat_1(A) = k1_relat_1(k1_sysrel(A)) & k2_relat_1(A) = k2_relat_1(k1_sysrel(A))) & (A = k5_relat_1(A,A) & k1_xboole_0 = k5_relat_1(k4_xboole_0(A,k6_relat_1(k1_relat_1(A))),A) -> k1_relat_1(k1_sysrel(A)) = k1_relat_1(A) & k2_relat_1(k1_sysrel(A)) = k1_relat_1(A)))) # label(t50_sysrel) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5553 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(np__0,B) -> -r2_hidden(B,A) & -r1_tarski(B,A) | k2_card_2(B,A) = A & k2_card_2(A,B) = A | v1_finset_1(A)))))) # label(t78_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5554 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k15_ordinal2(A,k1_ordinal1(k4_ordinal2))))) # label(t30_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5555 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> r1_tarski(B,k1_card_2(A,B)) & r1_tarski(A,k1_card_2(A,B)))))) # label(t72_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5556 (all A (-v1_finset_1(A) -> k2_card_2(k3_card_1(np__0),k1_card_1(A)) = k1_card_1(A))) # label(t84_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5557 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r1_tarski(A,B) | r2_hidden(A,B) -> r1_tarski(k2_card_2(C,A),k2_card_2(C,B)) & r1_tarski(k2_card_2(C,A),k2_card_2(B,C)) & r1_tarski(k2_card_2(A,C),k2_card_2(B,C)) & r1_tarski(k2_card_2(A,C),k2_card_2(C,B))))))))) # label(t69_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5558 (all A (-v1_xboole_0(A) -> k1_card_1(A) = k1_card_1(k4_finseq_2(np__1,A)) & r2_wellord2(k4_finseq_2(np__1,A),A))) # label(t56_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5559 (all A all B (v1_card_4(B) & v1_card_4(A) -> v1_card_4(k2_zfmisc_1(A,B)))) # label(t55_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5560 (all A (v1_card_1(A) -> r1_tarski(np__0,A))) # label(t19_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5561 (all A all B (v1_finset_1(B) -> r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A) | v1_finset_1(A))) # label(t36_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5562 (all A (v1_finset_1(A) & v1_card_1(A) -> (all B (v1_finset_1(B) & v1_card_1(B) -> v1_finset_1(k1_card_2(A,B)))))) # label(t38_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5563 (all A (v1_card_1(A) -> (r1_tarski(np__1,A) <-> r2_hidden(np__0,A)))) # label(t24_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5564 (all A (v3_ordinal1(A) -> (exists B (k15_ordinal2(A,k1_ordinal1(k4_ordinal2)) = k14_ordinal2(A,B) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t29_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5565 $T # label(t16_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5566 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (v1_finset_1(A) -> v1_finset_1(B) | r2_hidden(A,B) & r1_tarski(A,B)))))) # label(t13_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5567 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> k1_card_2(A,A) = A))) # label(t33_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5568 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> -(-v1_finset_1(A) & (r2_hidden(B,A) | r1_tarski(B,A)) & -(r1_tarski(k2_card_2(B,A),A) & r1_tarski(k2_card_2(A,B),A))))))) # label(t79_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5569 (all A (r2_hidden(k1_card_1(A),k3_card_1(np__0)) <-> v1_finset_1(A))) # label(t2_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5570 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(k2_card_2(A,B),k2_card_2(A,C)) -> r2_hidden(B,C)))))))) # label(t83_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5571 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r1_tarski(A,B) <-> r2_hidden(A,k2_card_1(B))))))) # label(t23_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5572 (all A (r2_hidden(A,a_0_2_card_4) <-> (exists B exists C exists D (p1_s3_card_4(B,C,D) & A = f1_s3_card_4(B,C,D) & m2_subset_1(D,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_2_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5573 (all A all B (v1_card_4(A) & v1_card_4(B) -> v1_card_4(k2_xboole_0(A,B)))) # label(t47_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5574 (all A (v1_finset_1(A) -> v1_card_4(A))) # label(t43_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5575 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> -(-(-(r2_hidden(A,B) & r2_hidden(C,D)) & -(r1_tarski(A,B) & r1_tarski(C,D)) & -(r1_tarski(C,D) & r2_hidden(A,B)) & -(r1_tarski(A,B) & r2_hidden(C,D))) & A != np__0 & -r1_tarski(k3_card_2(A,C),k3_card_2(B,D))))))))))) # label(t70_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5576 (all A ((exists B (v1_funct_1(B) & k1_relat_1(B) = k5_numbers & r1_tarski(A,k2_relat_1(B)) & v1_relat_1(B))) <-> v1_card_4(A))) # label(t45_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5577 (all A all B (v1_card_4(A) & v1_card_4(B) -> v1_card_4(k5_xboole_0(A,B)))) # label(t50_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5578 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (np__0 != A -> r1_tarski(B,k2_card_2(B,A)) & r1_tarski(B,k2_card_2(A,B))))))) # label(t73_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5579 (all A (v1_finset_1(A) -> r2_hidden(k1_card_1(A),k5_ordinal2) & r2_hidden(k1_card_1(A),k3_card_1(np__0)))) # label(t3_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5580 (all A all B (v1_card_4(B) & r1_tarski(A,B) -> v1_card_4(A))) # label(t46_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5581 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> v4_ordinal1(A)))) # label(t32_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5582 (all A (v3_ordinal1(A) -> (r1_ordinal1(k5_ordinal2,A) <-> -v1_finset_1(A)))) # label(t8_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5583 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (-v1_finset_1(A) -> -v1_finset_1(k1_card_2(A,B)) & -v1_finset_1(k1_card_2(B,A))))))) # label(t39_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5584 (all A all B (k1_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(A) & r2_hidden(k1_card_1(B),k1_card_1(A)) -> k1_card_1(A) = k1_card_1(k4_xboole_0(A,B)))) # label(t76_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5585 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (v1_card_4(A) -> v1_card_4(k4_finseq_2(B,A))))))) # label(t58_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5586 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> r2_wellord2(k2_zfmisc_1(k4_finseq_2(B,A),k4_finseq_2(C,A)),k4_finseq_2(k1_nat_1(B,C),A)) & k1_card_1(k4_finseq_2(k1_nat_1(B,C),A)) = k1_card_1(k2_zfmisc_1(k4_finseq_2(B,A),k4_finseq_2(C,A))))))))) # label(t57_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5587 (all A (-v1_xboole_0(A) -> (v1_card_4(A) -> v1_card_4(k3_finseq_2(A))))) # label(t65_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5588 (all A all B (v1_finset_1(A) -> k1_xboole_0 = A | v1_finset_1(B) | k1_card_1(B) = k2_card_2(k1_card_1(B),k1_card_1(A)))) # label(t85_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5589 (all A (v1_card_1(A) -> (v1_finset_1(A) <-> r2_hidden(A,k3_card_1(np__0))))) # label(t9_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5590 (all A all B (v1_finset_1(B) -> v1_finset_1(A) | r2_wellord2(k2_zfmisc_1(A,B),A) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(A) | k1_xboole_0 = B)) # label(t81_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5591 (all A all B (v1_card_1(B) -> (all C (v1_card_1(C) -> ((all D (r2_hidden(D,A) -> r1_tarski(k1_card_1(D),C))) & r1_tarski(k1_card_1(A),B) -> r1_tarski(k1_card_1(k3_tarski(A)),k2_card_2(B,C))))))) # label(t60_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5592 (all A all B -((r2_wellord2(B,A) | r2_wellord2(A,B)) & -(r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A)) & -v1_finset_1(A))) # label(t35_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5593 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r2_hidden(k1_card_2(A,B),k1_card_2(A,C)) -> r2_hidden(B,C)))))))) # label(t75_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5594 (all A (v1_card_1(A) -> (-v1_finset_1(A) <-> r1_ordinal1(k3_card_1(np__0),A)))) # label(t11_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5595 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B = A <-> k2_card_1(A) = k2_card_1(B)))))) # label(t21_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5596 (all A (v1_finset_1(A) & v1_card_1(A) -> (all B (v1_finset_1(B) & v1_card_1(B) -> v1_finset_1(k2_card_2(A,B)))))) # label(t40_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5597 (all A all B (m1_subset_1(B,k5_numbers) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k1_card_4(A,B),k1_numbers,k5_numbers))) # label(dt_k1_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5598 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_ordinal1(B) -> (r2_wellord2(B,A) -> A = B))))) # label(t6_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5599 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (-(-(r1_tarski(C,D) & r2_hidden(A,B)) & -(r1_tarski(C,D) & r1_tarski(A,B)) & -(r2_hidden(C,D) & r1_tarski(A,B)) & -(r2_hidden(A,B) & r2_hidden(C,D))) -> r1_tarski(k1_card_2(A,C),k1_card_2(B,D)) & r1_tarski(k1_card_2(C,A),k1_card_2(B,D))))))))))) # label(t41_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5600 (all A ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k1_card_1(B) = k1_card_1(A))) <-> v1_finset_1(A))) # label(t4_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5601 (all A (-v1_xboole_0(A) -> (-v1_finset_1(A) -> k1_card_1(A) = k1_card_1(k3_finseq_2(A))))) # label(t87_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5602 (all A (v3_ordinal1(A) -> A = k4_xboole_0(k1_ordinal1(A),k1_tarski(A)))) # label(t5_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.49 5603 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (r1_tarski(A,B) | r2_hidden(A,B) -> r1_tarski(k1_card_2(C,A),k1_card_2(C,B)) & r1_tarski(k1_card_2(C,A),k1_card_2(B,C)) & r1_tarski(k1_card_2(A,C),k1_card_2(B,C)) & r1_tarski(k1_card_2(A,C),k1_card_2(C,B))))))))) # label(t42_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5604 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-v1_finset_1(A) & -(r2_wellord2(k4_finseq_2(B,A),A) & k1_card_1(k4_finseq_2(B,A)) = k1_card_1(A)) & np__0 != B))))) # label(t86_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5605 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k2_nat_1(k1_card_4(np__2,C),k1_nat_1(k2_nat_1(np__2,D),np__1)) = k2_nat_1(k1_card_4(np__2,A),k1_nat_1(k2_nat_1(np__2,B),np__1)) -> A = C & D = B))))))))) # label(t52_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5606 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> r1_tarski(k2_card_2(k3_card_1(np__0),k1_card_1(A)),k3_card_1(np__0)) & r1_tarski(k2_card_2(k1_card_1(A),k3_card_1(np__0)),k3_card_1(np__0)))) # label(t67_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5607 (all A all B (v1_card_4(A) -> v1_card_4(k4_xboole_0(A,B)))) # label(t49_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5608 (all A (k1_card_1(A) = np__0 <-> A = k1_xboole_0)) # label(t17_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5609 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r1_tarski(k2_card_1(A),B) <-> r2_hidden(A,B)))))) # label(t22_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5610 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (-(-(r2_hidden(A,B) & r2_hidden(C,D)) & -(r1_tarski(A,B) & r2_hidden(C,D)) & -(r1_tarski(C,D) & r2_hidden(A,B)) & -(r1_tarski(C,D) & r1_tarski(A,B))) -> r1_tarski(k2_card_2(A,C),k2_card_2(B,D)) & r1_tarski(k2_card_2(C,A),k2_card_2(B,D))))))))))) # label(t68_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5611 (all A (-v1_xboole_0(A) -> r1_tarski(k3_card_1(np__0),k1_card_1(k3_finseq_2(A))))) # label(t66_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5612 (all A (-(-v1_finset_1(A) & (all B -(k3_card_1(np__0) = k1_card_1(B) & r1_tarski(B,A)))) & -(v1_finset_1(A) & (exists B (k1_card_1(B) = k3_card_1(np__0) & r1_tarski(B,A)))))) # label(t14_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5613 (all A all B -((r1_tarski(k1_card_1(B),k1_card_1(A)) | r2_hidden(k1_card_1(B),k1_card_1(A))) & -(k1_card_1(A) = k1_card_1(k2_xboole_0(A,B)) & r2_wellord2(k2_xboole_0(A,B),A)) & -v1_finset_1(A))) # label(t37_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5614 (all A (v1_finset_1(k1_card_1(A)) <-> v1_finset_1(A))) # label(t1_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5615 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> -(np__0 = k3_newton(B,A) & -(A != np__0 & np__0 = B)) & -(k3_newton(B,A) != np__0 & B = np__0 & np__0 != A))))) # label(t51_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5616 $T # label(t18_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5617 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> -(-v1_finset_1(A) & (r2_hidden(B,A) | r1_tarski(B,A)) & -(A = k1_card_2(B,A) & k1_card_2(A,B) = A)))))) # label(t34_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5618 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (r2_hidden(C,D) & r2_hidden(A,B) -> r2_hidden(k1_card_2(A,C),k1_card_2(B,D)) & r2_hidden(k1_card_2(C,A),k1_card_2(B,D))))))))))) # label(t74_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5619 $T # label(t64_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5620 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> (all D (v1_card_1(D) -> (r2_hidden(C,D) & r2_hidden(A,B) -> r2_hidden(k2_card_2(C,A),k2_card_2(B,D)) & r2_hidden(k2_card_2(A,C),k2_card_2(B,D))))))))))) # label(t82_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5621 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_finset_1(k1_funct_1(A,B)))) & v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k3_card_3(A))))) # label(t63_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5622 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_ordinal1(B) -> k14_ordinal2(B,k1_nat_1(A,np__1)) = k14_ordinal2(k1_ordinal1(B),A) & k14_ordinal2(B,k1_ordinal1(A)) = k14_ordinal2(k1_ordinal1(B),A))))) # label(t28_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5623 (all A (-v1_finset_1(A) -> r2_wellord2(k2_zfmisc_1(A,A),A) & k1_card_1(k2_zfmisc_1(A,A)) = k1_card_1(A))) # label(t80_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5624 (all A (r2_hidden(A,a_0_0_card_4) <-> (exists B (A = f1_s1_card_4(B) & p1_s1_card_4(B) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(fraenkel_a_0_0_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5625 (all A all B (k2_card_1(B) = k2_card_1(A) <-> k1_card_1(A) = k1_card_1(B))) # label(t20_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5626 (all A (v1_card_1(A) -> (r2_hidden(np__1,A) <-> r1_tarski(np__2,A)))) # label(t25_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5627 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (v1_finset_1(A) -> v1_finset_1(B) | -r2_hidden(B,A) & -r1_tarski(B,A)))))) # label(t26_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5628 (all A (v3_ordinal1(A) -> (r1_ordinal1(k5_ordinal2,A) -> k14_ordinal2(k4_ordinal2,A) = A))) # label(t31_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5629 (all A (r1_tarski(k1_card_1(A),k3_card_1(np__0)) <-> v1_card_4(A))) # label(d1_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5630 (all A (r2_hidden(A,a_0_1_card_4) <-> (exists B exists C (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers) & p1_s2_card_4(B,C) & A = f1_s2_card_4(B,C))))) # label(fraenkel_a_0_1_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5631 $T # label(t12_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5632 (all A (v1_card_4(A) & (all B (r2_hidden(B,A) -> v1_card_4(B))) -> v1_card_4(k3_tarski(A)))) # label(t62_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5633 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_card_4(k1_relat_1(A)) & (all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_4(k1_funct_1(A,B)))) -> v1_card_4(k3_card_3(A))))) # label(t61_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5634 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_card_1(k1_relat_1(C)),A) & (all D (r2_hidden(D,k1_relat_1(C)) -> r1_tarski(k1_card_1(k1_funct_1(C,D)),B))) -> r1_tarski(k1_card_1(k3_card_3(C)),k2_card_2(A,B))))))))) # label(t59_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5635 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> k1_card_4(A,B) = k2_newton(A,B))) # label(redefinition_k1_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5636 $T # label(t10_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5637 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) <-> (all B (v3_ordinal1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,A) -> r2_hidden(k14_ordinal2(B,C),A))))))))) # label(t27_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5638 (all A (v3_ordinal1(A) -> (v1_finset_1(A) <-> r2_hidden(A,k5_ordinal2)))) # label(t7_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5639 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (all C (v1_card_1(C) -> -(C != np__0 & -(r1_tarski(k3_card_2(A,C),k3_card_2(B,C)) & r1_tarski(k3_card_2(C,A),k3_card_2(C,B))) & (r1_tarski(A,B) | r2_hidden(A,B))))))))) # label(t71_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5640 (all A all B (v1_card_4(A) -> v1_card_4(k3_xboole_0(B,A)) & v1_card_4(k3_xboole_0(A,B)))) # label(t48_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5641 (all A (v1_card_1(A) -> (-v1_finset_1(A) -> A = k2_card_2(A,A)))) # label(t77_card_4) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5642 $T # label(t12_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5643 $T # label(t63_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5644 $T # label(t35_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5645 $T # label(t17_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5646 $T # label(t11_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5647 (all A v7_relat_2(k1_eqrel_1(A))) # label(t19_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5648 (all A all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k4_tarski(B,C),k1_eqrel_1(A)))) # label(t15_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5649 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C (v1_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> ((all D (m1_toler_1(D,A,B) & v1_toler_1(D,A,B) <-> m1_toler_1(D,A,C) & v1_toler_1(D,A,C))) -> C = B))))) # label(t53_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5650 $T # label(t60_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5651 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v1_relat_2(C) -> (all D ((all E (r2_hidden(E,D) <-> m1_toler_1(E,A,C) & r2_hidden(B,E))) -> k6_eqrel_1(A,C,B) = k3_tarski(D))))) # label(t59_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5652 $T # label(t22_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5653 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C ((all D (v1_toler_1(D,A,B) & m1_toler_1(D,A,B) <-> r2_hidden(D,C))) <-> k4_toler_1(A,B) = C)))) # label(d7_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5654 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> r3_relat_2(B,A))) # label(t29_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5655 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C (r2_hidden(C,A) -> m1_toler_1(k1_tarski(C),A,B))))) # label(t41_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5656 (all A all B all C (m2_relset_1(C,B,B) & v1_partfun1(C,B,B) & v3_relat_2(C) & v1_relat_2(C) -> (r1_tarski(A,B) -> v1_relat_2(k1_toler_1(C,A)) & v3_relat_2(k1_toler_1(C,A)) & m2_relset_1(k1_toler_1(C,A),A,A) & v1_partfun1(k1_toler_1(C,A),A,A)))) # label(t33_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5657 $T # label(t61_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5658 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_relat_2(C) -> ((all D (r2_hidden(D,A) -> r1_tarski(k6_eqrel_1(A,B,D),k6_eqrel_1(A,C,D)))) -> r1_tarski(B,C)))))) # label(t73_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5659 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (k4_toler_1(A,B) = k4_toler_1(A,C) -> B = C))))) # label(t65_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5660 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> A = k3_tarski(k4_toler_1(A,B)))) # label(t66_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5661 $T # label(t31_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5662 $T # label(t55_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5663 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (exists C m1_toler_1(C,A,B)))) # label(existence_m1_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5664 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C all D (r2_hidden(k4_tarski(C,D),B) -> m1_toler_1(k2_tarski(C,D),A,B))))) # label(t40_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5665 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C all D -((all E (m1_toler_1(E,A,B) & v1_toler_1(E,A,B) -> -(r2_hidden(D,E) & r2_hidden(C,E)))) & r2_hidden(k4_tarski(C,D),B))))) # label(t46_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5666 $T # label(t18_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5667 (all A all B (v1_relat_1(A) -> k1_toler_1(A,B) = k2_wellord1(A,B))) # label(redefinition_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5668 $T # label(t44_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5669 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> r1_relat_2(B,A))) # label(t28_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5670 $T # label(t26_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5671 $T # label(t23_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5672 (all A all B all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D (r2_hidden(k4_tarski(B,D),C) <-> r2_hidden(D,k6_eqrel_1(A,C,B)))))) # label(t54_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5673 $T # label(d5_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5674 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k5_relset_1(A,A,B) = A)) # label(t25_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5675 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> r1_tarski(k6_partfun1(A),B))) # label(t50_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5676 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v1_relat_2(C) -> (all D ((all E (v1_toler_1(E,A,C) & m1_toler_1(E,A,C) & r2_hidden(B,E) <-> r2_hidden(E,D))) -> k3_tarski(D) = k6_eqrel_1(A,C,B))))) # label(t58_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5677 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> r1_tarski(B,k1_eqrel_1(A)))) # label(t49_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5678 (all A exists B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,k3_tarski(A),k3_tarski(A)) & (all C (r2_hidden(C,A) -> m1_toler_1(C,k3_tarski(A),B))) & m2_relset_1(B,k3_tarski(A),k3_tarski(A)))) # label(t51_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5679 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C all D (v1_toler_1(D,A,B) & m1_toler_1(D,A,B) -> (r2_hidden(C,D) -> r1_tarski(D,k6_eqrel_1(A,B,C))))))) # label(t70_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5680 $T # label(dt_m1_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5681 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> A = k3_tarski(k3_toler_1(A,B)))) # label(t67_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5682 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (m1_toler_1(k1_xboole_0,A,B) & v1_toler_1(k1_xboole_0,A,B) -> B = k1_xboole_0))) # label(t38_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5683 (all A all B all C all D (m2_relset_1(D,A,B) -> (v3_relat_2(D) -> v3_relat_2(k1_toler_1(D,C))))) # label(t32_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5684 $T # label(t57_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5685 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (v8_relat_2(B) -> (all C (r2_hidden(C,A) -> m1_toler_1(k6_eqrel_1(A,B,C),A,B) & v1_toler_1(k6_eqrel_1(A,B,C),A,B)))))) # label(t69_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5686 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> m1_toler_1(k1_xboole_0,A,B))) # label(t34_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5687 (all A (r2_hidden(A,f1_s1_toler_1) -> p1_s1_toler_1(A,A))) & (all A all B (r2_hidden(A,f1_s1_toler_1) & p1_s1_toler_1(A,B) & r2_hidden(B,f1_s1_toler_1) -> p1_s1_toler_1(B,A))) -> (exists A (v3_relat_2(A) & (all B all C (r2_hidden(B,f1_s1_toler_1) & r2_hidden(C,f1_s1_toler_1) -> (p1_s1_toler_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))) & m2_relset_1(A,f1_s1_toler_1,f1_s1_toler_1) & v1_partfun1(A,f1_s1_toler_1,f1_s1_toler_1) & v1_relat_2(A))) # label(s1_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5688 $T # label(t24_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5689 $T # label(t36_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5690 (all A v6_relat_2(k1_eqrel_1(A))) # label(t21_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5691 $T # label(t14_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5692 (all A all B (v3_relat_2(B) & v1_partfun1(B,k3_tarski(A),k3_tarski(A)) & m2_relset_1(B,k3_tarski(A),k3_tarski(A)) & v1_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,k3_tarski(A),k3_tarski(A)) & m2_relset_1(C,k3_tarski(A),k3_tarski(A)) & v1_relat_2(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),B) <-> (exists F (r2_hidden(F,A) & r2_hidden(D,F) & r2_hidden(E,F))))) & (all D all E ((exists F (r2_hidden(D,F) & r2_hidden(E,F) & r2_hidden(F,A))) <-> r2_hidden(k4_tarski(D,E),C))) -> C = B))))) # label(t52_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5693 $T # label(t10_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5694 $T # label(t62_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5695 $T # label(t37_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5696 $T # label(d2_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5697 (all A all B all C (r2_hidden(C,k3_relat_1(k1_eqrel_1(A))) & r2_hidden(B,k3_relat_1(k1_eqrel_1(A))) -> r2_hidden(k4_tarski(B,C),k1_eqrel_1(A)))) # label(t16_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5698 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C all D (m1_toler_1(D,A,B) & m1_toler_1(C,A,B) -> m1_toler_1(k3_xboole_0(C,D),A,B))))) # label(t42_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5699 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C ((all D all E (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))) <-> m1_toler_1(C,A,B))))) # label(d3_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5700 (all A all B all C (v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v3_relat_2(C) & v1_relat_2(C) -> (m1_toler_1(A,B,C) -> r1_tarski(A,B)))) # label(t43_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5701 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_relset_1(B,A,A) & v1_relat_2(B) -> k2_toler_1(A,B,C) = k2_wellord1(B,C))) # label(redefinition_k2_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5702 $T # label(d1_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5703 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> r1_tarski(k4_toler_1(A,B),k3_toler_1(A,B)))) # label(t72_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5704 (all A all B (v1_relat_1(A) -> m2_relset_1(k1_toler_1(A,B),B,B))) # label(dt_k1_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5705 $T # label(dt_k3_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5706 (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 (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (r1_tarski(k3_toler_1(A,B),k3_toler_1(A,C)) <-> r1_tarski(B,C)))))) # label(t71_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5707 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C -((all D (m1_toler_1(D,A,B) & v1_toler_1(D,A,B) -> -r2_hidden(C,D))) & r2_hidden(C,A))))) # label(t47_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5708 (all A all B all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) -> (r2_hidden(k4_tarski(B,B),C) <-> r2_hidden(B,A)))) # label(t27_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5709 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C (m1_toler_1(C,A,B) -> (exists D (m1_toler_1(D,A,B) & r1_tarski(C,D) & v1_toler_1(D,A,B))))))) # label(t45_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5710 $T # label(dt_k4_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5711 $T # label(t30_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5712 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> r1_tarski(B,k7_relset_1(A,A,A,A,B,B)))) # label(t74_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5713 (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(C,k1_zfmisc_1(A)) -> v1_relat_2(k2_toler_1(A,B,C)) & v1_partfun1(k2_toler_1(A,B,C),C,C) & m2_relset_1(k2_toler_1(A,B,C),C,C) & v3_relat_2(k2_toler_1(A,B,C)))) # label(dt_k2_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5714 $T # label(t20_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5715 (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 ((all D (m1_toler_1(D,A,B) <-> r2_hidden(D,C))) <-> k3_toler_1(A,B) = C)))) # label(d6_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5716 $T # label(t48_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5717 (all A all B (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> (exists C (m1_toler_1(C,A,B) & v1_toler_1(C,A,B))))) # label(rc1_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5718 (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 (m1_toler_1(C,A,B) -> (v1_toler_1(C,A,B) <-> (all D -(-r2_hidden(D,C) & r2_hidden(D,A) & (all E -(-r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,C)))))))))) # label(d4_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5719 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> (all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & v1_relat_2(C) -> (r1_tarski(k4_toler_1(A,B),k4_toler_1(A,C)) -> r1_tarski(B,C)))))) # label(t64_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5720 $T # label(t56_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5721 (all A A = k5_relset_1(A,A,k1_eqrel_1(A))) # label(t13_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5722 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> ((all C (r2_hidden(C,A) -> m1_toler_1(k6_eqrel_1(A,B,C),A,B))) -> v8_relat_2(B)))) # label(t68_toler_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5723 (all A (m2_finseq_1(A,k1_numbers) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) -> r1_xreal_0(C,B) | r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,B))))))) <-> v1_rfinseq(A)))) # label(t32_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5724 (all A (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finset_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> k4_card_1(k1_relat_1(A)) = k4_card_1(k1_relat_1(B))))))) # label(t10_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5725 (all A (v1_rfinseq(A) & m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> v1_rfinseq(k1_rfinseq(k1_numbers,A,B)) & m2_finseq_1(k1_rfinseq(k1_numbers,A,B),k1_numbers))))) # label(t34_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5726 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B = k8_finseq_1(A,k16_finseq_1(A,B,C),k1_rfinseq(A,B,C)))))))) # label(t21_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5727 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),A) & r1_tarski(k2_relat_1(B),A) -> (r1_rfinseq(B,C) <-> (all D (m1_subset_1(D,A) -> k1_card_1(k10_relat_1(C,k1_tarski(D))) = k1_card_1(k10_relat_1(B,k1_tarski(D))))))))))))) # label(t5_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5728 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_finseq_1(B,k1_numbers) -> (B = k2_rfinseq(A) <-> k3_finseq_1(A) = k3_finseq_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k5_real_1(k3_finseq_1(B),np__1)) & r1_xreal_0(np__1,C) -> k5_real_1(k2_seq_1(k5_numbers,k1_numbers,A,C),k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(C,np__1))) = k2_seq_1(k5_numbers,k1_numbers,B,C)))) & k2_seq_1(k5_numbers,k1_numbers,A,k3_finseq_1(A)) = k2_seq_1(k5_numbers,k1_numbers,B,k3_finseq_1(B))))))) # label(d3_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5729 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_finset_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finset_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(B),A) & r1_tarski(k2_relat_1(C),A) -> ((all D (m1_subset_1(D,A) -> k4_card_1(k10_relat_1(C,k1_tarski(D))) = k4_card_1(k10_relat_1(B,k1_tarski(D))))) <-> r1_rfinseq(B,C))))))))) # label(t11_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5730 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> k1_card_1(k1_relat_1(B)) = k1_card_1(k1_relat_1(A))))))) # label(t7_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5731 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_rfinseq(A,C) & r1_rfinseq(A,B) -> r1_rfinseq(B,C)))))))) # label(t2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5732 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_rfinseq(A,B) <-> (exists C (v1_relat_1(C) & k1_relat_1(B) = k2_relat_1(C) & A = k5_relat_1(C,B) & v2_funct_1(C) & k1_relat_1(C) = k1_relat_1(A) & v1_funct_1(C)))))))) # label(t3_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5733 (all A (m2_finseq_1(A,k1_numbers) -> (k3_finseq_1(A) != np__0 -> k2_seq_1(k5_numbers,k1_numbers,A,np__1) = k15_rvsum_1(k2_rfinseq(A))))) # label(t29_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5734 (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 k4_card_1(k10_relat_1(A,C)) = k4_card_1(k10_relat_1(B,C))) <-> r1_rfinseq(A,B)))))) # label(t13_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5735 (all A (v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finset_1(B) & v1_relat_1(B) -> (r1_rfinseq(A,B) <-> (all C k4_card_1(k10_relat_1(B,C)) = k4_card_1(k10_relat_1(A,C)))))))) # label(t9_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5736 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k3_finseq_1(A) = k1_nat_1(D,np__2) & k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,np__2)) = C & k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(D,np__1)) = B -> k8_finseq_1(k1_numbers,k16_finseq_1(k1_numbers,k2_rfinseq(A),D),k2_finseq_4(k1_numbers,k5_real_1(B,C),C)) = k2_rfinseq(A)))))))))) # label(t24_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5737 (all A (m1_subset_1(A,k1_numbers) -> k2_rfinseq(k12_finseq_1(k1_numbers,A)) = k12_finseq_1(k1_numbers,A))) # label(t26_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5738 (all A (m2_finseq_1(A,k1_numbers) -> k3_funct_2(k5_numbers,k1_numbers,k9_rvsum_1(np__0,A),k1_tarski(np__0)) = k4_finseq_1(A))) # label(t38_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5739 (all A all B (v1_relat_1(A) & v1_finset_1(B) & v1_funct_1(A) -> v1_finset_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5740 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_rfinseq(A,B) <-> (all C k1_card_1(k10_relat_1(A,k1_tarski(C))) = k1_card_1(k10_relat_1(B,k1_tarski(C))))))))) # label(d1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5741 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> r1_rfinseq(A,A))) # label(reflexivity_r1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5742 (all A all B all C (m1_subset_1(C,k5_numbers) & m1_finseq_1(B,A) -> m2_finseq_1(k1_rfinseq(A,B,C),A))) # label(dt_k1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5743 (all A (v1_rfinseq(A) & m2_finseq_1(A,k1_numbers) -> (all B (v1_rfinseq(B) & m2_finseq_1(B,k1_numbers) -> (r1_rfinseq(A,B) -> B = A))))) # label(t36_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5744 (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) -> (r1_rfinseq(A,B) <-> r1_rfinseq(k7_finseq_1(A,C),k7_finseq_1(B,C))))))))) # label(t14_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5745 (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) -> ((exists C (v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & A = k5_relat_1(C,B) & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & v3_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_1(C))) <-> r1_rfinseq(A,B)))))) # label(t17_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5746 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k2_rfinseq(k1_rfinseq(k1_numbers,A,B)) = k1_rfinseq(k1_numbers,k2_rfinseq(A),B))))) # label(t28_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5747 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finset_1(B) -> (exists C (r1_rfinseq(k7_relat_1(A,B),C) & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))))) # label(t18_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5748 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C k1_card_1(k10_relat_1(A,C)) = k1_card_1(k10_relat_1(B,C))) <-> r1_rfinseq(A,B)))))) # label(t4_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5749 $T # label(t12_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5750 (all A (m2_finseq_1(A,k1_numbers) & v1_rfinseq(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_finseq_1(k16_finseq_1(k1_numbers,A,B),k1_numbers) & v1_rfinseq(k16_finseq_1(k1_numbers,A,B)))))) # label(t33_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5751 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k2_rfinseq(k2_finseq_4(k1_numbers,A,B)) = k2_finseq_4(k1_numbers,k5_real_1(A,B),B))))) # label(t27_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5752 $T # label(t8_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5753 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (B = k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(C,np__1)) & k1_nat_1(C,np__2) = k3_finseq_1(A) -> k2_rfinseq(k16_finseq_1(k1_numbers,A,k1_nat_1(C,np__1))) = k8_finseq_1(k1_numbers,k16_finseq_1(k1_numbers,k2_rfinseq(A),C),k12_finseq_1(k1_numbers,B))))))))) # label(t23_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5754 (all A (m2_finseq_1(A,k1_numbers) -> (exists B (r1_rfinseq(A,B) & m2_finseq_1(B,k1_numbers) & v1_rfinseq(B))))) # label(t35_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5755 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> r1_rfinseq(k7_finseq_1(A,B),k7_finseq_1(B,A)))))) # label(t15_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5756 (exists A (m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v1_finset_1(A) & v1_rfinseq(A) & v1_finseq_1(A) & v1_funct_1(A))) # label(rc1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5757 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_rfinseq(A,B) -> k2_relat_1(B) = k2_relat_1(A)))))) # label(t1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5758 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (B != np__0 -> k3_funct_2(k5_numbers,k1_numbers,A,k1_tarski(k6_real_1(C,B))) = k3_funct_2(k5_numbers,k1_numbers,k9_rvsum_1(B,A),k1_tarski(C))))))))) # label(t37_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5759 (all A (m2_finseq_1(A,k1_numbers) -> (v1_rfinseq(A) <-> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(A)) & r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> r1_xreal_0(k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)),k2_seq_1(k5_numbers,k1_numbers,A,B)))))))) # label(d4_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5760 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (k3_finseq_1(B) = k1_nat_1(C,np__1) & k1_funct_1(B,k1_nat_1(C,np__1)) = D -> k7_finseq_1(k16_finseq_1(A,B,C),k9_finseq_1(D)) = B)))))))) # label(t20_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5761 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_finseq_1(B,k1_numbers) -> (r1_rfinseq(A,B) -> k15_rvsum_1(B) = k15_rvsum_1(A)))))) # label(t22_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5762 (all A all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_finseq_1(D,A) -> (r1_xreal_0(C,k3_finseq_1(B)) -> (k5_real_1(k3_finseq_1(B),C) = k3_finseq_1(D) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k1_funct_1(B,k1_nat_1(E,C))))) <-> k1_rfinseq(A,B,C) = D)) & (-r1_xreal_0(C,k3_finseq_1(B)) -> (D = k1_rfinseq(A,B,C) <-> k6_finseq_1(A) = D)))))))) # label(d2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5763 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k2_finseq_1(C)) -> r2_hidden(D,k4_finseq_1(B)) & k1_funct_1(k16_finseq_1(A,B,C),D) = k1_funct_1(B,D)))))))))) # label(t19_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5764 (all A (m2_finseq_1(A,k1_numbers) -> (k3_finseq_1(A) = np__1 | k3_finseq_1(A) = np__0 -> v1_rfinseq(A)))) # label(t31_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5765 (all A (m1_finseq_1(A,k1_numbers) -> m2_finseq_1(k2_rfinseq(A),k1_numbers))) # label(dt_k2_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5766 (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) -> (r1_rfinseq(A,B) -> k4_finseq_1(B) = k4_finseq_1(A) & k3_finseq_1(A) = k3_finseq_1(B)))))) # label(t16_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5767 (all A (m2_finseq_1(A,k1_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,B) -> k2_seq_1(k5_numbers,k1_numbers,A,k1_nat_1(B,np__1)) = k15_rvsum_1(k2_rfinseq(k1_rfinseq(k1_numbers,A,B))) | r1_xreal_0(k3_finseq_1(A),B)))))) # label(t30_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5768 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> (r1_rfinseq(A,B) -> r1_rfinseq(B,A)))) # label(symmetry_r1_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5769 (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) -> ((exists C (m2_relset_1(C,k1_relat_1(A),k1_relat_1(A)) & A = k5_relat_1(C,B) & v3_funct_2(C,k1_relat_1(A),k1_relat_1(A)) & v1_funct_2(C,k1_relat_1(A),k1_relat_1(A)) & v1_funct_1(C))) <-> r1_rfinseq(A,B))))))) # label(t6_rfinseq) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5770 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) -> a_2_1_card_fil(A,B) = k7_setfam_1(A,B))))) # label(t9_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5771 (all A (-v1_xboole_0(A) -> m1_subset_1(k4_card_fil(A),k1_zfmisc_1(k1_zfmisc_1(k1_zfmisc_1(A)))) & -v1_xboole_0(k4_card_fil(A)))) # label(dt_k4_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5772 (all A (v1_card_1(A) & -v2_card_1(A) & -v1_finset_1(A) -> v1_ordinal1(k7_card_fil(A)) & v2_ordinal1(k7_card_fil(A)) & -v1_xboole_0(k7_card_fil(A)) & v1_card_1(k7_card_fil(A)) & -v1_finset_1(k7_card_fil(A)) & v3_ordinal1(k7_card_fil(A)))) # label(fc4_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5773 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v2_card_1(A) & r3_card_fil -> v5_card_fil(A)))) # label(t28_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5774 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_0_card_fil(A,B,C) = k3_card_fil(A,B,C))))))) # label(d8_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5775 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v5_card_fil(A) -> v2_card_1(A)))) # label(t27_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5776 (all A (v1_card_1(A) & -v1_finset_1(A) -> v2_ordinal1(k2_card_1(A)) & v3_ordinal1(k2_card_1(A)) & -v1_xboole_0(k2_card_1(A)) & -v1_finset_1(k2_card_1(A)) & -v2_card_1(k2_card_1(A)) & v1_card_1(k2_card_1(A)) & v1_ordinal1(k2_card_1(A)))) # label(fc3_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5777 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (v2_card_fil(B,A) <-> (exists C ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) -> r1_tarski(C,D)))) & r2_hidden(C,B) & m1_subset_1(C,k1_zfmisc_1(A))))))))) # label(d6_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5778 (all A all B (-v1_finset_1(B) -> r2_hidden(k1_card_1(k1_tarski(A)),k1_card_1(B)))) # label(t1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5779 (all A all B (-v1_finset_1(B) -> ((exists C (C = A & r2_hidden(k1_card_1(k1_card_fil(B,C)),k1_card_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)))) <-> r2_hidden(A,a_1_1_card_fil(B))))) # label(fraenkel_a_1_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.50 5780 (all A all B all C all D (m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & m1_subset_1(D,k7_card_fil(B)) & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & v1_funct_1(C) & -v2_card_1(B) & v1_card_1(B) & -v1_finset_1(B) -> (r2_hidden(A,a_3_2_card_fil(B,C,D)) <-> (exists E (A = k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,D,E) & r2_hidden(E,B) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5781 (all A (v1_card_1(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> (r1_card_fil(B,A,C) -> r2_card_fil(B,A,k7_setfam_1(B,C))))))))) # label(t12_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5782 (all A (-v2_card_1(A) & v1_card_1(A) -> (all B (v1_card_1(B) -> (A = k2_card_1(B) <-> B = k7_card_fil(A)))))) # label(d17_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5783 (all A (-v1_xboole_0(A) -> (all B (v1_card_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(C) -> (r2_card_fil(A,B,C) <-> (all D (-v1_xboole_0(D) -> (r2_hidden(k1_card_1(D),B) & r1_tarski(D,C) -> r2_hidden(k3_tarski(D),C))))))))))) # label(d4_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5784 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v4_card_fil(A)))) # label(t39_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5785 (all A (v1_card_1(A) -> r1_tarski(k2_card_1(A),k3_card_2(np__2,A)))) # label(t24_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5786 (all A (-v1_xboole_0(A) -> (exists B m1_card_fil(B,A)))) # label(existence_m1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5787 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((exists E (r1_tarski(k5_subset_1(A,E,B),D) & r2_hidden(E,C) & m1_subset_1(E,k1_zfmisc_1(A)))) <-> r2_hidden(D,k3_card_fil(A,C,B))))))))))) # label(t13_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5788 (all A all B (-v1_xboole_0(A) & m1_card_fil(B,A) -> B = k2_card_fil(A,k2_card_fil(A,B)))) # label(involutiveness_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5789 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (r1_card_fil(A,k1_card_1(A),B) & v3_card_fil(B,A) -> v1_card_fil(B,A) | v2_card_fil(B,A)))))) # label(t23_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5790 (all A (v1_card_1(A) & -v2_card_1(A) & -v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> -(v3_card_fil(B,A) & r1_card_fil(A,A,B) & v1_card_fil(B,A)))))) # label(t37_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5791 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_tarski(A)) & (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r2_hidden(B,k1_tarski(A)) -> r2_hidden(C,k1_tarski(A))) & (r2_hidden(C,k1_tarski(A)) & r2_hidden(B,k1_tarski(A)) -> r2_hidden(k5_subset_1(A,B,C),k1_tarski(A))))))) & -r2_hidden(k1_xboole_0,k1_tarski(A)) & m1_subset_1(k1_tarski(A),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(t2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5792 (all A all B k1_card_fil(A,B) = k4_xboole_0(A,B)) # label(redefinition_k1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5793 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (r1_tarski(k5_card_fil(A),B) -> v1_card_fil(B,A)))))) # label(t20_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5794 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> -(r2_hidden(B,C) & r2_hidden(k1_card_fil(A,B),C)))))))) # label(t6_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5795 (all A (r2_hidden(A,a_0_0_card_fil) <-> (exists B (m1_subset_1(B,f1_s1_card_fil) & B = A & p1_s1_card_fil(B))))) # label(fraenkel_a_0_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5796 r2_hidden(f2_s1_card_fil,a_0_0_card_fil) -> p1_s1_card_fil(f2_s1_card_fil) # label(s1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5797 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> (r2_hidden(A,a_2_1_card_fil(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(B)) & k3_subset_1(B,D) = A & r2_hidden(D,C)))))) # label(fraenkel_a_2_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5798 (all A (-v1_finset_1(A) -> (exists B (-v1_xboole_0(B) & v3_card_fil(B,A) & -v2_card_fil(B,A) & m1_card_fil(B,A))))) # label(rc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5799 (all A (-v1_finset_1(A) & -v2_card_1(A) & v1_card_1(A) -> (all B (m2_card_fil(B,A) -> -(r1_tarski(k6_card_fil(A),B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> -((all D -(r2_hidden(D,C) & r2_hidden(D,B))) & (all D all E (r2_hidden(E,C) & r2_hidden(D,C) -> E = D | r1_xboole_0(D,E))) & A = k1_card_1(C)))) & r2_card_fil(A,A,B)))))) # label(t35_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5800 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) <-> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k5_subset_1(A,C,D),B)) & (r2_hidden(C,B) & r1_tarski(C,D) -> r2_hidden(D,B)))))) & -r2_hidden(k1_xboole_0,B) & -v1_xboole_0(B))))) # label(t3_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5801 (all A (-v2_card_1(A) & v1_card_1(A) -> v1_card_1(k7_card_fil(A)))) # label(dt_k7_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5802 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_card_fil(B,A) & -v1_xboole_0(A) -> m1_subset_1(k3_card_fil(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(k3_card_fil(A,B,C)))) # label(dt_k3_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5803 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_card_fil(B)) <-> (exists C (A = C & m1_card_fil(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B)))))))) # label(fraenkel_a_1_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5804 (all A (-v1_finset_1(A) & v4_card_fil(A) & v1_card_1(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_card_1(A) & v2_card_1(A) & v1_card_5(A) & -v1_finset_1(A) & -v1_xboole_0(A) & v1_ordinal1(A))) # label(cc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5805 (all A (-v1_xboole_0(A) -> m1_card_fil(k1_tarski(A),A))) # label(t4_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5806 (all A all B all C all D (v1_card_1(B) & -v2_card_1(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & m2_relset_1(C,k2_zfmisc_1(k7_card_fil(B),B),k1_zfmisc_1(B)) & m1_subset_1(D,B) & -v1_finset_1(B) -> (r2_hidden(A,a_3_3_card_fil(B,C,D)) <-> (exists E (k2_binop_1(k7_card_fil(B),B,k1_zfmisc_1(B),C,E,D) = A & r2_hidden(E,k7_card_fil(B)) & m1_subset_1(E,k7_card_fil(B))))))) # label(fraenkel_a_3_3_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5807 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> k1_card_1(A) = k1_card_1(C)))) <-> v1_card_fil(B,A)))))) # label(d5_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5808 (all A (-v1_xboole_0(A) -> (exists B m2_card_fil(B,A)))) # label(existence_m2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5809 (all A (-v1_finset_1(A) -> m2_card_fil(k6_card_fil(A),A))) # label(dt_k6_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5810 (all A all B all C all D (m1_card_fil(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_card_fil(B,C,D)) <-> (exists E ((exists F (m1_subset_1(F,k1_zfmisc_1(B)) & r2_hidden(F,a_3_1_card_fil(B,C,D)) & r1_tarski(F,E))) & A = E & m1_subset_1(E,k1_zfmisc_1(B))))))) # label(fraenkel_a_3_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5811 (all A (-v1_xboole_0(A) -> (all B (m2_card_fil(B,A) -> -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))))))) # label(dt_m2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5812 (all A (-v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r2_hidden(k1_card_1(k1_card_fil(A,B)),k1_card_1(A)) <-> r2_hidden(B,k5_card_fil(A))))))) # label(t18_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5813 (all A (-v2_card_1(A) & v1_card_1(A) & -v1_finset_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) -> (r4_card_fil(A,B) <-> (all C (m1_subset_1(C,k7_card_fil(A)) -> r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_2_card_fil(A,B,C)))),k7_card_fil(A)))) & (all C (m1_subset_1(C,A) -> r1_tarski(k1_card_1(k1_card_fil(A,k3_tarski(a_3_3_card_fil(A,B,C)))),k7_card_fil(A)))) & (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,k7_card_fil(A)) -> (all E (m1_subset_1(E,k7_card_fil(A)) -> (D != E -> v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,D,C),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,E,C)))))))))) & (all C (m1_subset_1(C,k7_card_fil(A)) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (E != D -> v1_xboole_0(k5_subset_1(A,k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,D),k2_binop_1(k7_card_fil(A),A,k1_zfmisc_1(A),B,C,E))))))))))))))) # label(d18_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5814 (exists A (v3_ordinal1(A) & -v1_xboole_0(A) & -v1_finset_1(A) & -v2_card_1(A) & v1_card_1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5815 (all A (-v1_finset_1(A) -> v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & -v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & -v1_finset_1(k1_card_1(A)))) # label(fc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5816 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v6_card_fil(A) -> v4_card_fil(A)))) # label(t30_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5817 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v7_card_fil(A) -> v6_card_fil(A)))) # label(t41_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5818 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v7_card_fil(A) -> v1_card_5(A)))) # label(t33_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5819 (all A (-v1_xboole_0(A) -> (all B (v1_card_1(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (-v1_xboole_0(D) -> (r1_tarski(D,C) & r2_hidden(k1_card_1(D),B) -> r2_hidden(k1_setfam_1(D),C)))) <-> r1_card_fil(A,B,C)))))))) # label(d3_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5820 (all A (-v1_finset_1(A) & v1_card_1(A) & -v2_card_1(A) -> (exists B (v1_funct_2(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & r4_card_fil(A,B) & m2_relset_1(B,k2_zfmisc_1(k7_card_fil(A),A),k1_zfmisc_1(A)) & v1_funct_1(B))))) # label(t34_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5821 (all A (-v1_finset_1(A) & -v2_card_1(A) & v1_card_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A) & -v1_finset_1(A) & v1_card_1(A) & v1_card_5(A))) # label(cc6_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5822 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) & v3_card_fil(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (-r2_hidden(C,k2_card_fil(A,B)) <-> r2_hidden(C,B)))))))) # label(t22_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5823 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (v1_card_fil(B,A) & v3_card_fil(B,A) -> -v2_card_fil(B,A)))))) # label(cc1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5824 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & -v1_xboole_0(C) -> ((exists D (D = A & r2_hidden(k3_subset_1(B,D),C) & m1_subset_1(D,k1_zfmisc_1(B)))) <-> r2_hidden(A,a_2_0_card_fil(B,C))))) # label(fraenkel_a_2_0_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5825 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,B) = a_2_0_card_fil(A,B))))) # label(t8_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5826 (all A (-v1_finset_1(A) -> a_1_1_card_fil(A) = k5_card_fil(A))) # label(d10_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5827 (all A all B (v1_card_1(B) -> -((all C -(k1_card_1(C) = B & r1_tarski(C,A))) & r1_tarski(B,k1_card_1(A))))) # label(t36_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5828 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v7_card_fil(A) -> v5_card_fil(A)))) # label(t40_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5829 (all A (-v1_finset_1(A) -> (all B (m1_card_fil(B,A) -> (v3_card_fil(B,A) & v1_card_fil(B,A) -> r1_tarski(k5_card_fil(A),B)))))) # label(t21_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5830 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(k3_subset_1(A,D),B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (r1_tarski(E,D) & r2_hidden(D,C) -> r2_hidden(E,C)) & (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k4_subset_1(A,D,E),C)))))) & -r2_hidden(A,C)))))))) # label(t7_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5831 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) -> (m1_card_fil(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(C,B) & r1_tarski(C,D) -> r2_hidden(D,B)) & (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k5_subset_1(A,C,D),B)))))) & -r2_hidden(k1_xboole_0,B)))))) # label(d1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5832 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B))))) # label(dt_m1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5833 (all A all B all C all D (-v1_xboole_0(B) & m1_card_fil(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,k1_zfmisc_1(B)) & k5_subset_1(B,E,D) = A & r2_hidden(E,C))) <-> r2_hidden(A,a_3_1_card_fil(B,C,D))))) # label(fraenkel_a_3_1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5834 (all A (v3_ordinal1(A) & v4_ordinal1(A) -> (all B (r1_tarski(B,A) & A = k7_ordinal2(B) -> k3_tarski(B) = A)))) # label(t32_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5835 (all A all B (-v1_xboole_0(A) & m1_card_fil(B,A) -> k7_setfam_1(A,B) = k2_card_fil(A,B))) # label(redefinition_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5836 (all A all B m1_subset_1(k1_card_fil(A,B),k1_zfmisc_1(A))) # label(dt_k1_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5837 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (v3_card_fil(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> r2_hidden(k1_card_fil(A,C),B) | r2_hidden(C,B)))))))) # label(d7_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5838 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k4_card_fil(A))) & -v1_xboole_0(B) -> (v6_ordinal1(B) -> m1_card_fil(k3_tarski(B),A)))))) # label(t16_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5839 (all A (-v1_xboole_0(A) -> k4_card_fil(A) = a_1_0_card_fil(A))) # label(d9_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5840 (all A (-v1_finset_1(A) -> m1_card_fil(k5_card_fil(A),A))) # label(dt_k5_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5841 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v1_card_5(A) & v2_card_1(A) <-> v4_card_fil(A)))) # label(d13_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5842 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k4_subset_1(A,C,D),B)) & (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B)))))) & -r2_hidden(A,B) <-> m2_card_fil(B,A)))))) # label(d2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5843 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) <-> r2_hidden(B,k4_card_fil(A)))))) # label(t15_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.51 5844 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v6_card_fil(A) <-> v5_card_fil(A) & v1_card_5(A)))) # label(d15_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5845 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v7_card_fil(A) <-> (exists B (m1_card_fil(B,A) & r1_card_fil(A,A,B) & -v2_card_fil(B,A) & v3_card_fil(B,A)))))) # label(d16_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5846 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_card_fil(C,A) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,C) & r1_xboole_0(D,B)))) -> r2_hidden(B,k3_card_fil(A,C,B)) & m1_card_fil(k3_card_fil(A,C,B),A) & r1_tarski(C,k3_card_fil(A,C,B))))))))) # label(t14_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5847 (all A (-v1_finset_1(A) & v1_card_1(A) -> (v5_card_fil(A) <-> (all B (v1_card_1(B) -> (r2_hidden(B,A) -> r2_hidden(k3_card_2(np__2,B),A))))))) # label(d14_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5848 (all A (v6_card_fil(A) & v1_card_1(A) & -v1_finset_1(A) -> v2_ordinal1(A) & -v1_xboole_0(A) & v1_card_1(A) & v1_card_5(A) & v4_card_fil(A) & v2_card_1(A) & -v1_finset_1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc5_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5849 (all A (-v1_finset_1(A) & v5_card_fil(A) & v1_card_1(A) -> v3_ordinal1(A) & v2_card_1(A) & v1_card_1(A) & -v1_finset_1(A) & -v1_xboole_0(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5850 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k7_setfam_1(A,B)))) # label(fc2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5851 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> r2_hidden(A,B))))) # label(t5_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5852 (all A (-v1_xboole_0(A) -> (all B (m2_card_fil(B,A) -> r2_hidden(k1_xboole_0,B))))) # label(t11_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5853 (all A (-v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r2_hidden(B,k6_card_fil(A)) <-> r2_hidden(k1_card_1(B),k1_card_1(A))))))) # label(t19_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5854 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (exists C (m1_card_fil(C,A) & v3_card_fil(C,A) & r1_tarski(B,C))))))) # label(t17_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5855 (all A (-v1_finset_1(A) -> k2_card_fil(A,k5_card_fil(A)) = k6_card_fil(A))) # label(d11_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5856 (all A (v1_card_1(A) & -v1_finset_1(A) -> k2_card_1(A) = k3_card_2(np__2,A))) <-> r3_card_fil # label(d12_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5857 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v7_card_fil(A) -> v2_card_1(A)))) # label(t38_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5858 (all A all B (-v1_xboole_0(A) & m1_card_fil(B,A) -> m2_card_fil(k2_card_fil(A,B),A))) # label(dt_k2_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5859 (all A (v1_card_1(A) & -v1_finset_1(A) -> (v4_card_fil(A) & r3_card_fil -> v6_card_fil(A)))) # label(t31_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5860 (all A (v1_card_1(A) & v6_card_fil(A) & -v1_finset_1(A) -> v2_ordinal1(A) & v3_ordinal1(A) & -v1_finset_1(A) & v1_card_1(A) & v2_card_1(A) & v5_card_fil(A) & v1_card_5(A) & -v1_xboole_0(A) & v1_ordinal1(A))) # label(cc4_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5861 (all A (-v1_xboole_0(A) -> (all B (m1_card_fil(B,A) -> (all C (m2_card_fil(C,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,k2_card_fil(A,B)) & r2_hidden(D,B)))) & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,C) & r2_hidden(D,k7_setfam_1(A,C))))))))))) # label(t10_card_fil) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5862 (exists A (m1_pboole(A,f1_s2_pre_circ) & (all B (m1_subset_1(B,f1_s2_pre_circ) -> (r2_hidden(B,f1_s2_pre_circ) -> (p1_s2_pre_circ(B) -> f2_s2_pre_circ(B) = k1_funct_1(A,B)) & (-p1_s2_pre_circ(B) -> f3_s2_pre_circ(B) = k1_funct_1(A,B))))))) # label(s2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5863 (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(A,B) & r1_xboole_0(k1_relat_1(A),k1_relat_1(C)) -> r1_tarski(A,k1_funct_4(B,C))))))))) # label(t4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5864 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> v1_finset_1(k1_funct_1(B,C)))) <-> v1_pre_circ(B,A)))) # label(d3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5865 (all A (r2_hidden(A,a_0_0_pre_circ) <-> (exists B (f2_s1_pre_circ(B) = A & p1_s1_pre_circ(B) & m1_subset_1(B,f1_s1_pre_circ))))) # label(fraenkel_a_0_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5866 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v2_relat_1(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v2_relat_1(k5_relat_1(B,A)))) # label(fc3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5867 (all A all B k2_pre_circ(A,B) = k2_funcop_1(A,B)) # label(redefinition_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5868 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (m1_trees_1(B,A) -> r2_tarski(k4_trees_1(A,B),a_2_0_pre_circ(A,B)))))) # label(t13_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5869 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) -> k3_pre_circ(A,B,C) = k7_relat_1(B,C))) # label(redefinition_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5870 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v2_membered(A) -> v1_xreal_0(k1_pre_circ(A)))) # label(dt_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5871 (exists A (-v1_xboole_0(A) & v2_membered(A) & v5_membered(A) & v4_membered(A) & v3_membered(A) & v1_membered(A) & v1_finset_1(A))) # label(rc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5872 (all A (v1_relat_1(A) & v6_trees_3(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> r2_hidden(k12_finseq_1(k5_numbers,B),k13_trees_3(k2_funct_6(A)))))))) # label(t17_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5873 (all A (v1_relat_1(A) & v1_funct_1(A) & v4_trees_3(A) & v1_finseq_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(B,np__1),k4_finseq_1(A)) -> k4_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,B)) = k1_funct_1(A,k1_nat_1(B,np__1))))))) # label(t16_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5874 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v4_trees_3(B) & v1_funct_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> ((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(B,D) | k1_nat_1(C,np__1) = D))) & r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) & k3_finseq_1(B) = k3_finseq_1(A) -> (all D (-v1_xboole_0(D) & v1_trees_1(D) -> (k1_funct_1(B,k1_nat_1(C,np__1)) = D -> k13_trees_3(B) = k5_trees_1(k13_trees_3(A),k12_finseq_1(k5_numbers,C),D))))))))))) # label(t18_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5875 $T # label(d2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5876 (all A (m1_subset_1(A,f1_s4_pre_circ) -> (r2_hidden(A,f2_s4_pre_circ) -> v1_funct_2(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A)) & m2_relset_1(f5_s4_pre_circ(A),k1_funct_1(f3_s4_pre_circ,A),k1_funct_1(f4_s4_pre_circ,A)) & v1_funct_1(f5_s4_pre_circ(A))))) -> (exists A (m3_pboole(A,f2_s4_pre_circ,f3_s4_pre_circ,f4_s4_pre_circ) & (all B (m1_subset_1(B,f1_s4_pre_circ) -> (r2_hidden(B,f2_s4_pre_circ) -> f5_s4_pre_circ(B) = k1_funct_1(A,B)))))) # label(s4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5877 (all A all B m1_pboole(k2_pre_circ(A,B),A)) # label(dt_k2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5878 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_card_1(A) = k1_card_1(k1_relat_1(A)))) # label(t21_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5879 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_trees_3(A)) -> v1_finset_1(B))))) # label(cc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5880 (exists A (v1_funct_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> f3_s3_pre_circ(B,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,B)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(B,np__1)))) & k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0) = f2_s3_pre_circ & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) & v1_funct_2(A,k5_numbers,f1_s3_pre_circ))) # label(s3_pre_circ_AndLHS) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5881 (all A (v1_funct_2(A,k5_numbers,f1_s3_pre_circ) & m2_relset_1(A,k5_numbers,f1_s3_pre_circ) & v1_funct_1(A) -> (all B (m2_relset_1(B,k5_numbers,f1_s3_pre_circ) & v1_funct_2(B,k5_numbers,f1_s3_pre_circ) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,B,C)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,B,k1_nat_1(C,np__1)))) & f2_s3_pre_circ = k8_funct_2(k5_numbers,f1_s3_pre_circ,B,np__0) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> f3_s3_pre_circ(C,k8_funct_2(k5_numbers,f1_s3_pre_circ,A,C)) = k8_funct_2(k5_numbers,f1_s3_pre_circ,A,k1_nat_1(C,np__1)))) & k8_funct_2(k5_numbers,f1_s3_pre_circ,A,np__0) = f2_s3_pre_circ -> A = B))))) # label(s3_pre_circ_AndRHS) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5882 (all A (v1_relat_1(k1_trees_4(A)) & v1_finset_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) & v1_funct_1(k1_trees_4(A)))) # label(fc6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5883 (all A all B all C (v1_relat_1(A) & v1_finset_1(A) & v3_trees_2(C) & v1_finset_1(C) & v1_funct_1(C) & v1_relat_1(C) & m1_subset_1(B,k1_relat_1(A)) & v3_trees_2(A) & v1_funct_1(A) -> v3_trees_2(k8_trees_2(A,B,C)) & v1_finset_1(k8_trees_2(A,B,C)) & v1_funct_1(k8_trees_2(A,B,C)) & v1_relat_1(k8_trees_2(A,B,C)))) # label(fc5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5884 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (k2_relat_1(A) = k1_tarski(C) & k1_relat_1(A) = k1_tarski(B) -> A = k1_tarski(k4_tarski(B,C)))))) # label(t2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5885 (all A (v5_membered(A) & v1_finset_1(A) & -v1_xboole_0(A) -> v1_xcmplx_0(k2_seq_4(A)) & v1_xreal_0(k2_seq_4(A)) & v4_ordinal2(k2_seq_4(A)))) # label(fc1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5886 (all A k4_card_1(k1_trees_4(A)) = np__1) # label(t24_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5887 (all A (-v1_xboole_0(A) -> (all B all C (m1_pboole(C,A) & v2_relat_1(C) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> k1_relat_1(k10_funct_6(D)) = B)))))) # label(t8_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5888 (all A (v3_trees_2(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) -> (all C (m1_trees_1(C,k1_relat_1(A)) -> k1_nat_1(k4_card_1(k8_trees_2(A,C,B)),k4_card_1(k5_trees_2(A,C))) = k1_nat_1(k4_card_1(A),k4_card_1(B)))))))) # label(t23_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5889 (all A k1_xboole_0 = k4_funct_5(k2_pre_circ(A,k1_xboole_0))) # label(t7_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5890 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (m1_trees_1(B,A) -> -(k1_xboole_0 != B & r1_xreal_0(k4_card_1(A),k4_card_1(k4_trees_1(A,B)))))))) # label(t20_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5891 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (m1_subset_1(D,k4_card_3(B)) -> (r1_tarski(k1_relat_1(C),k1_relat_1(B)) & (all E (r2_hidden(E,k1_relat_1(C)) -> r2_hidden(k1_funct_1(C,E),k1_funct_1(B,E)))) -> m1_subset_1(k1_funct_4(D,C),k4_card_3(B))))))))) # label(t9_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5892 (all A (-v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) -> (all B (v1_trees_1(B) & v1_finset_1(B) & -v1_xboole_0(B) -> (all C (m1_trees_1(C,A) -> (all D (m2_finseq_1(D,k5_numbers) -> -(r2_hidden(D,k5_trees_1(A,C,B)) & (all E (m1_trees_1(E,B) -> k8_finseq_1(k5_numbers,C,E) != D)) & r1_tarski(C,D)))))))))) # label(t15_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5893 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> r1_tarski(k1_funct_4(A,C),k1_funct_4(B,C))))))))) # label(t3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5894 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_pboole(B,A) -> m1_pboole(k3_pre_circ(A,B,C),C))) # label(dt_k3_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5895 (all A all B (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v2_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5896 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k4_card_3(k2_finseq_2(A,k1_tarski(B))) = k1_tarski(k2_finseq_2(A,B))))) # label(t12_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5897 (all A all B all C all D (-v1_xboole_0(B) & v1_trees_1(B) & v1_trees_1(C) & m1_trees_1(D,B) & v1_finset_1(C) & -v1_xboole_0(C) & v1_finset_1(B) -> ((exists E (A = k8_finseq_1(k5_numbers,D,E) & m1_trees_1(E,C))) <-> r2_hidden(A,a_3_0_pre_circ(B,C,D))))) # label(fraenkel_a_3_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5898 (all A (-v1_xboole_0(A) & v1_trees_1(A) & v1_finset_1(A) -> (all B (-v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) -> (all C (m1_trees_1(C,A) -> k2_xboole_0(a_2_1_pre_circ(A,C),a_3_0_pre_circ(A,B,C)) = k5_trees_1(A,C,B))))))) # label(t14_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5899 (all A exists B (v2_relat_1(B) & v1_funct_1(B) & v1_pre_circ(B,A) & v1_relat_1(B) & m1_pboole(B,A))) # label(rc2_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5900 (all A all B (m1_pboole(B,A) -> k1_tarski(k1_xboole_0) = k1_funct_1(k6_pboole(A,B),k6_finseq_1(A)))) # label(t5_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5901 (all A all B (m1_subset_1(B,k1_relat_1(A)) & v3_trees_2(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)) & v1_finset_1(k5_trees_2(A,B)))) # label(fc4_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5902 (all A (-v1_xboole_0(A) & v2_membered(A) & v1_finset_1(A) -> k1_pre_circ(A) = k2_seq_4(A))) # label(redefinition_k1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5903 (all A all B all C (-v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) & m1_trees_1(C,B) -> (r2_hidden(A,a_2_0_pre_circ(B,C)) <-> (exists D (r1_tarski(C,D) & A = D & m1_trees_1(D,B)))))) # label(fraenkel_a_2_0_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5904 $T # label(t1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5905 (all A (v1_finset_1(A) & v1_trees_1(A) & -v1_xboole_0(A) -> (all B (v1_finset_1(B) & v1_trees_1(B) & -v1_xboole_0(B) -> (all C (m1_trees_1(C,A) -> k1_nat_1(k4_card_1(k5_trees_1(A,C,B)),k4_card_1(k4_trees_1(A,C))) = k1_nat_1(k4_card_1(A),k4_card_1(B)))))))) # label(t22_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5906 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> -v1_xboole_0(k3_tarski(k2_relat_1(B))))))) # label(t6_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5907 (all A (-v1_xboole_0(A) & v2_membered(A) & v1_finset_1(A) -> (all B (v1_xreal_0(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r1_xreal_0(C,B)))) & r2_hidden(B,A) <-> k1_pre_circ(A) = B))))) # label(d1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5908 (all A all B all C (-v1_xboole_0(B) & m1_trees_1(C,B) & v1_trees_1(B) & v1_finset_1(B) -> ((exists D (m1_trees_1(D,B) & -r1_tarski(C,D) & D = A)) <-> r2_hidden(A,a_2_1_pre_circ(B,C))))) # label(fraenkel_a_2_1_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5909 (all A all B (m1_pboole(B,A) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(C,k4_card_3(B)) -> r2_hidden(k5_relat_1(D,C),k4_card_3(k5_relat_1(D,B)))))))))) # label(t11_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5910 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,k2_pre_circ(A,B),C) -> (all E (m1_subset_1(E,B) -> (exists F (m1_pboole(F,A) & F = k1_funct_1(k10_funct_6(D),E) & r3_pboole(A,F,C))))))))))))) # label(t10_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5911 (all A (v3_trees_2(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & v1_finset_1(B) -> (all C all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v6_trees_3(E) & v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> -(r2_hidden(k12_finseq_1(k5_numbers,D),k1_relat_1(A)) & (all F (v1_relat_1(F) & v1_funct_1(F) & v6_trees_3(F) & v1_finseq_1(F) -> -(k4_trees_4(C,F) = k8_trees_2(A,k12_finseq_1(k5_numbers,D),B) & k1_funct_1(F,k1_nat_1(D,np__1)) = B & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r2_hidden(G,k4_finseq_1(E)) -> k1_nat_1(D,np__1) = G | k1_funct_1(E,G) = k1_funct_1(F,G)))) & k3_finseq_1(F) = k3_finseq_1(E)))) & A = k4_trees_4(C,E)))))))))) # label(t19_pre_circ) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5912 (all A all B (m1_pboole(B,A) -> v1_funct_1(k1_mboolean(A,B)) & v2_relat_1(k1_mboolean(A,B)) & v1_relat_1(k1_mboolean(A,B)))) # label(fc1_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5913 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k1_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t9_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5914 (all A all B (v1_pre_circ(B,A) & m1_pboole(B,A) & v2_relat_1(B) -> ((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & r1_pboole(A,D,B) & -r2_pboole(A,D,C) & -r2_pboole(A,C,D)))))) -> r1_pboole(A,k2_mboolean(A,B),B)))) # label(t37_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5915 (all A all B (m1_pboole(B,A) -> m1_pboole(k2_mboolean(A,B),A))) # label(dt_k2_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5916 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k3_tarski(B)))) # label(t23_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5917 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k5_pboole(A,C,D)) <-> r5_pboole(A,B,k3_pboole(A,C,D)) & r2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t13_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5918 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,k2_tarski(k1_xboole_0,k1_tarski(B))))) # label(t4_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5919 (all A r6_pboole(A,k2_mboolean(A,k1_pboole(A)),k1_pboole(A))) # label(t22_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5920 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) <-> r1_pboole(A,D,B)))) <-> r6_pboole(A,B,k1_mboolean(A,C))))))) # label(t1_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5921 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_mboolean(A,k1_mboolean(A,B)),B))) # label(t30_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5922 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k2_pboole(A,k2_pre_circ(A,k1_tarski(k1_xboole_0)),k4_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)))))))) # label(t10_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5923 (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,k5_pboole(A,B,D),C)))))))) # label(t17_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5924 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (k2_mboolean(A,B) = C <-> (all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k3_tarski(k1_funct_1(B,D))))))))) # label(d2_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5925 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k2_mboolean(A,B),C) & r1_pboole(A,D,B) -> r2_pboole(A,D,C)))))))) # label(t32_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5926 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,k4_pboole(A,B,C)),k1_mboolean(A,k4_pboole(A,C,B))),k1_mboolean(A,k5_pboole(A,B,C))))))) # label(t12_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5927 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))) -> (all D (r2_hidden(D,A) -> r3_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(t8_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5928 (all A all B (m1_pboole(B,A) -> r2_pboole(A,B,k1_mboolean(A,k2_mboolean(A,B))))) # label(t31_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5929 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t5_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5930 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) -> r2_pboole(A,D,B)))) -> r2_pboole(A,k2_mboolean(A,C),B)))))) # label(t33_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5931 $T # label(t14_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5932 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (k1_mboolean(A,B) = C <-> (all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_zfmisc_1(k1_funct_1(B,D))))))))) # label(d1_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5933 (all A all B r6_pboole(A,k1_mboolean(A,k2_pre_circ(A,B)),k2_pre_circ(A,k1_zfmisc_1(B)))) # label(t3_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5934 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t29_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5935 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> r2_pboole(A,B,k2_mboolean(A,C))))))) # label(t26_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5936 (all A (v1_relat_1(k2_mboolean(A,k1_pboole(A))) & v1_funct_1(k2_mboolean(A,k1_pboole(A))) & v3_relat_1(k2_mboolean(A,k1_pboole(A))))) # label(fc2_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5937 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,k2_mboolean(A,C)) <-> (exists D (m1_pboole(D,A) & r1_pboole(A,B,D) & r1_pboole(A,D,C)))))))) # label(t21_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5938 (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,k3_pboole(A,B,D),C)))))))) # label(t15_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5939 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k4_pboole(A,C,D)) <-> r5_pboole(A,B,D) & r2_pboole(A,B,C)))))))) # label(t11_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5940 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))))))) # label(t6_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5941 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t27_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5942 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(k2_pboole(A,B,C)) & (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,k2_pboole(A,B,C)) & r1_pboole(A,E,k2_pboole(A,B,C)) -> D = E | r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A))))))) -> r6_pboole(A,k2_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C)))))))) # label(t35_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5943 (all A all B (m1_pboole(B,A) -> m1_pboole(k1_mboolean(A,B),A))) # label(dt_k1_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5944 (all A r6_pboole(A,k1_mboolean(A,k1_pboole(A)),k2_pre_circ(A,k1_tarski(k1_xboole_0)))) # label(t2_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5945 (all A all B all C r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k2_tarski(k1_tarski(B),k1_tarski(C)))),k2_pre_circ(A,k2_tarski(B,C)))) # label(t25_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5946 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,D),C)))))))) # label(t16_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5947 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_mboolean(A,k2_pboole(A,B,C)),k2_pboole(A,k2_mboolean(A,B),k2_mboolean(A,C))))))) # label(t28_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5948 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,C) -> r6_pboole(A,k3_pboole(A,D,B),k1_pboole(A))))) -> r6_pboole(A,k3_pboole(A,k2_mboolean(A,C),B),k1_pboole(A))))))) # label(t34_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5949 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> (r2_pboole(A,C,k2_mboolean(A,k2_pboole(A,B,D))) & (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r6_pboole(A,k3_pboole(A,E,C),k1_pboole(A))))) -> r2_pboole(A,C,k2_mboolean(A,B))))))))) # label(t36_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5950 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k11_pboole(A,B,C),k1_mboolean(A,k1_mboolean(A,k2_pboole(A,B,C)))))))) # label(t18_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5951 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,k1_mboolean(A,C)) <-> r2_pboole(A,B,C)))))) # label(t19_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5952 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k12_pboole(A,B,C),k1_mboolean(A,k11_pboole(A,B,C))))))) # label(t20_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5953 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))))))) # label(t7_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5954 (all A all B r6_pboole(A,k2_mboolean(A,k2_pre_circ(A,k1_tarski(B))),k2_pre_circ(A,B))) # label(t24_mboolean) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5955 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> (exists C (m4_pboole(C,A,k1_mboolean(A,B)) & v2_relat_1(C) & v1_funct_1(C) & v1_pre_circ(C,A) & v1_relat_1(C))))) # label(rc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5956 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & v1_funcop_1(B) -> v1_relat_1(k14_pboole(A,C,B)) & v1_pre_circ(k14_pboole(A,C,B),A) & v1_funct_1(k14_pboole(A,C,B)))) # label(fc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5957 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,E) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,k3_pboole(A,k6_mssubfam(A,B,E),D),k1_pboole(A))))))))))) # label(t48_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5958 (all A all B all C (m1_pboole(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & v1_pre_circ(B,A) -> v1_relat_1(k2_pboole(A,B,C)) & v1_pre_circ(k2_pboole(A,B,C),A) & v1_funct_1(k2_pboole(A,B,C)))) # label(fc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5959 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> r1_tarski(k8_setfam_1(A,B),k5_setfam_1(A,B))))) # label(t1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5960 (all A all B all C (m1_pboole(C,B) & v1_funcop_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (D = k1_funct_1(C,A) & r2_hidden(A,B) -> k2_relat_1(D) = k1_funct_1(k2_mssubfam(B,C),A)))))) # label(t13_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5961 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,C) -> r1_tarski(k8_setfam_1(A,C),B)))) # label(t2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5962 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (r2_hidden(D,C) -> r1_tarski(B,D))) -> r1_tarski(B,k8_setfam_1(A,C)) | k1_xboole_0 = C))) # label(t5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5963 (all A all B (m1_pboole(B,A) -> (exists C (v1_funct_1(C) & v1_pre_circ(C,A) & v3_relat_1(C) & v1_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5964 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) & v2_relat_1(B) -> -((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(-r2_pboole(A,C,D) & -r2_pboole(A,D,C) & r1_pboole(A,D,B) & r1_pboole(A,C,B)))))) & (all C (m1_pboole(C,A) -> -(r1_pboole(A,C,B) & (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,C,D)))))))))) # label(t28_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5965 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,k6_mssubfam(A,B,D)) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,C,E))))))))))) # label(t52_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5966 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> v1_relat_1(k1_mboolean(A,B)) & v2_relat_1(k1_mboolean(A,B)) & v1_funct_1(k1_mboolean(A,B)) & v1_pre_circ(k1_mboolean(A,B),A))) # label(fc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5967 (all A all B all C (v1_pre_circ(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_relat_1(k11_pboole(A,B,C)) & v1_pre_circ(k11_pboole(A,B,C),A) & v1_funct_1(k11_pboole(A,B,C)))) # label(fc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5968 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v1_pre_circ(k11_pboole(A,C,B),A) & v2_relat_1(B) -> v1_pre_circ(C,A)))))) # label(t19_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5969 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k2_mboolean(A,C),B))))) # label(t40_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5970 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> m1_pboole(k1_mssubfam(A,B),A))) # label(dt_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5971 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)) -> r2_pboole(A,k6_mssubfam(A,B,C),k2_mboolean(A,C)))))) # label(t42_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5972 (all A all B (m1_pboole(B,A) -> k1_mboolean(A,B) = k3_mssubfam(A,B))) # label(redefinition_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5973 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v6_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5974 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k2_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t34_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5975 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> m4_pboole(k4_pboole(A,D,B),A,k1_mboolean(A,C)))))))) # label(t36_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5976 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k5_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t37_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5977 (all A all B all C (m4_pboole(C,A,k1_mboolean(A,B)) & m1_pboole(B,A) -> k5_mssubfam(A,B,C) = k6_mssubfam(A,B,C))) # label(redefinition_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5978 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> m4_pboole(k1_pzfmisc1(A,B),A,k1_mboolean(A,C))))))) # label(t38_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5979 (all A all B (m1_pboole(B,A) -> m4_pboole(k3_mssubfam(A,B),A,k1_mboolean(A,B)))) # label(dt_k3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5980 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> m1_pboole(k2_mssubfam(A,B),A))) # label(dt_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5981 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & v1_pre_circ(C,A) -> v1_pre_circ(B,A)))))) # label(t18_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5982 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (r2_hidden(D,B) -> r1_tarski(C,D))) -> r1_tarski(C,k8_setfam_1(A,B))))))) # label(t4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5983 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (all E (m4_pboole(E,A,B) -> (r6_pboole(A,C,k2_pzfmisc1(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,D,E))))))))))) # label(t51_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5984 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k6_mssubfam(A,B,D),C)))) <-> v4_mssubfam(C,A,B)))))) # label(d6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5985 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v5_mssubfam(C,A,B) <-> r1_pboole(A,B,C)))))) # label(d7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5986 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) -> v1_pre_circ(B,A)))) # label(cc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5987 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> k1_mssubfam(A,B) = k2_funct_6(B))) # label(redefinition_k1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5988 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_xboole_0(B,C) & r2_hidden(B,D) -> r1_xboole_0(k8_setfam_1(A,D),C)))) # label(t7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5989 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,k1_pboole(A),C) <-> v6_mssubfam(C,A,B)))))) # label(d8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5990 (all A all B all C (v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_relat_1(k3_pboole(A,C,B)) & v1_pre_circ(k3_pboole(A,C,B),A) & v1_funct_1(k3_pboole(A,C,B)))) # label(fc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5991 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k1_pboole(A)) -> r6_pboole(A,k6_mssubfam(A,B,C),B)))))) # label(t41_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5992 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v1_mssubfam(C,A,B)))))) # label(cc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5993 (all A all B (m1_pboole(B,A) -> (exists C (m4_pboole(C,A,B) & v3_relat_1(C) & v1_pre_circ(C,A) & v1_funct_1(C) & v1_relat_1(C))))) # label(rc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5994 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & v1_pre_circ(C,A) -> v1_relat_1(k3_pboole(A,B,C)) & v1_funct_1(k3_pboole(A,B,C)) & v1_pre_circ(k3_pboole(A,B,C),A))) # label(fc3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5995 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,C))))))))) # label(t46_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5996 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,E,C) & r1_pboole(A,D,C) -> r1_pboole(A,k3_pboole(A,D,E),C)))))) <-> v3_mssubfam(C,A,B)))))) # label(d5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5997 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (r1_pboole(A,k1_pboole(A),C) -> r6_pboole(A,k6_mssubfam(A,B,C),k1_pboole(A))))))) # label(t44_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5998 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m4_pboole(D,A,k1_mboolean(A,C)) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r2_pboole(A,B,E)))) -> r2_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t45_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 5999 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & v1_pre_circ(k11_pboole(A,B,C),A) -> v1_pre_circ(C,A)))))) # label(t20_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6000 (all A all B (m1_pboole(B,A) -> k7_mssubfam(A,B) = k1_mboolean(A,B))) # label(redefinition_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6001 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r2_pboole(A,C,D) & r1_pboole(A,C,E) -> r2_pboole(A,k6_mssubfam(A,B,E),D)))))))))) # label(t47_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6002 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (k1_tarski(C) = B -> k8_setfam_1(A,B) = C))))) # label(t9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6003 (all A all B all C (v1_funcop_1(C) & m1_pboole(C,B) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & D = k1_funct_1(C,A) -> k1_funct_1(k1_mssubfam(B,C),A) = k1_relat_1(D)))))) # label(t14_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6004 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,B) -> (r6_pboole(A,C,k1_pzfmisc1(A,D)) -> r6_pboole(A,k6_mssubfam(A,B,C),D)))))))) # label(t50_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6005 (all A all B all C (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) -> m4_pboole(k6_mssubfam(A,B,C),A,B))) # label(dt_k6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6006 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(k1_xboole_0,B) -> k1_xboole_0 = k8_setfam_1(A,B)))) # label(t3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6007 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> ((all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r1_pboole(A,D,C) & r1_pboole(A,E,C) -> r1_pboole(A,k2_pboole(A,D,E),C)))))) <-> v1_mssubfam(C,A,B)))))) # label(d3_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6008 (all A all B all C (m4_pboole(C,A,k1_mboolean(A,B)) & m1_pboole(B,A) -> m1_pboole(k5_mssubfam(A,B,C),A))) # label(dt_k5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6009 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> (r2_pboole(A,B,k2_mssubfam(A,C)) & (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(D,A) & k1_funct_1(C,D) = E -> v1_finset_1(k10_relat_1(E,k1_funct_1(B,D)))))) -> v1_pre_circ(B,A)))))) # label(t25_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6010 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> v1_funcop_1(k13_pboole(B,C)) & m1_pboole(k13_pboole(B,C),A))))) # label(t15_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6011 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> m4_pboole(k2_pzfmisc1(A,B,D),A,k1_mboolean(A,C))))))))) # label(t39_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6012 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (k2_tarski(C,D) = B -> k5_subset_1(A,C,D) = k8_setfam_1(A,B)))))))) # label(t10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6013 (all A all B (v2_relat_1(B) & v1_pre_circ(B,A) & m1_pboole(B,A) -> -((all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r1_pboole(A,C,B) & -r2_pboole(A,C,D) & -r2_pboole(A,D,C) & r1_pboole(A,D,B)))))) & (all C (m1_pboole(C,A) -> -(r1_pboole(A,C,B) & (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r2_pboole(A,D,C)))))))))) # label(t29_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6014 (all A all B all C (v1_pre_circ(B,A) & m1_pboole(B,A) & m1_pboole(C,A) & v1_pre_circ(C,A) -> v1_funct_1(k5_pboole(A,B,C)) & v1_pre_circ(k5_pboole(A,B,C),A) & v1_relat_1(k5_pboole(A,B,C)))) # label(fc10_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6015 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,C)) -> (r1_pboole(A,B,D) -> m4_pboole(B,A,C)))))))) # label(t33_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6016 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) -> m2_pboole(B,A,C)))))) # label(t11_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6017 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v3_mssubfam(C,A,B)))))) # label(cc4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6018 (all A all B (m1_pboole(B,A) & v1_pre_circ(B,A) -> (all C (m4_pboole(C,A,B) -> v1_pre_circ(C,A))))) # label(cc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6019 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (m3_pboole(C,A,B,k1_pboole(A)) -> r6_pboole(A,C,k1_pboole(A)))))) # label(t16_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6020 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> k2_mssubfam(A,B) = k3_funct_6(B))) # label(redefinition_k2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6021 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k4_subset_1(k1_zfmisc_1(A),C,D) -> k8_setfam_1(A,B) = k5_subset_1(A,k8_setfam_1(A,C),k8_setfam_1(A,D))))))))) # label(t8_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6022 (all A all B all C all D (m4_pboole(C,A,k1_mboolean(A,B)) & m1_subset_1(D,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> k4_mssubfam(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6023 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (all E (m4_pboole(E,A,k1_mboolean(A,B)) -> (r6_pboole(A,C,k2_pboole(A,D,E)) -> r6_pboole(A,k6_mssubfam(A,B,C),k3_pboole(A,k6_mssubfam(A,B,D),k6_mssubfam(A,B,E)))))))))))) # label(t49_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6024 (all A all B all C (m1_pboole(C,B) -> (all D (m4_pboole(D,B,k1_mboolean(B,C)) -> (r2_hidden(A,B) -> m1_subset_1(k1_funct_1(D,A),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(C,A))))))))) # label(t32_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6025 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(v1_pre_circ(B,A) & r2_pboole(A,B,k11_pboole(A,C,D)) & (all E (m1_pboole(E,A) -> (all F (m1_pboole(F,A) -> -(v1_pre_circ(E,A) & v1_pre_circ(F,A) & r2_pboole(A,B,k11_pboole(A,E,F)) & r2_pboole(A,F,D) & r2_pboole(A,E,C))))))))))))) # label(t26_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6026 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v5_mssubfam(C,A,B) -> v2_relat_1(C)))))) # label(cc6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.52 6027 (all A all B all C all D (m1_pboole(B,A) & m4_pboole(C,A,k1_mboolean(A,B)) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k4_mssubfam(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,D)))))) # label(dt_k4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6028 (all A all B all C (v1_pre_circ(B,A) & v1_pre_circ(C,A) & m1_pboole(C,A) & m1_pboole(B,A) -> v1_funct_1(k12_pboole(A,B,C)) & v1_pre_circ(k12_pboole(A,B,C),A) & v1_relat_1(k12_pboole(A,B,C)))) # label(fc9_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6029 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(B,A) <-> v1_pre_circ(k1_mboolean(A,B),A)))) # label(t21_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6030 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> ((all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A)))) & v1_pre_circ(B,A) -> v1_pre_circ(k2_mboolean(A,B),A)))) # label(t22_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6031 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(v1_pre_circ(B,A) & (all E (m1_pboole(E,A) -> -(v1_pre_circ(E,A) & r2_pboole(A,B,k11_pboole(A,E,C)) & r2_pboole(A,E,D)))) & r2_pboole(A,B,k11_pboole(A,D,C)) & v1_pre_circ(C,A)))))))) # label(t27_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6032 (all A all B (m1_pboole(B,A) -> (exists C (v1_relat_1(C) & v1_funct_1(C) & v2_relat_1(C) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6033 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) & v1_pre_circ(C,A) -> v1_relat_1(k4_pboole(A,C,B)) & v1_pre_circ(k4_pboole(A,C,B),A) & v1_funct_1(k4_pboole(A,C,B)))) # label(fc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6034 (all A all B (m1_pboole(B,A) -> v3_relat_1(k1_pboole(A)) & v1_pre_circ(k1_pboole(A),A) & m4_pboole(k1_pboole(A),A,k1_mboolean(A,B)))) # label(t31_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6035 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) -> v6_mssubfam(C,A,B)))))) # label(cc7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6036 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (v1_pre_circ(k1_mssubfam(A,B),A) -> v1_pre_circ(k2_mssubfam(A,B),A)))) # label(t24_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6037 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v1_funcop_1(D) & m1_pboole(D,A) -> (m3_pboole(D,A,B,C) & r1_pzfmisc1(A,B,C) -> r6_pboole(A,k1_mssubfam(A,D),B) & r2_pboole(A,k2_mssubfam(A,D),C)))))))) # label(t17_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6038 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m4_pboole(D,A,k1_mboolean(A,C)) -> (r1_pboole(A,B,C) & (all E (m1_pboole(E,A) -> (r1_pboole(A,E,D) -> r1_pboole(A,B,E)))) -> r1_pboole(A,B,k6_mssubfam(A,C,D))))))))) # label(t53_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6039 $T # label(d1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6040 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m1_pboole(D,A) -> ((all E -((all F (m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(B,E)))) -> -(k8_setfam_1(k1_funct_1(B,E),F) = k1_funct_1(D,E) & k1_funct_1(C,E) = F))) & r2_hidden(E,A))) <-> k5_mssubfam(A,B,C) = D))))))) # label(d2_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6041 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) & v2_relat_1(C) -> (m2_pboole(B,A,C) -> r1_pboole(A,B,C)))))) # label(t12_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6042 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v2_mssubfam(C,A,B) <-> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r2_pboole(A,D,C) -> r1_pboole(A,k2_mboolean(A,D),C))))))))) # label(d4_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6043 (all A all B (m1_pboole(B,A) -> v1_mssubfam(k7_mssubfam(A,B),A,B) & v2_mssubfam(k7_mssubfam(A,B),A,B) & v3_mssubfam(k7_mssubfam(A,B),A,B) & v4_mssubfam(k7_mssubfam(A,B),A,B) & v6_mssubfam(k7_mssubfam(A,B),A,B) & m4_pboole(k7_mssubfam(A,B),A,k1_mboolean(A,B)) & v5_mssubfam(k7_mssubfam(A,B),A,B))) # label(dt_k7_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6044 (all A (v1_relat_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)) & v1_pre_circ(k1_pboole(A),A))) # label(fc1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6045 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (v4_mssubfam(C,A,B) -> v5_mssubfam(C,A,B)))))) # label(cc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6046 (all A all B (m1_pboole(B,A) & v1_funcop_1(B) -> (all C (m1_pboole(C,A) -> -(r2_pboole(A,C,k2_mssubfam(A,B)) & (all D (m1_pboole(D,A) -> -(r2_pboole(A,D,k1_mssubfam(A,B)) & v1_pre_circ(D,A) & r6_pboole(A,k14_pboole(A,D,B),C)))) & v1_pre_circ(C,A)))))) # label(t30_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6047 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,k1_mboolean(A,B)) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> m4_pboole(k3_pboole(A,C,D),A,k1_mboolean(A,B)))))))) # label(t35_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6048 (all A all B (m1_pboole(B,A) -> (exists C (v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) & v2_mssubfam(C,A,B) & v6_mssubfam(C,A,B) & v5_mssubfam(C,A,B) & v4_mssubfam(C,A,B) & v3_mssubfam(C,A,B) & v1_mssubfam(C,A,B) & m4_pboole(C,A,k1_mboolean(A,B)))))) # label(rc5_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6049 (all A all B (m1_pboole(B,A) -> (v1_pre_circ(k2_mboolean(A,B),A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,C,B) -> v1_pre_circ(C,A)))) & v1_pre_circ(B,A)))) # label(t23_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6050 (all A (r2_hidden(A,f1_s1_mssubfam) -> (all B -((all C -(p1_s1_mssubfam(C,B,A) & r2_hidden(C,k1_funct_1(f3_s1_mssubfam,A)))) & r2_hidden(B,k1_funct_1(f2_s1_mssubfam,A)))))) -> (exists A ((all B -((all C (v1_funct_1(C) & v1_funct_2(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) & m2_relset_1(C,k1_funct_1(f2_s1_mssubfam,B),k1_funct_1(f3_s1_mssubfam,B)) -> -(C = k1_funct_1(A,B) & (all D (r2_hidden(D,k1_funct_1(f2_s1_mssubfam,B)) -> p1_s1_mssubfam(k1_funct_1(C,D),D,B)))))) & r2_hidden(B,f1_s1_mssubfam))) & m3_pboole(A,f1_s1_mssubfam,f2_s1_mssubfam,f3_s1_mssubfam))) # label(s1_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6051 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m4_pboole(D,A,k1_mboolean(A,B)) -> (r1_pboole(A,C,D) -> r2_pboole(A,k6_mssubfam(A,B,D),C)))))))) # label(t43_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6052 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,C) & r2_hidden(B,D) -> r1_tarski(k8_setfam_1(A,D),C)))) # label(t6_mssubfam) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6053 (all A all B (v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)) & -v1_xboole_0(k3_cqc_lang(A,B)))) # label(fc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6054 $T # label(dt_k7_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6055 $T # label(dt_k6_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6056 p1_s5_funct_7(k1_xboole_0) & (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_finseq_1(A) -> (p1_s5_funct_7(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> p1_s5_funct_7(k7_finseq_1(A,k9_finseq_1(B)))))))) -> (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> p1_s5_funct_7(A))) # label(s5_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6057 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(B)) -> E = D | k4_finseq_4(k5_numbers,A,B,E) = k4_finseq_4(k5_numbers,A,k3_funct_7(A,B,D,C),E)))))))))))) # label(t39_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6058 (all A k9_finseq_1(A) = k5_funct_7(k1_xboole_0,A)) # label(t42_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6059 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_funcop_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k7_finseq_1(k5_funct_7(B,A),k9_finseq_1(k1_funct_1(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1))))) = k5_funct_7(k7_finseq_1(B,k9_finseq_1(C)),A))))) # label(t44_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6060 (all A all B (v1_relat_1(A) & v1_finseq_1(A) & v1_finseq_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_relat_1(B) & v1_funcop_1(A) & v1_funct_1(A) -> v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_funcop_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc8_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6061 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k4_funct_7(A,k9_finseq_1(B)) = k5_relat_1(k6_partfun1(A),B))) # label(t47_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6062 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & -v1_xboole_0(B) -> (exists C ((all D (m2_subset_1(D,k1_zfmisc_1(A),B) -> (r1_tarski(D,C) -> C = D))) & m2_subset_1(C,k1_zfmisc_1(A),B))))))) # label(t23_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6063 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D k2_funct_7(A,D,C) = k2_funct_7(k2_funct_7(A,D,B),D,C)))) # label(t36_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6064 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_7(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k7_funct_7(A),k1_relat_1(B)) -> v1_relat_1(k7_finseq_1(A,k9_finseq_1(B))) & v1_funct_7(k7_finseq_1(A,k9_finseq_1(B))) & v1_finseq_1(k7_finseq_1(A,k9_finseq_1(B))) & v1_funct_1(k7_finseq_1(A,k9_finseq_1(B)))))))) # label(t66_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6065 (all A all B (v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (B != k1_xboole_0 -> r1_tarski(k2_relat_1(k4_funct_7(A,B)),k7_funct_7(B))))) # label(t61_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6066 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k5_relat_1(A,k9_funct_7(A,B)) = k9_funct_7(A,k1_nat_1(B,np__1)))))) # label(t71_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6067 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k9_funct_7(k1_xboole_0,A) = k1_xboole_0)) # label(t82_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6068 (all A all B all C (v1_funcop_1(C) & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_finseq_1(D) & v1_funcop_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(k4_funct_7(A,C)),B) -> k4_funct_7(A,k7_finseq_1(C,D)) = k5_relat_1(k4_funct_7(A,C),k4_funct_7(B,D))))))) # label(t50_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6069 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B A = k2_funct_7(A,B,k1_funct_1(A,B))))) # label(t37_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6070 (all A (v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_funct_7(A) & v1_funcop_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(cc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6071 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((exists D (m2_relset_1(D,k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) & C = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,B) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (exists F (v1_relat_1(F) & v1_funct_1(F) & F = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,E) & k5_relat_1(A,F) = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,k1_nat_1(E,np__1)))))) & k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) = k8_funct_2(k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),D,np__0) & v1_funct_2(D,k5_numbers,k4_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) & v1_funct_1(D))) <-> k9_funct_7(A,B) = C))))))) # label(d11_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6072 (all A (v1_relat_1(A) & v1_funct_1(A) -> -v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc4_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6073 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k4_finseq_4(k5_numbers,A,k3_funct_7(A,B,D,C),D) = C))))))))) # label(t38_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6074 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_tarski(k2_relat_1(A),k1_relat_1(A)) -> k9_funct_7(k9_funct_7(A,B),C) = k9_funct_7(A,k2_nat_1(B,C))))))))) # label(t81_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6075 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B ((-v1_xboole_0(A) -> (k7_funct_7(A) = B <-> B = k2_funct_5(k1_funct_1(A,k3_finseq_1(A))))) & (v1_xboole_0(A) -> (B = k7_funct_7(A) <-> v1_xboole_0(B))))))) # label(d7_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6076 (all A all B (v1_funct_1(B) & v1_relat_1(B) & m1_subset_1(A,k5_numbers) -> v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) & v1_funcop_1(k2_finseq_2(A,B)) & v1_finset_1(k2_finseq_2(A,B)))) # label(fc7_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6077 $T # label(t9_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6078 (all A (m1_subset_1(A,f2_s3_funct_7) -> (all B (m1_subset_1(B,f2_s3_funct_7) -> (f3_s3_funct_7(A) = f3_s3_funct_7(B) -> B = A))))) & (all A -((all B (m1_subset_1(B,f2_s3_funct_7) -> A != f3_s3_funct_7(B))) & r2_hidden(A,f1_s3_funct_7))) -> r2_tarski(f1_s3_funct_7,a_0_1_funct_7) # label(s3_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6079 (all A (v1_relat_1(A) & v1_funct_1(A) -> k9_funct_7(A,np__1) = A)) # label(t72_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6080 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k7_relat_1(C,A),k4_funct_7(k9_relat_1(C,A),B)) = k4_funct_7(A,k7_finseq_1(k9_finseq_1(C),B)))))) # label(t45_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6081 (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_funct_7(k11_finseq_1(B,C,D),A) = k7_finseq_1(k9_finseq_1(A),k11_finseq_1(k1_funct_1(B,A),k1_funct_1(C,k1_funct_1(B,A)),k1_funct_1(D,k1_funct_1(C,k1_funct_1(B,A))))))))))) # label(t58_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6082 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k7_relat_1(A,k1_tarski(B)) = k3_cqc_lang(B,k1_funct_1(A,B)))))) # label(t6_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6083 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k6_funct_7(k7_finseq_1(k9_finseq_1(A),B)) = k1_relat_1(A) & k2_relat_1(A) = k7_funct_7(k7_finseq_1(B,k9_finseq_1(A))))))) # label(t60_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6084 $T # label(t17_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6085 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_funct_7(A,B,C) <-> k7_relat_1(B,k4_xboole_0(k1_relat_1(B),C)) = k7_relat_1(A,k4_xboole_0(k1_relat_1(A),C)))))))) # label(d2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6086 (all A all B ((v1_xboole_0(B) -> v1_xboole_0(A)) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_funct_7(C) & v1_relat_1(C) -> (A = k6_funct_7(C) & r1_tarski(k7_funct_7(C),B) <-> m1_funct_7(C,A,B)))))) # label(d9_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6087 (all A (v1_finseq_1(A) & v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) & -v1_xboole_0(A) -> (exists B m2_funct_7(B,A)))) # label(existence_m2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6088 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k6_partfun1(A) = k9_funct_7(B,np__0))) # label(t86_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6089 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (v1_funct_7(k7_finseq_1(A,B)) -> v1_funct_7(B) & v1_funct_7(A)))))) # label(t62_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6090 (all A all B m1_subset_1(k1_funct_7(A,B),B)) # label(dt_k1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6091 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k6_partfun1(A) = k9_funct_7(k6_partfun1(A),B))) # label(t83_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6092 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k4_funct_7(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)),k2_finseq_2(B,A)) = k9_funct_7(A,B))))) # label(t90_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6093 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D k1_funct_4(A,k2_funcop_1(B,D)) = k1_funct_4(k1_funct_4(A,k2_funcop_1(B,C)),k2_funcop_1(B,D))))) # label(t16_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6094 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (v1_funct_7(A) <-> (exists B (v1_funct_1(B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),k1_funct_2(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__1))))))) & k3_finseq_1(B) = k1_nat_1(k3_finseq_1(A),np__1) & v1_finseq_1(B) & v1_relat_1(B)))))) # label(d8_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6095 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (r2_hidden(k8_funct_2(A,B,C,D),k2_funct_2(A,B,C,E)) -> r2_hidden(D,E))))))))))))) # label(t3_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6096 (all A ((exists B (r2_hidden(f4_s2_funct_7(B),f1_s2_funct_7) & f3_s2_funct_7(B) = A & m1_subset_1(B,f2_s2_funct_7))) <-> r2_hidden(A,a_0_0_funct_7))) # label(fraenkel_a_0_0_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6097 (all A (m1_subset_1(A,f1_s1_funct_7) -> (all B (m1_subset_1(B,f2_s1_funct_7) -> r2_hidden(f4_s1_funct_7(A,B),f3_s1_funct_7))))) -> (exists A ((all B (m1_subset_1(B,f1_s1_funct_7) -> (all C (m1_subset_1(C,f2_s1_funct_7) -> k8_funct_2(k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7,A,k1_domain_1(f1_s1_funct_7,f2_s1_funct_7,B,C)) = f4_s1_funct_7(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7) & v1_funct_2(A,k2_zfmisc_1(f1_s1_funct_7,f2_s1_funct_7),f3_s1_funct_7) & v1_funct_1(A))) # label(s1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6098 (all A all B (v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k4_funct_7(A,k7_finseq_1(B,k9_finseq_1(C))) = k5_relat_1(k4_funct_7(A,B),C))))) # label(t43_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6099 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_funct_7(B) -> (k1_xboole_0 != B -> k3_xboole_0(k6_funct_7(B),A) = k1_relat_1(k4_funct_7(A,B))))) # label(t63_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6100 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (r2_hidden(k8_funct_2(A,B,C,D),k6_subset_1(B,k2_funct_2(A,B,C,E),F)) -> r2_hidden(D,k6_subset_1(A,E,k3_funct_2(A,B,C,F))))))))))))))))) # label(t4_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6101 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k1_funct_4(k5_relat_1(A,B),k5_relat_1(A,C)) = k5_relat_1(A,k1_funct_4(B,C)))))))) # label(t11_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6102 (all A (v1_funct_7(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),k6_funct_7(A)) -> v1_relat_1(k7_finseq_1(k9_finseq_1(B),A)) & v1_funct_7(k7_finseq_1(k9_finseq_1(B),A)) & v1_finseq_1(k7_finseq_1(k9_finseq_1(B),A)) & v1_funct_1(k7_finseq_1(k9_finseq_1(B),A))))))) # label(t65_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6103 (all A (v1_relat_1(A) & v1_funct_1(A) -> k9_funct_7(A,np__0) = k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))))) # label(t70_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6104 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(B),A) | r1_tarski(k1_relat_1(k5_relat_1(B,C)),A) -> k4_funct_7(A,k10_finseq_1(B,C)) = k5_relat_1(B,C)))))) # label(t54_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6105 (exists A (v1_relat_1(A) & v2_relat_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funct_7(A) & v1_funcop_1(A) & v1_funct_1(A) & -v1_xboole_0(A))) # label(rc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6106 (all A all B (r2_hidden(A,B) -> A = k1_funct_7(A,B))) # label(d1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6107 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_tarski(k2_relat_1(A),k1_relat_1(A)) -> r1_tarski(k2_relat_1(k9_funct_7(A,B)),k1_relat_1(A)) & k1_relat_1(A) = k1_relat_1(k9_funct_7(A,B))))))) # label(t76_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6108 (all A (-v1_xboole_0(A) & v1_finseq_1(A) & v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> (all B (m2_funct_7(B,A) -> v2_relat_1(B) & v1_funct_7(B))))) # label(cc3_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6109 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> k3_funct_7(A,B,E,k4_finseq_4(k5_numbers,A,B,E)) = B)))))))))) # label(t40_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6110 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (np__0 != B -> k9_funct_7(A,k2_nat_1(C,B)) = k9_funct_7(k9_funct_7(A,C),B)))))))) # label(t80_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6111 (all A ((exists B (m1_subset_1(B,f2_s4_funct_7) & A = f3_s4_funct_7(B) & r2_hidden(B,f1_s4_funct_7))) <-> r2_hidden(A,a_0_2_funct_7))) # label(fraenkel_a_0_2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6112 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D (D != C -> k1_funct_1(k2_funct_7(A,C,B),D) = k1_funct_1(A,D))))) # label(t34_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6113 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B r1_funct_7(A,A,B)))) # label(t27_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6114 (all A (-v1_xboole_0(A) & v1_finseq_1(A) & v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> (all B (m2_funct_7(B,A) -> v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))))) # label(dt_m2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6115 (exists A (-v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_funcop_1(A) & v1_finseq_1(A))) # label(rc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6116 (all A all B (v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((exists D (v1_funcop_1(D) & C = k1_funct_1(D,k3_finseq_1(B)) & k1_funct_1(D,np__0) = k6_partfun1(A) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(E,np__1),k4_finseq_1(B)) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (all G (v1_relat_1(G) & v1_funct_1(G) -> (k1_funct_1(B,k1_nat_1(E,np__1)) = G & F = k1_funct_1(D,E) -> k1_funct_1(D,k1_nat_1(E,np__1)) = k5_relat_1(F,G))))))))) & m1_pboole(D,k5_numbers))) <-> C = k4_funct_7(A,B)))))) # label(d4_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6117 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) & -v1_xboole_0(A) -> (all B (m2_funct_7(B,A) -> k1_funct_1(A,np__1) = k1_relat_1(k4_funct_7(k1_funct_1(A,np__1),B)) & r1_tarski(k2_relat_1(k4_funct_7(k1_funct_1(A,np__1),B)),k1_funct_1(A,k3_finseq_1(A))))))) # label(t69_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6118 (all A (v2_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) & -v1_xboole_0(A) -> (all B (m2_funct_7(B,A) -> (k1_xboole_0 != B -> r1_tarski(k7_funct_7(B),k1_funct_1(A,k3_finseq_1(A))) & k1_funct_1(A,np__1) = k6_funct_7(B)))))) # label(t68_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6119 (all A all B (v1_relat_1(B) & v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> v1_relat_1(k4_funct_7(A,B)) & v1_funct_1(k4_funct_7(A,B)))) # label(dt_k4_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6120 (all A (v1_funct_1(A) & v1_relat_1(A) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(A)) -> k1_xboole_0 = k9_funct_7(A,np__2)))) # label(t84_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6121 (all A all B (r1_tarski(k3_finseq_2(A),k3_finseq_2(B)) -> r1_tarski(A,B))) # label(t21_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6122 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_funct_7(A,B,C) -> r1_funct_7(B,A,C))))))) # label(t28_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6123 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (r2_hidden(D,k6_subset_1(B,k2_funct_2(A,B,C,E),F)) -> r2_hidden(k1_funct_1(k2_funct_1(C),D),k6_subset_1(A,E,k3_funct_2(A,B,C,F))))))))))))))))) # label(t5_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6124 (all A (-v1_xboole_0(A) & v1_finseq_1(A) & v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k1_nat_1(k3_finseq_1(B),np__1) = k3_finseq_1(A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> r2_hidden(k1_funct_1(B,C),k1_funct_2(k1_funct_1(A,C),k1_funct_1(A,k1_nat_1(C,np__1))))))) <-> m2_funct_7(B,A)))))) # label(d10_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6125 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> v1_funct_2(k9_funct_7(C,B),A,A) & m2_relset_1(k9_funct_7(C,B),A,A) & v1_funct_1(k9_funct_7(C,B)))))) # label(t85_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6126 (all A all B all C all D (m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,A) -> k3_funct_7(A,B,C,D) = k2_funct_7(B,C,D))) # label(redefinition_k3_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6127 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(A,B) = k5_relat_1(k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A))),k9_funct_7(A,B)))))) # label(t77_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6128 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k9_funct_7(D,k2_nat_1(B,C)) = k9_funct_7(k9_funct_7(D,B),C))))))) # label(t87_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6129 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B ((-v1_xboole_0(A) -> (k1_funct_5(k1_funct_1(A,np__1)) = B <-> B = k6_funct_7(A))) & (v1_xboole_0(A) -> (k6_funct_7(A) = B <-> v1_xboole_0(B))))))) # label(d6_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6130 (all A all B all C (m1_funct_7(C,A,B) -> v1_funct_1(C) & v1_finseq_1(C) & v1_funct_7(C) & v1_relat_1(C))) # label(dt_m1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6131 (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 (r1_funct_7(A,B,D) & r1_funct_7(B,C,D) -> r1_funct_7(A,C,D))))))))) # label(t29_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6132 (all A all B (v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_funcop_1(C) & v1_relat_1(C) -> k1_rewrite1(k5_funct_7(B,A),k5_funct_7(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1)))) = k5_funct_7(k7_finseq_1(B,C),A))))) # label(t52_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6133 (all A all B all C (-v1_xboole_0(A) & m1_funct_7(C,B,A) -> v1_funct_1(k8_funct_7(A,B,C)) & v1_funct_2(k8_funct_7(A,B,C),B,A) & m2_relset_1(k8_funct_7(A,B,C),B,A))) # label(dt_k8_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6134 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (-(-r1_tarski(k1_relat_1(k5_relat_1(B,k5_relat_1(C,D))),A) & -r1_tarski(k1_relat_1(k5_relat_1(B,C)),A) & -r1_tarski(k1_relat_1(B),A)) -> k5_relat_1(B,k5_relat_1(C,D)) = k4_funct_7(A,k11_finseq_1(B,C,D))))))))) # label(t57_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6135 (all A all B (m1_pboole(B,A) -> (all C (r2_hidden(C,A) -> k7_relat_1(B,k1_tarski(C)) = k3_cqc_lang(C,k1_funct_1(B,C)))))) # label(t7_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6136 (all A all B all C (-r1_xboole_0(A,k2_relat_1(k1_funct_4(k6_partfun1(B),k2_funcop_1(A,C)))) -> r2_hidden(C,A))) # label(t13_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6137 (all A all B (v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_funct_7(k7_finseq_1(k9_finseq_1(C),B),A) = k7_finseq_1(k9_finseq_1(A),k5_funct_7(B,k1_funct_1(C,A))))))) # label(t46_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6138 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,k1_funct_4(C,B)) = k5_relat_1(A,C)))))))) # label(t12_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6139 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> (all D all E (r2_hidden(E,B) & r2_hidden(D,A) -> k7_relat_1(C,k2_zfmisc_1(k1_tarski(D),k1_tarski(E))) = k9_funct_2(D,E,k1_binop_1(C,D,E)))))) # label(t8_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6140 (all A (m1_subset_1(A,f2_s4_funct_7) -> (all B (m1_subset_1(B,f2_s4_funct_7) -> (f3_s4_funct_7(B) = f3_s4_funct_7(A) -> B = A))))) & r1_tarski(f1_s4_funct_7,f2_s4_funct_7) -> r2_tarski(f1_s4_funct_7,a_0_2_funct_7) # label(s4_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6141 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> r1_tarski(k2_relat_1(k9_funct_7(A,B)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))) & r1_tarski(k1_relat_1(k9_funct_7(A,B)),k2_xboole_0(k1_relat_1(A),k2_relat_1(A))))))) # label(t74_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6142 (all A all B all C (r2_hidden(A,k3_xboole_0(B,C)) -> k1_funct_7(A,C) = k1_funct_7(A,B))) # label(t26_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6143 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_relset_1(C,A,A) & v1_funct_1(C) -> v1_funct_1(k9_funct_7(C,B)) & m2_relset_1(k9_funct_7(C,B),A,A))))) # label(t88_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6144 (all A all B all C (m1_funct_7(C,B,A) & -v1_xboole_0(A) -> k4_funct_7(B,C) = k8_funct_7(A,B,C))) # label(redefinition_k8_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6145 (all A (v1_funct_1(A) & v1_relat_1(A) -> -v1_xboole_0(k5_finseq_1(A)) & v1_funcop_1(k5_finseq_1(A)) & v1_funct_7(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc10_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6146 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> v1_relat_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_funcop_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc5_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6147 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k5_relat_1(k1_funct_4(B,C),A) = k1_funct_4(k5_relat_1(B,A),k5_relat_1(C,A))))))))) # label(t10_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6148 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k4_funct_7(A,k11_finseq_1(B,C,D)) = k5_relat_1(k6_partfun1(A),k5_relat_1(B,k5_relat_1(C,D))))))))) # label(t56_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6149 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(k2_relat_1(A),B) -> A = k5_relat_1(A,k6_partfun1(B)))))) # label(t1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6150 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> k1_funct_4(A,k3_cqc_lang(B,C)) = k2_funct_7(A,B,C)) & (-r2_hidden(B,k1_relat_1(A)) -> k2_funct_7(A,B,C) = A))))) # label(d3_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6151 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_funct_7(A,B,C) -> k4_xboole_0(k1_relat_1(A),C) = k4_xboole_0(k1_relat_1(B),C))))))) # label(t30_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6152 (all A (r2_hidden(A,a_0_1_funct_7) <-> (exists B (m1_subset_1(B,f2_s3_funct_7) & r2_hidden(f3_s3_funct_7(B),f1_s3_funct_7) & B = A)))) # label(fraenkel_a_0_1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6153 (all A all B (r2_hidden(A,B) <-> r2_hidden(k9_finseq_1(A),k3_finseq_2(B)))) # label(t20_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6154 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_7(A,B,C)) & v1_relat_1(k2_funct_7(A,B,C)))) # label(dt_k2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6155 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k5_relat_1(k6_partfun1(A),k5_relat_1(B,C)) = k4_funct_7(A,k10_finseq_1(B,C)))))) # label(t53_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6156 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_7(C) & v1_funct_1(C) -> (r2_hidden(A,B) & r2_hidden(A,k6_funct_7(C)) -> k1_funct_1(k4_funct_7(B,C),A) = k1_funct_1(k5_funct_7(C,A),k1_nat_1(k3_finseq_1(C),np__1))))) # label(t67_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6157 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(C) & v1_funct_1(C) -> v1_finset_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_funcop_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc6_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6158 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_relat_1(A) = k1_relat_1(k2_funct_7(A,C,B))))) # label(t32_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6159 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k5_relat_1(k9_funct_7(A,B),k6_partfun1(k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) = k9_funct_7(A,B))))) # label(t78_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6160 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (r1_tarski(E,k2_funct_2(A,B,C,D)) -> r1_tarski(k3_funct_2(A,B,C,E),D))))))))))) # label(t2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6161 (all A all B all C all D (m1_finseq_1(B,A) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,A) -> m2_finseq_1(k3_funct_7(A,B,C,D),A))) # label(dt_k3_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6162 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k9_funct_7(A,k1_nat_1(B,np__1)) = k5_relat_1(k9_funct_7(A,B),A))))) # label(t73_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6163 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k4_funct_7(A,k9_finseq_1(B))))) # label(t48_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6164 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_xboole_0(A,k1_tarski(B)) -> k1_funct_4(k7_relat_1(C,A),k3_cqc_lang(B,k1_funct_1(C,B))) = C))) # label(t15_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6165 (all A all B all C (v1_funct_1(A) & m1_subset_1(B,k5_numbers) & v1_finseq_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_7(A,B,C)) & v1_finset_1(k2_funct_7(A,B,C)) & v1_finseq_1(k2_funct_7(A,B,C)) & v1_relat_1(k2_funct_7(A,B,C)))) # label(fc9_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6166 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(A,B) & C = k2_funcop_1(B,A) -> np__0 = D | k9_funct_7(C,D) = C))))) # label(t89_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6167 (all A (v1_funcop_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k5_funct_7(A,B) = C <-> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(D,k4_finseq_1(A)) & E = k1_funct_1(A,D) -> k1_funct_1(C,k1_nat_1(D,np__1)) = k1_funct_1(E,k1_funct_1(C,D))))))) & B = k1_funct_1(C,np__1) & k1_nat_1(k3_finseq_1(A),np__1) = k3_finseq_1(C)))))) # label(d5_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6168 (all A all B all C all D (-v1_xboole_0(k4_funct_4(A,B,C,D)) & v1_funct_1(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6169 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D all E (E != D -> k2_funct_7(k2_funct_7(A,E,C),D,B) = k2_funct_7(k2_funct_7(A,D,B),E,C))))) # label(t35_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6170 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k11_finseq_1(A,k1_funct_1(B,A),k1_funct_1(C,k1_funct_1(B,A))) = k5_funct_7(k10_finseq_1(B,C),A))))) # label(t55_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6171 (all A k4_funct_7(A,k1_xboole_0) = k6_partfun1(A)) # label(t41_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6172 (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) -> (v1_funcop_1(k7_finseq_1(A,B)) -> v1_funcop_1(B) & v1_funcop_1(A)))))) # label(t25_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6173 (all A (v1_finseq_1(A) & v1_funct_7(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_funcop_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(cc1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6174 (all A all B (v1_funcop_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funcop_1(C) & v1_funct_1(C) -> k1_funct_1(k5_funct_7(C,k1_funct_1(k5_funct_7(B,A),k1_nat_1(k3_finseq_1(B),np__1))),k1_nat_1(k3_finseq_1(C),np__1)) = k1_funct_1(k5_funct_7(k7_finseq_1(B,C),A),k1_nat_1(k3_finseq_1(k7_finseq_1(B,C)),np__1)))))) # label(t51_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.53 6175 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (B != np__0 -> r1_tarski(k2_relat_1(k9_funct_7(A,B)),k2_relat_1(A)) & r1_tarski(k1_relat_1(k9_funct_7(A,B)),k1_relat_1(A))))))) # label(t75_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6176 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> ((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(B,A) -> r1_xreal_0(B,C) | r2_hidden(C,A)))))) -> v1_card_1(A)))) # label(t22_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6177 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k9_funct_7(A,k1_nat_1(B,C)) = k5_relat_1(k9_funct_7(A,C),k9_funct_7(A,B)))))))) # label(t79_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6178 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_tarski(k1_relat_1(B),C) -> r1_funct_7(A,k1_funct_4(A,B),C))))))) # label(t31_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6179 (all A (v1_finseq_1(A) & v1_funct_7(A) & v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(k4_funct_7(k6_funct_7(A),A)) = k6_funct_7(A))) # label(t64_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6180 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k10_finseq_1(A,k1_funct_1(B,A)) = k5_funct_7(k9_finseq_1(B),A))) # label(t49_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6181 (all A all B (v1_relat_1(A) & v1_funct_1(A) & m1_subset_1(B,k5_numbers) -> v1_funct_1(k9_funct_7(A,B)) & v1_relat_1(k9_funct_7(A,B)))) # label(dt_k9_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6182 (all A all B all C -(A != B & r2_hidden(A,k2_relat_1(k1_funct_4(k6_partfun1(C),k3_cqc_lang(A,B)))))) # label(t14_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6183 v1_finset_1(f1_s2_funct_7) & (all A (m1_subset_1(A,f2_s2_funct_7) -> (all B (m1_subset_1(B,f2_s2_funct_7) -> (f4_s2_funct_7(B) = f4_s2_funct_7(A) -> A = B))))) -> v1_finset_1(a_0_0_funct_7) # label(s2_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6184 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> B = k1_funct_1(k2_funct_7(A,C,B),C))))) # label(t33_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6185 (all A all B exists C m1_funct_7(C,A,B)) # label(existence_m1_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6186 (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) -> (k3_finseq_1(A) = k1_nat_1(k3_finseq_1(B),np__1) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(k1_nat_1(C,np__1),k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) <-> r2_hidden(C,k4_finseq_1(B)))))))))) # label(t24_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6187 (all A all B (v1_finseq_1(A) & v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k5_funct_7(A,B)) & v1_finseq_1(k5_funct_7(A,B)) & v1_relat_1(k5_funct_7(A,B)))) # label(dt_k5_funct_7) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6188 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6189 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6190 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_struct_0(A) & -v3_struct_0(A) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6191 (exists A (v1_struct_0(A) & l1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6192 (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]. 23.44/22.54 6193 (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]. 23.44/22.54 6194 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6195 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> A = C & B = D)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6196 (exists A (v2_struct_0(A) & l2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6197 (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]. 23.44/22.54 6198 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k1_struct_0(A,B) = k1_tarski(B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6199 (exists A (l2_struct_0(A) & -v3_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6200 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6201 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_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]. 23.44/22.54 6202 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6203 (all A (l1_struct_0(A) -> (v1_xboole_0(u1_struct_0(A)) <-> v3_struct_0(A)))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6204 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6205 (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]. 23.44/22.54 6206 (exists A (-v3_struct_0(A) & l1_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6207 (all A all B all C (l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6208 (all A all B (m1_subset_1(B,A) -> l2_struct_0(g2_struct_0(A,B)) & v2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6209 (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]. 23.44/22.54 6210 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_struct_0(A) -> (all C (m1_struct_0(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6211 (all A all B (g1_struct_0(A) = g1_struct_0(B) -> A = B)) # label(free_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6212 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> k2_struct_0(A,B,C) = k2_struct_0(A,C,B))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6213 (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]. 23.44/22.54 6214 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6215 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6216 (all A all B all C all D all E (l1_cat_1(A) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) & v2_cat_1(C) & v2_cat_1(B) & 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]. 23.44/22.54 6217 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,D,E) -> (F = G -> k1_xboole_0 = k6_cat_1(A,B,C) | E = C & B = D | k1_xboole_0 = k6_cat_1(A,D,E)))))))))))))))) # label(t24_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6218 (exists A (l1_cat_1(A) & v1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6219 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6220 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E))))))))))) # label(t97_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6221 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r1_cat_1(A,B,B))))) # label(t91_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6222 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B))))) # label(d2_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6223 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6224 (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)) -> k13_cat_1(A,B,C,D) = E))))))))))) # label(t107_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6225 (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]. 23.44/22.54 6226 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6227 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v5_cat_1(k10_cat_1(A,B),A))))) # label(t74_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6228 (all A (l1_cat_1(A) -> v1_funct_1(u3_cat_1(A)) & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u3_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6229 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> 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]. 23.44/22.54 6230 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) -> k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) & k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B)))))))) # label(t42_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6231 (all A all B k7_cat_1(A,B) = k3_cqc_lang(A,B)) # label(redefinition_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6232 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6233 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> 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]. 23.44/22.54 6234 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)))) # label(dt_k5_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6235 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v9_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> 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))))))))))))) # label(t132_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6236 (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]. 23.44/22.54 6237 (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(D,A,B) & v9_cat_1(E,B,C) -> v9_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t127_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6238 (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]. 23.44/22.54 6239 (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)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,E) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) & k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))))))) # label(t99_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6240 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6241 (all A (v2_cat_1(A) & l1_cat_1(A) -> v8_cat_1(k15_cat_1(A),A,A))) # label(t122_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6242 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6243 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) -> k1_xboole_0 = k6_cat_1(A,B,C) | k6_cat_1(A,C,B) = k1_xboole_0 | v3_cat_1(E,A)))))))))))) # label(t63_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6244 (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)) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A))) <-> k2_cat_1(A,B) = k3_cat_1(A,C)))))))) # label(t40_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6245 (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]. 23.44/22.54 6246 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k4_cat_1(A,B,C) = k4_cat_1(A,B,D) & k3_cat_1(A,C) = k3_cat_1(A,D) & k2_cat_1(A,D) = k3_cat_1(A,B) -> D = C))))) <-> v4_cat_1(B,A)))))) # label(d11_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6247 (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]. 23.44/22.54 6248 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k5_cat_1(A,B) = k5_cat_1(A,C) -> B = C))))))) # label(t45_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6249 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6250 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v6_cat_1(B,A) -> v3_cat_1(D,A) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))) # label(t90_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6251 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6252 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6253 (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 | k6_cat_1(A,C,D) = k1_xboole_0 | v3_cat_1(E,A)))))))))))))) # label(t62_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6254 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v3_cat_1(k10_cat_1(A,B),A))))) # label(t64_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6255 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) != k1_xboole_0 -> (all F (m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> k6_cat_1(A,D,E) != k1_xboole_0 & (exists G (m1_cat_1(G,A,D,E) & F = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G)))))))))) <-> v9_cat_1(C,A,B)))))))) # label(d23_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6256 (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]. 23.44/22.54 6257 (all A all B all C all D (m1_subset_1(D,k1_tarski(A)) -> (all E (m1_subset_1(E,k1_tarski(B)) -> C = k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)))))) # label(t9_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6258 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (exists C m2_cat_1(C,A,B)))) # label(existence_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6259 (all A (l1_cat_1(A) -> v1_funct_1(u4_cat_1(A)) & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u4_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6260 (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]. 23.44/22.54 6261 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6262 (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]. 23.44/22.54 6263 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) <-> E = k11_cat_1(A,B,C,D))))))))))))) # label(d14_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6264 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> ((exists D (m1_cat_1(D,A,B,C) & v5_cat_1(D,A))) & 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]. 23.44/22.54 6265 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k6_cat_1(A,B,C) != k1_xboole_0 & (exists D (m1_cat_1(D,A,B,C) & (exists E (k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) & k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & m1_cat_1(E,A,C,B))))) & k6_cat_1(A,C,B) != k1_xboole_0 <-> r1_cat_1(A,B,C)))))))) # label(t81_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6266 (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) -> -(k6_cat_1(A,B,C) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,C,D) & k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H)) != k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) & k1_xboole_0 != k6_cat_1(A,D,E)))))))))))))))))) # label(t54_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6267 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6268 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6269 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> 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]. 23.44/22.54 6270 (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]. 23.44/22.54 6271 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = k13_cat_1(A,B,C,D))))))))) # label(d20_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6272 (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) -> C = k10_cat_1(A,B)))))))) # label(t83_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6273 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(A),k4_tarski(C,B)) = k4_cat_1(A,B,C)))))))) # label(d4_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6274 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (r1_cat_1(A,B,C) & r1_cat_1(A,C,D) -> r1_cat_1(A,B,D)))))))))) # label(t93_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6275 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) != k1_xboole_0 & (exists D (m1_cat_1(D,A,B,C) & (all E (m1_cat_1(E,A,B,C) -> D = E)))))) <-> v7_cat_1(B,A)))))) # label(d16_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6276 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6277 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k8_funct_2(u1_cat_1(A),u1_cat_1(A),k12_cat_1(A,A,k15_cat_1(A)),B))))) # label(t116_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6278 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6279 (all A all B k8_cat_1(A,B) = g1_cat_1(k1_tarski(A),k1_tarski(B),k7_cat_1(B,A),k7_cat_1(B,A),k1_cat_1(B,B,B),k7_cat_1(A,B))) # label(d9_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6280 (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]. 23.44/22.54 6281 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> C = A)) # label(t34_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6282 (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) -> k10_cat_1(A,B) = C))))))) # label(t87_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6283 (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]. 23.44/22.54 6284 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k9_cat_1(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)) = k10_cat_1(A,B))))) # label(t59_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6285 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6286 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> k5_cat_1(A,B) = k10_cat_1(A,B))) # label(redefinition_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6287 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6288 (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)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))))) # label(t98_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6289 (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)) -> (k2_cat_1(A,C) = B -> k4_cat_1(A,k5_cat_1(A,B),C) = C))))))) # label(t47_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6290 (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]. 23.44/22.54 6291 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6292 (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) -> v3_cat_1(D,A) & v4_cat_1(D,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t73_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6293 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6294 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((exists C (k3_cat_1(A,B) = k2_cat_1(A,C) & k5_cat_1(A,k2_cat_1(A,B)) = k4_cat_1(A,B,C) & k5_cat_1(A,k3_cat_1(A,B)) = k4_cat_1(A,C,B) & k2_cat_1(A,B) = k3_cat_1(A,C) & m1_subset_1(C,u2_cat_1(A)))) <-> v5_cat_1(B,A)))))) # label(d12_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6295 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6296 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k3_cat_1(A,D)) & k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k2_cat_1(A,D)))))))))) # label(t109_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6297 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6298 (all A all B (m2_relset_1(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) & v1_funct_2(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) & v1_funct_1(k7_cat_1(A,B)))) # label(dt_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6299 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) -> m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)))) # label(dt_k13_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6300 (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,C,B) & (exists E (m1_cat_1(E,A,C,B) & (exists F (m1_cat_1(F,A,C,B) & k9_cat_1(A,B,C,B,D,F) = k10_cat_1(A,B) & E != F & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D))))) & k1_xboole_0 != k6_cat_1(A,B,C)))))))))) # label(t71_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6301 (all A all B all C all D all E (m2_cat_1(C,A,B) & m1_subset_1(E,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & l1_cat_1(B) & v2_cat_1(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]. 23.44/22.54 6302 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) -> 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]. 23.44/22.54 6303 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(B,A) & v7_cat_1(C,A) -> r1_cat_1(A,B,C)))))))) # label(t84_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6304 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_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]. 23.44/22.54 6305 (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]. 23.44/22.54 6306 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> m1_cat_1(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t125_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6307 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k6_cat_1(A,B,C) != k1_xboole_0 & k4_cat_1(A,E,F) != k9_cat_1(A,B,C,D,E,F) & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))) # label(d13_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6308 (all A all B all C (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) -> 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]. 23.44/22.54 6309 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(B,A) & r1_cat_1(A,B,C) -> v7_cat_1(C,A)))))))) # label(t85_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6310 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (all C (m2_cat_1(C,A,B) -> v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C))))) # label(dt_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6311 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,C,B) & (exists D ((all E (m1_cat_1(E,A,C,B) -> D = E)) & m1_cat_1(D,A,C,B))))) <-> v6_cat_1(B,A)))))) # label(d15_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6312 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6313 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (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]. 23.44/22.54 6314 (all A all B all C (m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)))) # label(dt_k4_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6315 (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)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t104_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6316 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(E,A) & v5_cat_1(F,A) -> k1_xboole_0 = k6_cat_1(A,C,D) | k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) = k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E)) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t77_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6317 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) <-> (all C (m1_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)))))))))) # label(t82_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6318 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (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))))) <-> v3_cat_1(B,A)))))) # label(d10_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6319 (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,C,D) & -r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) & k1_xboole_0 != k6_cat_1(A,B,C)))))))))))))) # label(t51_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6320 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,B,B))))) # label(t56_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6321 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k3_cat_1(A,C) -> k4_cat_1(A,C,k5_cat_1(A,B)) = C))))))) # label(t46_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6322 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6323 (all A (v2_cat_1(A) & l1_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]. 23.44/22.54 6324 (all A all B all C (k1_relat_1(k1_cat_1(A,B,C)) = k1_tarski(k4_tarski(A,B)) & k1_relat_1(k1_cat_1(A,B,C)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B)))) # label(t7_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6325 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u2_cat_1(A)) -> k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E))))))) & (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)))))) -> m2_cat_1(C,A,B)))))))) # label(t96_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6326 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(F,A) & v4_cat_1(E,A) -> v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k1_xboole_0 = k6_cat_1(A,C,D) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t66_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6327 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u1_cat_1(k8_cat_1(A,B))) -> (all F (m1_subset_1(F,u1_cat_1(k8_cat_1(A,B))) -> (all G (m1_cat_1(G,k8_cat_1(A,B),C,D) -> (all H (m1_cat_1(H,k8_cat_1(A,B),E,F) -> G = H)))))))))))) # label(t39_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6328 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v10_cat_1(D,A,B) & v10_cat_1(E,B,C) -> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t128_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6329 (all A all B all C (l1_cat_1(A) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) -> (exists D m1_cat_1(D,A,B,C)))) # label(existence_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6330 (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) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)))))) -> (all D (v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(D) -> (k12_cat_1(A,B,C) = D <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),E)) -> F = k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)))))))))))))))) # label(d19_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6331 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (k1_xboole_0 != k6_cat_1(A,C,B) & (exists E (m1_cat_1(E,A,C,B) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D))) <-> v5_cat_1(D,A))))))))))) # label(t70_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6332 (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]. 23.44/22.54 6333 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> k6_cat_1(k8_cat_1(A,B),C,D) != k1_xboole_0)))) # label(t38_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6334 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> B = k2_cat_1(A,D) & k3_cat_1(A,D) = C))))))))) # label(t23_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6335 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (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]. 23.44/22.54 6336 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6337 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> v4_cat_1(F,A) | k1_xboole_0 = k6_cat_1(A,C,D) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))) # label(t67_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6338 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)))))) # label(t19_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6339 (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]. 23.44/22.54 6340 (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]. 23.44/22.54 6341 (all A (v2_cat_1(A) & l1_cat_1(A) -> m2_cat_1(k15_cat_1(A),A,A))) # label(dt_k15_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6342 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6343 (exists A (l1_cat_1(A) & v2_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6344 (all A all B all C all D all E (v2_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) & l1_cat_1(A) -> k5_relat_1(D,E) = k14_cat_1(A,B,C,D,E))) # label(redefinition_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6345 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6346 (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)) -> 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]. 23.44/22.54 6347 (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]. 23.44/22.54 6348 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6349 (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]. 23.44/22.54 6350 (all A all B all C all D all E all F (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_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)) & 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]. 23.44/22.54 6351 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6352 (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]. 23.44/22.54 6353 (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]. 23.44/22.54 6354 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (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]. 23.44/22.54 6355 (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)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k13_cat_1(A,B,C,D)))))))))) # label(t108_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6356 (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) -> k6_cat_1(A,C,D) = k1_xboole_0 | v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))) # label(t61_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6357 (exists A (l1_cat_1(A) & v2_cat_1(A) & v1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6358 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,B,A) & m1_relset_1(C,B,A) & m1_relset_1(D,B,A) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_1(F) & v1_funct_2(F,A,B) & m1_relset_1(F,A,B) & v1_funct_1(E) & v1_funct_2(D,B,A) & v1_funct_1(D) & -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]. 23.44/22.54 6359 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6360 (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) -> v4_cat_1(D,A) | k6_cat_1(A,C,B) = k1_xboole_0 | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))) # label(t68_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.54 6361 (all A all B (l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)))) # label(dt_k3_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6362 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (r2_hidden(F,k6_cat_1(A,D,E)) -> r2_hidden(k1_funct_1(C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t123_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6363 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6364 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> D = k9_cat_1(A,B,B,C,k10_cat_1(A,B),D)))))))))) # label(t58_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6365 (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) & 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)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D))))))))))))) # label(t102_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6366 (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]. 23.44/22.55 6367 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(k4_tarski(E,D),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(B),k4_tarski(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k1_funct_1(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D)))))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u4_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & k8_funct_2(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),u3_cat_1(A),D))))) & (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,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))))) <-> m2_cat_1(C,A,B)))))))) # label(d18_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6368 (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,G,D) = k9_cat_1(A,E,B,C,F,D) -> G = F | k6_cat_1(A,E,B) = k1_xboole_0))))))))))))))))) # label(t60_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6369 (all A all B all C k1_funct_1(k1_cat_1(A,B,C),k4_tarski(A,B)) = C) # label(t8_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6370 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6371 (all A all B all C all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,D) & m2_relset_1(E,A,D) -> (r1_tarski(B,A) & r1_tarski(k2_funct_2(A,D,E,B),C) -> v1_funct_2(k2_partfun1(A,D,E,B),B,C) & m2_relset_1(k2_partfun1(A,D,E,B),B,C) & v1_funct_1(k2_partfun1(A,D,E,B))))))) # label(t4_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6372 (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]. 23.44/22.55 6373 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (m1_cat_1(D,A,B,C) <-> r2_hidden(D,k6_cat_1(A,B,C)))))))))))) # label(d7_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6374 (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) & k3_cat_1(A,C) = k2_cat_1(A,D) -> k4_cat_1(A,B,k4_cat_1(A,C,D)) = k4_cat_1(A,k4_cat_1(A,B,C),D)))))))))) # label(t43_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6375 (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) -> (v2_funct_1(C) & u2_cat_1(B) = k2_relat_1(C) & u1_cat_1(B) = k2_relat_1(k12_cat_1(A,B,C)) <-> v8_cat_1(C,A,B)))))))) # label(d22_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6376 (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]. 23.44/22.55 6377 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,C,E) -> (all G (m1_cat_1(G,A,C,E) -> (k9_cat_1(A,B,C,E,D,F) = k9_cat_1(A,B,C,E,D,G) -> G = F | k1_xboole_0 = k6_cat_1(A,C,E)))))))) <-> v4_cat_1(D,A))))))))))) # label(t65_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6378 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))))))))) # label(t105_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6379 (all A all B all C all D (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & m1_cat_1(D,A,B,C) & l1_cat_1(A) & v2_cat_1(A) -> m1_cat_1(k11_cat_1(A,B,C,D),A,C,B))) # label(dt_k11_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6380 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> -(k1_xboole_0 = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) & k6_cat_1(A,D,E) != k1_xboole_0))))))))))) # label(t126_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6381 (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]. 23.44/22.55 6382 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> (all G (m1_cat_1(G,A,D,E) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) -> F = G)))))))))) <-> v10_cat_1(C,A,B)))))))) # label(d24_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6383 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> 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]. 23.44/22.55 6384 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.44/22.55 6385 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6386 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6387 (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) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k13_cat_1(A,C,k14_cat_1(A,B,C,D,E),F) = k13_cat_1(B,C,E,k13_cat_1(A,B,D,F)))))))))))))) # label(t113_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6388 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6389 (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]. 23.58/22.62 6390 (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) -> k1_xboole_0 = k6_cat_1(A,B,C) | 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]. 23.58/22.62 6391 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6392 (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]. 23.58/22.62 6393 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6394 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6395 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,E)))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k2_cat_1(A,F) = k3_cat_1(A,E) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F))))))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> 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)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)))) -> m2_cat_1(C,A,B)))))))))) # label(t100_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6396 (all A (l1_cat_1(A) -> v1_funct_1(u6_cat_1(A)) & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)))) # label(dt_u6_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6397 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,C,B) & k6_cat_1(A,C,B) = k1_tarski(D)))))))))) # label(t86_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6398 (all A all B all C all D (l1_cat_1(B) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(B)) -> (r2_hidden(A,a_3_0_cat_1(B,C,D)) <-> (exists E (m1_subset_1(E,u2_cat_1(B)) & A = E & k3_cat_1(B,E) = D & C = k2_cat_1(B,E)))))) # label(fraenkel_a_3_0_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.58/22.62 6399 (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]. 23.58/22.62 6400 (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) -> k3_cat_1(A,C) = k3_cat_1(A,k4_cat_1(A,B,C)) & k2_cat_1(A,B) = k2_cat_1(A,k4_cat_1(A,B,C))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D))))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = B -> k4_cat_1(A,k5_cat_1(A,B),C) = C))) & (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))) & k3_cat_1(A,k5_cat_1(A,B)) = B & B = k2_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)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) <-> k2_cat_1(A,C) = k3_cat_1(A,B)))))) -> v2_cat_1(A)))) # label(t29_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6401 (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]. 23.76/22.85 6402 (all A (l1_cat_1(A) -> (v2_cat_1(A) <-> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,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))))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) -> k1_funct_1(u5_cat_1(A),k4_tarski(C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))) = C))) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B)) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) -> k1_funct_1(u5_cat_1(A),k4_tarski(k1_funct_1(u5_cat_1(A),k4_tarski(D,C)),B)) = k1_funct_1(u5_cat_1(A),k4_tarski(D,k1_funct_1(u5_cat_1(A),k4_tarski(C,B))))))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = 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),u3_cat_1(A),B) = k1_funct_1(u3_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B)))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) <-> r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))))))))))) # label(d8_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6403 (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_tarski(D) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t26_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6404 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k2_cat_1(A,k5_cat_1(A,B)) = B & k3_cat_1(A,k5_cat_1(A,B)) = B)))) # label(t44_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6405 (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]. 23.76/22.85 6406 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_2(C,B,A) & m1_relset_1(C,B,A) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(F,A,B) & m1_relset_1(F,A,B) & v1_funct_1(F) & v1_funct_1(E) & v1_funct_1(D) & v1_funct_1(C) & -v1_xboole_0(A) -> (all G all H all I all J all K all L (g1_cat_1(G,H,I,J,K,L) = g1_cat_1(A,B,C,D,E,F) -> A = G & I = C & F = L & K = E & J = D & B = H)))) # label(free_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6407 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> -(r2_tarski(k6_cat_1(A,B,C),k6_cat_1(A,D,E)) & (all G (m1_cat_1(G,A,D,E) -> k1_tarski(G) != k6_cat_1(A,D,E))) & k6_cat_1(A,B,C) = k1_tarski(F)))))))))))))) # label(t27_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6408 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & 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) & l1_cat_1(A) -> v1_funct_1(k12_cat_1(A,B,C)) & m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)))) # label(dt_k12_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6409 (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]. 23.76/22.85 6410 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) = k1_tarski(D) -> (all E (m1_cat_1(E,A,B,C) -> D = E))))))))))) # label(t25_cat_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6411 (exists A (l3_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6412 (all A (-v3_struct_0(A) & l1_lattices(A) -> (v7_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))))))))))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6413 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6414 (all A (l2_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k1_lattices(A,C,B))))) <-> v4_lattices(A)))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6415 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6416 (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]. 23.76/22.85 6417 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v11_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k3_lattices(A,B,C) = k3_lattices(A,B,D) & k4_lattices(A,B,C) = k4_lattices(A,B,D) -> C = D))))))))) # label(t32_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6418 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6419 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6420 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6421 (all A (l3_lattices(A) -> (v11_lattices(A) & v16_lattices(A) & v15_lattices(A) & -v3_struct_0(A) -> v17_lattices(A) & -v3_struct_0(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6422 (all 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)) -> (B = k2_lattices(A,B,C) <-> r1_lattices(A,B,C)))))))) # label(t21_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6423 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) -> k4_lattices(A,B,C) = k2_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.85 6424 (all A (l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,C) -> r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D))))))))))) # label(t27_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6425 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k7_lattices(A,B),B) = k5_lattices(A))))) # label(t47_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6426 (all A (-v3_struct_0(A) & l1_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = k2_lattices(A,C,B))))) <-> v6_lattices(A)))) # label(d6_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6427 (all A (-v3_struct_0(A) & v6_lattices(A) & v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & v5_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,B,k1_lattices(A,B,C)))))))) # label(t22_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6428 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C all D (g2_lattices(C,D) = g2_lattices(A,B) -> D = B & A = C)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6429 (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]. 23.76/22.86 6430 (all A all B all C (v6_lattices(A) & v9_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & v8_lattices(A) & -v3_struct_0(A) -> (r3_lattices(A,B,C) <-> r1_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6431 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6432 (all A (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_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]. 23.76/22.86 6433 (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)) -> k3_lattices(A,k6_lattices(A),B) = k6_lattices(A))))) # label(t44_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6434 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> 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]. 23.76/22.86 6435 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) <-> (exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B)) & m1_subset_1(B,u1_struct_0(A))))))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6436 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6437 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6438 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6439 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6440 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v11_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)) = k2_lattices(A,B,k1_lattices(A,C,D))))))))))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6441 (exists A (v1_lattices(A) & -v3_struct_0(A) & l1_lattices(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6442 (exists A (v3_lattices(A) & l3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6443 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6444 (all A (-v3_struct_0(A) & l2_lattices(A) & v4_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,C,B) & r1_lattices(A,B,C) -> B = C))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6445 (all A all B (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_struct_0(g2_lattices(A,B)) & v2_lattices(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6446 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v10_lattices(A) & v16_lattices(A) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattices(A,C,B) <-> C = k7_lattices(A,B))))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6447 (all A (l1_lattices(A) & -v3_struct_0(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,C) & k2_lattices(A,C,B) = B)) & m1_subset_1(B,u1_struct_0(A)))) <-> v13_lattices(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6448 (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)) -> (k2_lattices(A,C,B) = k5_lattices(A) & k2_lattices(A,B,C) = k5_lattices(A) & k1_lattices(A,C,B) = k6_lattices(A) & k1_lattices(A,B,C) = k6_lattices(A) <-> r2_lattices(A,B,C)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6449 (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]. 23.76/22.86 6450 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6451 (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]. 23.76/22.86 6452 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> 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]. 23.76/22.86 6453 (all A all B all C (v6_lattices(A) & l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6454 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_1(B) -> l3_lattices(g3_lattices(A,B,C)) & v3_lattices(g3_lattices(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6455 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k5_lattices(A),B) = k5_lattices(A))))) # label(t40_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6456 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6457 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B))))))))) # label(t53_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6458 (exists A (v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v13_lattices(A) & v10_lattices(A) & v7_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6459 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6460 (all A (l3_lattices(A) -> (v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & -v3_struct_0(A) -> v10_lattices(A) & -v3_struct_0(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6461 (exists A (l1_lattices(A) & v1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6462 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,k1_lattices(A,B,C)) = B)))) <-> v9_lattices(A)))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6463 (all A (v10_lattices(A) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_lattices(A,C,D)))))))))) # label(t31_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6464 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all D all E all F (g3_lattices(D,E,F) = g3_lattices(A,B,C) -> C = F & E = B & D = A)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6465 (exists A (-v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v14_lattices(A) & v15_lattices(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & v7_lattices(A) & l3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6466 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6467 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v15_lattices(A) & v11_lattices(A) & v16_lattices(A) <-> v17_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6468 (all A (v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,k5_lattices(A),B))))) # label(t41_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6469 (all A all B all C (v4_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l2_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]. 23.76/22.86 6470 (all A (-v3_struct_0(A) & v11_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6471 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6472 (exists A (l1_lattices(A) & -v3_struct_0(A) & v6_lattices(A) & v7_lattices(A) & v1_lattices(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6473 (all A (l3_lattices(A) -> (v10_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v10_lattices(A) & v12_lattices(A) & v9_lattices(A) & v6_lattices(A) & v4_lattices(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6474 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k7_lattices(A,k3_lattices(A,B,C)) = k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))))))) # label(t51_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6475 (exists A (l2_lattices(A) & v2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6476 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6477 (exists A (-v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v7_lattices(A) & v13_lattices(A) & v17_lattices(A) & v16_lattices(A) & v15_lattices(A) & v14_lattices(A) & v11_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & l3_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6478 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6479 (all A (l1_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6480 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6481 (all A (l3_lattices(A) -> (v14_lattices(A) & v13_lattices(A) & -v3_struct_0(A) -> v15_lattices(A) & -v3_struct_0(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6482 (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]. 23.76/22.86 6483 (all A (l3_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6484 (all A (v14_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,B,k6_lattices(A)))))) # label(t45_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6485 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v16_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_lattices(A,C,B) & m1_subset_1(C,u1_struct_0(A))))))))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6486 (exists A (l2_lattices(A) & -v3_struct_0(A) & v2_lattices(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6487 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) -> m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6488 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v12_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,D) -> k2_lattices(A,k1_lattices(A,B,C),D) = k1_lattices(A,B,k2_lattices(A,C,D)))))))))))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6489 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v8_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_lattices(A,k2_lattices(A,B,C),C)))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6490 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6491 (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) -> v1_lattices(g1_lattices(A,B)) & l1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6492 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6493 (all A (l3_lattices(A) -> (v10_lattices(A) & -v3_struct_0(A) -> v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v6_lattices(A) & -v3_struct_0(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6494 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k7_lattices(A,k7_lattices(A,B)))))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6495 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6496 (exists A (v4_lattices(A) & v5_lattices(A) & v2_lattices(A) & -v3_struct_0(A) & l2_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6497 (all A all B (-v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v1_lattices(g1_lattices(A,B)) & -v3_struct_0(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6498 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6499 (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) -> l2_lattices(g2_lattices(A,B)) & v2_lattices(g2_lattices(A,B)))) # label(dt_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6500 (all A (l1_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,C,B) = B & B = k2_lattices(A,B,C))))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6501 (exists A (v3_lattices(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v14_lattices(A) & v13_lattices(A) & v12_lattices(A) & v11_lattices(A) & v10_lattices(A) & v6_lattices(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6502 (all A (l1_lattices(A) -> v1_funct_1(u1_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)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6503 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6504 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_lattices(A) = k3_lattices(A,k7_lattices(A,B),B))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6505 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6506 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6507 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6508 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6509 (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)) -> (C = k1_lattices(A,B,C) <-> r1_lattices(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6510 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_lattices(C,D) = g1_lattices(A,B) -> C = A & B = D)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6511 (all A all B all C (l2_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_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]. 23.76/22.86 6512 (all A (v5_lattices(A) & l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,C) & r1_lattices(A,C,D) -> r1_lattices(A,B,D)))))))))) # label(t25_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6513 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6514 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,k7_lattices(A,C)) <-> k4_lattices(A,B,C) = k5_lattices(A)))))))) # label(t52_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6515 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,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]. 23.76/22.86 6516 (all A (l2_lattices(A) -> v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6517 (all A (l3_lattices(A) -> (v17_lattices(A) & -v3_struct_0(A) -> v11_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v13_lattices(A) & -v3_struct_0(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6518 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_lattices(A,k5_lattices(A),B))))) # label(t39_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6519 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v10_lattices(A) <-> v8_lattices(A) & v6_lattices(A) & v9_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6520 (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]. 23.76/22.86 6521 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6522 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B)) <-> k6_lattices(A) = B)))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6523 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> k3_lattices(A,B,C) = k3_lattices(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6524 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6525 (all A all B all C (-v3_struct_0(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6526 (all A (l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) = k1_lattices(A,B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6527 (all A (-v3_struct_0(A) & l3_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,B,B) = B)))) # label(t18_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6528 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6529 (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]. 23.76/22.86 6530 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k7_lattices(A,B),u1_struct_0(A)))) # label(dt_k7_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6531 (exists A (v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6532 (all A (l1_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k5_lattices(A),u1_struct_0(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6533 (all A (v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_lattices(A,B,B) = B)))) # label(t17_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6534 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v15_lattices(A) <-> v14_lattices(A) & v13_lattices(A)))) # label(d15_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6535 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6536 (all A (l3_lattices(A) -> l2_lattices(A) & l1_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6537 (all A all B all C (m1_relset_1(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) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) & -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]. 23.76/22.86 6538 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v2_pre_topc(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)))) # label(fc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6539 (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]. 23.76/22.86 6540 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6541 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> l1_pre_topc(g1_pre_topc(A,B)) & v1_pre_topc(g1_pre_topc(A,B)))) # label(dt_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6542 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6543 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_subset_1(u1_struct_0(A),B) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B))))) # label(t17_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6544 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_hidden(C,B))) & k1_pre_topc(A) != B))))) # label(t41_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6545 (all A (l1_struct_0(A) -> v1_xboole_0(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)) & v1_membered(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6546 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6547 (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]. 23.76/22.86 6548 (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) -> C = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6549 (all A (l1_pre_topc(A) -> m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_u1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6550 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6551 (all A all B all C all D (l1_struct_0(A) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) -> k4_pre_topc(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6552 (all A all B all C all D (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> 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]. 23.76/22.86 6553 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) -> v4_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6554 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)) = k2_pre_topc(A))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6555 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6556 (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]. 23.76/22.86 6557 (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]. 23.76/22.86 6558 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6559 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6560 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6561 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6562 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (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)))))))) <-> m1_pre_topc(B,A)))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6563 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6564 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6565 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6566 (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]. 23.76/22.86 6567 (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]. 23.76/22.86 6568 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6569 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (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)))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6570 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (k3_pre_topc(A,B) = C <-> B = k2_pre_topc(C)))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6571 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6572 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6573 (all A (l1_struct_0(A) -> k2_pre_topc(A) = u1_struct_0(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6574 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & -v3_struct_0(A) -> -v3_struct_0(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)))) # label(fc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6575 (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]. 23.76/22.86 6576 (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]. 23.76/22.86 6577 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6578 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6579 (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]. 23.76/22.86 6580 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6581 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6582 (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]. 23.76/22.86 6583 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6584 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6585 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6586 (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]. 23.76/22.86 6587 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6588 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6589 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = k3_xboole_0(D,k2_pre_topc(B)) & v4_pre_topc(D,A))) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6590 (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]. 23.76/22.86 6591 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6592 (all A (l1_pre_topc(A) -> (r2_hidden(u1_struct_0(A),u1_pre_topc(A)) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,u1_pre_topc(A)) & r2_hidden(B,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_pre_topc(A))))))) & (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) <-> v2_pre_topc(A)))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6593 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6594 (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]. 23.76/22.86 6595 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k2_pre_topc(A)))))) # label(t13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6596 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6597 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) <-> v3_pre_topc(B,A)))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6598 (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]. 23.76/22.86 6599 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6600 (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]. 23.76/22.86 6601 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & v2_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6602 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)) = k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t50_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6603 (exists A (v1_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6604 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6605 (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]. 23.76/22.86 6606 (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) -> C = A & B = D)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6607 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_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) & -(k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) & B != k2_pre_topc(A)))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6608 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(t42_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6609 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6610 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6611 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))) # label(t22_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6612 (exists A (l1_pre_topc(A) & v1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6613 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6614 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6615 (all A all B all C all D (l1_struct_0(A) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) -> k10_relat_1(C,D) = k5_pre_topc(A,B,C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.86 6616 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) & r1_tarski(B,D) <-> r2_hidden(D,C)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6617 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> B = k6_pre_topc(A,B)) & (v2_pre_topc(A) & B = k6_pre_topc(A,B) -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6618 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_pre_topc(A) & k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) -> v3_pre_topc(B,A)) & (v3_pre_topc(B,A) -> k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6619 (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]. 23.76/22.87 6620 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & -v1_xboole_0(B))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6621 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6622 (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]. 23.76/22.87 6623 (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]. 23.76/22.87 6624 (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]. 23.76/22.87 6625 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6626 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> r2_hidden(k1_xboole_0,u1_pre_topc(A)))) # label(t5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6627 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6628 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6629 (all A all B all C all D (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) & l1_struct_0(A) -> 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]. 23.76/22.87 6630 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k1_xboole_0)) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6631 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (r2_hidden(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) & r1_tarski(B,D) -> r2_hidden(C,D)))) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6632 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k6_pre_topc(A,B) <-> (all D (r2_hidden(D,u1_struct_0(A)) -> (r2_hidden(D,C) <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r2_hidden(D,E) & r1_xboole_0(B,E)))))))))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6633 (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]. 23.76/22.87 6634 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> k1_xboole_0 = k1_tops_1(A,B)))))) # label(t84_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6635 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6636 (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]. 23.76/22.87 6637 (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]. 23.76/22.87 6638 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),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)) & v1_xboole_0(k1_pre_topc(A)))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6639 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6640 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) <-> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t29_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6641 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v3_tops_1(B,A) & v2_tops_1(B,A) & v2_membered(B) & v1_membered(B) & v4_pre_topc(B,A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6642 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) <-> k6_pre_topc(A,k1_tops_1(A,B)) = B))))) # label(d7_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6643 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6644 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,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]. 23.76/22.87 6645 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(A),B) -> B = C))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6646 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v3_pre_topc(C,A) -> C = k1_xboole_0))) <-> v2_tops_1(B,A)))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6647 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v3_pre_topc(B,A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6648 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6649 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6650 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6651 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t64_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6652 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6653 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),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)) & v3_pre_topc(k1_pre_topc(A),A) & v1_xboole_0(k1_pre_topc(A)))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6654 (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]. 23.76/22.87 6655 (all A all B (v3_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A))) # label(fc11_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6656 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v2_tops_1(B,A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6657 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) <-> v2_tops_1(k6_pre_topc(A,B),A)))))) # label(d5_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6658 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(C,A) & v3_tops_1(B,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6659 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6660 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6661 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6662 (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]. 23.76/22.87 6663 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6664 (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,k1_tops_1(A,B))) & r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B) <-> v4_tops_1(B,A)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6665 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6666 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6667 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != C & v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,C) & k1_xboole_0 != D & r1_xboole_0(B,D) & v3_pre_topc(D,A))))))))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6668 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C))))))))) # label(t34_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6669 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)) = k2_pre_topc(A))))) # label(t2_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6670 (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]. 23.76/22.87 6671 (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]. 23.76/22.87 6672 (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))) -> (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]. 23.76/22.87 6673 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_tops_1(B,A) -> v1_membered(k1_tops_1(A,B)) & v2_membered(k1_tops_1(A,B)) & v4_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A) & v3_membered(k1_tops_1(A,B)) & v1_xboole_0(k1_tops_1(A,B)))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6674 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))))) # label(t51_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6675 (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]. 23.76/22.87 6676 (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))) -> k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6677 (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]. 23.76/22.87 6678 (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),k4_subset_1(u1_struct_0(A),k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) = k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)))))))) # label(t70_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6679 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) = k2_tops_1(A,B))))) # label(d2_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6680 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6681 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & v2_pre_topc(A) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6682 (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))) -> -(C != k1_xboole_0 & v3_pre_topc(C,A) & r1_xboole_0(B,C)))) <-> v1_tops_1(B,A)))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6683 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6684 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (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]. 23.76/22.87 6685 (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]. 23.76/22.87 6686 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6687 (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]. 23.76/22.87 6688 (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]. 23.76/22.87 6689 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) <-> v3_pre_topc(B,A)))))) # label(t30_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6690 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6691 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6692 (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]. 23.76/22.87 6693 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> (all C ((exists D (r2_hidden(C,D) & r1_tarski(D,B) & v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_hidden(C,B)))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6694 (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]. 23.76/22.87 6695 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B))) = k6_pre_topc(A,B)))))) # label(t59_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6696 (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) -> 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]. 23.76/22.87 6697 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6698 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6699 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6700 (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]. 23.76/22.87 6701 (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]. 23.76/22.87 6702 (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]. 23.76/22.87 6703 (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]. 23.76/22.87 6704 (all A all B (v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6705 (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),B,k1_tops_1(A,B)) = k2_tops_1(A,B) <-> v4_pre_topc(B,A)))))) # label(t77_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6706 (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]. 23.76/22.87 6707 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6708 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_pre_topc(B,A) -> k1_xboole_0 = B))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6709 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_pre_topc(B,A) -> v1_xboole_0(B) & v3_pre_topc(B,A) & v3_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v5_membered(B) & v4_membered(B) & v2_membered(B) & v1_membered(B) & v4_pre_topc(B,A)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6710 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t67_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6711 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6712 (all A (l1_pre_topc(A) & v2_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]. 23.76/22.87 6713 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6714 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v4_pre_topc(B,A) -> (v6_tops_1(B,A) <-> v5_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6715 (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]. 23.76/22.87 6716 (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]. 23.76/22.87 6717 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & r1_tarski(B,C) -> v1_tops_1(C,A)))))))) # label(t79_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6718 (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]. 23.76/22.87 6719 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6720 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6721 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & v3_pre_topc(B,A) & -v1_xboole_0(B))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6722 (all A (l1_pre_topc(A) -> k1_pre_topc(A) = k1_tops_1(A,k1_pre_topc(A)))) # label(t47_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6723 (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,B)) = k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))))))) # label(t75_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6724 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6725 (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]. 23.76/22.87 6726 (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]. 23.76/22.87 6727 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v4_pre_topc(B,A) & v3_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6728 (all A all B (v2_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6729 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t96_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6730 (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]. 23.76/22.87 6731 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k2_pre_topc(A) = k6_pre_topc(A,B) <-> v1_tops_1(B,A)))))) # label(d3_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6732 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v3_tops_1(B,A) <-> B = k2_tops_1(A,B))))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6733 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6734 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_tops_1(B,A) -> v3_tops_1(B,A)))))) # label(t93_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6735 (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]. 23.76/22.87 6736 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v3_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(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6737 (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]. 23.76/22.87 6738 (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]. 23.76/22.87 6739 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t50_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6740 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6741 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A) & v3_pre_topc(k2_pre_topc(A),A))) # label(fc8_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6742 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6743 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_tops_1(A,k6_pre_topc(A,B)) = B <-> v6_tops_1(B,A)))))) # label(d8_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6744 (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]. 23.76/22.87 6745 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6746 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6747 (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]. 23.76/22.87 6748 (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]. 23.76/22.87 6749 (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]. 23.76/22.87 6750 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(C,A) & v5_tops_1(B,A) -> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t108_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6751 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6752 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_tops_1(B,A) -> v3_tops_1(B,A) & v2_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6753 (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]. 23.76/22.87 6754 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k1_tops_1(A,C)) <-> (exists D (v3_pre_topc(D,A) & r2_hidden(B,D) & r1_tarski(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6755 (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]. 23.76/22.87 6756 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),A))) # label(t22_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6757 (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]. 23.76/22.87 6758 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6759 (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]. 23.76/22.87 6760 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,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(B,D) & -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D))))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6761 (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]. 23.76/22.87 6762 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6763 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t37_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6764 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t65_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6765 (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]. 23.76/22.87 6766 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6767 (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]. 23.76/22.87 6768 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) & v6_tops_1(C,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6769 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6770 (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]. 23.76/22.87 6771 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k2_tops_1(A,B)) <-> v2_tops_1(B,A)))))) # label(t88_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6772 (all A (l1_pre_topc(A) -> v2_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))) & v1_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6773 (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]. 23.76/22.87 6774 (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_tops_1(C,A) & v4_pre_topc(C,A)) & (v4_pre_topc(D,B) & v4_tops_1(D,B) -> v5_tops_1(D,B)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6775 (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]. 23.76/22.87 6776 (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]. 23.76/22.87 6777 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k1_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t71_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6778 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6779 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_pre_topc(B) = k2_relat_1(C) -> k2_tops_2(B,A,k2_tops_2(A,B,C)) = C))))))) # label(t64_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6780 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C)))))))))) # label(t38_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6781 $T # label(t7_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6782 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t21_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6783 (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))) -> (v3_pre_topc(C,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & C = k3_xboole_0(D,k2_pre_topc(B))))))))))) # label(t32_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6784 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (exists D (v1_relat_1(D) & v1_funct_1(D) & C = k1_relat_1(D) & (all E (r2_hidden(E,C) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (F = E -> k1_funct_1(D,E) = k5_subset_1(u1_struct_0(A),F,B)))))) & k1_tops_2(A,B,C) = k2_relat_1(D))))))))) # label(t50_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6785 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t25_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6786 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v5_pre_topc(C,A,B) & v2_tops_2(D,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (E = k9_relat_1(k3_funct_3(C),D) -> v2_tops_2(E,A))))))))))))) # label(t60_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6787 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (k2_pre_topc(B) = k2_relat_1(C) & v5_pre_topc(C,A,B) & v5_pre_topc(k2_tops_2(A,B,C),B,A) & v2_funct_1(C) & k1_relat_1(C) = k2_pre_topc(A) <-> v3_tops_2(C,A,B)))))))) # label(d5_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6788 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k5_relat_1(C,k2_tops_2(A,B,C)) = k6_relat_1(k1_relat_1(C)) & k6_relat_1(k2_relat_1(C)) = k5_relat_1(k2_tops_2(A,B,C),C)))))))) # label(t65_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6789 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_pre_topc(A,B,C,k6_pre_topc(A,D)),k6_pre_topc(B,k4_pre_topc(A,B,C,D))))) <-> v5_pre_topc(C,A,B)))))))) # label(t57_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6790 $T # label(t61_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6791 $T # label(t30_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6792 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(D,B) -> v3_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(t55_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6793 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) -> k5_pre_topc(B,A,k2_tops_2(A,B,C),D) = k4_pre_topc(A,B,C,D)))))))))) # label(t67_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6794 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) -> v1_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t47_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6795 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v3_tops_2(C,A,B) -> v3_tops_2(k2_tops_2(A,B,C),B,A)))))))) # label(t70_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6796 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),C)) -> B = k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C))))))))) # label(t43_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6797 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> v2_funct_1(k2_tops_2(A,B,C))))))))) # label(t63_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6798 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(B,k1_zfmisc_1(k2_pre_topc(A))))))) # label(t1_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6799 $T # label(t2_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6800 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v3_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (B = D -> v3_pre_topc(D,C))))))))))) # label(t33_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6801 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k5_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k6_setfam_1(A,B))))) # label(t12_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6802 $T # label(t39_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6803 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(E) -> (v3_tops_2(E,B,C) & v3_tops_2(D,A,B) -> v3_tops_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t71_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6804 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))) -> ((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> ((exists F (r2_hidden(F,C) & E = k5_subset_1(u1_struct_0(A),F,B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_hidden(E,D)))) <-> D = k1_tops_2(A,B,C)))))))))) # label(d3_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.87 6805 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(C,A) & v2_tops_2(B,A) -> v2_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t23_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6806 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k5_pre_topc(A,B,C,D) = k4_pre_topc(B,A,k2_tops_2(A,B,C),D)))))))))) # label(t68_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6807 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C)),k5_setfam_1(u1_struct_0(A),C)))))))) # label(t44_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6808 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) -> (all E (m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(B)) & v1_funct_1(E) -> (v5_pre_topc(E,C,B) & v5_pre_topc(D,A,C) -> v5_pre_topc(k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(B),D,E),A,B)))))))))))) # label(t58_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6809 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(k9_relat_1(k3_funct_3(C),D),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t54_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6810 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k6_pre_topc(A,k5_pre_topc(A,B,C,D)),k5_pre_topc(A,B,C,k6_pre_topc(B,D))))) <-> v5_pre_topc(C,A,B)))))))) # label(t56_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6811 $T # label(t37_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6812 $T # label(t53_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6813 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> -(v1_tops_2(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v1_tops_2(D,A) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (k2_pre_topc(B) = E -> k1_tops_2(A,E,D) = C))))))))))))) # label(t49_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6814 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(C,D) -> r1_tarski(k1_tops_2(A,B,C),k1_tops_2(A,B,D))))))))))) # label(t40_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6815 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),C)),k5_setfam_1(u1_struct_0(A),k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))))))))) # label(t6_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6816 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t31_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6817 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k2_pre_topc(A) = k1_relat_1(C) & r1_tarski(k2_relat_1(C),k2_pre_topc(B)))))))) # label(t51_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6818 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) & v1_finset_1(B) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t28_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6819 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(C) -> v1_finset_1(k1_tops_2(A,B,C))))))))) # label(t46_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6820 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) & v1_tops_2(B,A) -> v3_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t27_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6821 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v2_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (D = B -> v2_tops_2(D,C))))))))))) # label(t36_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6822 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t29_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6823 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) <-> v2_tops_2(k7_setfam_1(u1_struct_0(A),B),A)))))) # label(t17_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6824 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) <-> v2_tops_2(B,A)))))) # label(d2_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6825 $T # label(t15_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6826 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) -> k2_funct_1(C) = k2_tops_2(A,B,C)))))))) # label(d4_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6827 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) -> (v4_pre_topc(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (D = B -> v4_pre_topc(D,C))))))))))) # label(t34_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6828 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & k1_xboole_0 = B))))) # label(t5_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6829 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v3_pre_topc(C,A))))))))) # label(d1_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6830 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k5_setfam_1(A,B))))) # label(t11_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6831 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) & v1_tops_2(B,A) -> v1_tops_2(k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t20_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6832 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k5_pre_topc(A,B,C,k2_pre_topc(B)) = k2_pre_topc(A))))))) # label(t52_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6833 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (r1_tarski(C,B) -> m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))))))) # label(t3_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6834 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v3_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t26_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6835 $T # label(t69_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6836 $T # label(t8_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6837 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(C,A) -> v2_tops_2(k1_tops_2(A,B,C),k3_pre_topc(A,B))))))))) # label(t48_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6838 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r2_hidden(B,D) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k1_tops_2(A,C,D))))))))))) # label(t41_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6839 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_pre_topc(C,A) -> (v1_tops_2(B,A) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) -> (B = D -> v1_tops_2(D,C))))))))))) # label(t35_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6840 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(k7_setfam_1(u1_struct_0(A),B)) <-> v1_finset_1(B)))))) # label(t13_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6841 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (k2_pre_topc(A) = k1_relat_1(C) & k2_pre_topc(B) = k2_relat_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) <-> v4_pre_topc(k4_pre_topc(A,B,C,D),B)))) & v2_funct_1(C) <-> v3_tops_2(C,A,B)))))))) # label(t72_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6842 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) <-> v1_tops_2(k7_setfam_1(u1_struct_0(A),B),A)))))) # label(t16_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6843 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_tops_2(C,A,B) <-> k1_relat_1(C) = k2_pre_topc(A) & k2_pre_topc(B) = k2_relat_1(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k6_pre_topc(A,k5_pre_topc(A,B,C,D)) = k5_pre_topc(A,B,C,k6_pre_topc(B,D)))) & v2_funct_1(C)))))))) # label(t73_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6844 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(B,A) -> v1_tops_2(k6_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t22_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6845 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k1_tops_2(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B))))))) # label(dt_k1_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6846 $T # label(t14_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6847 (all A all B all C (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)) -> v1_funct_1(k2_tops_2(A,B,C)) & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)))) # label(dt_k2_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6848 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(B,A) -> v2_tops_2(k5_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A)))))))) # label(t24_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6849 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_tops_2(C,A) & r1_tarski(B,C) -> v1_tops_2(B,A)))))))) # label(t18_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6850 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) -> k2_pre_topc(A) = k2_relat_1(k2_tops_2(A,B,C)) & k1_relat_1(k2_tops_2(A,B,C)) = k2_pre_topc(B)))))))) # label(t62_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6851 $T # label(t9_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6852 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(A),D)) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,C),k5_setfam_1(u1_struct_0(k3_pre_topc(A,C)),k1_tops_2(A,C,D)))))))))))) # label(t42_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6853 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v2_tops_2(C,A) & r1_tarski(B,C) -> v2_tops_2(B,A)))))))) # label(t19_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6854 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> (v1_tops_2(D,B) & v5_pre_topc(C,A,B) -> (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k9_relat_1(k3_funct_3(C),D) = E -> v1_tops_2(E,A))))))))))))) # label(t59_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6855 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> k4_pre_topc(A,B,C,k6_pre_topc(A,D)) = k6_pre_topc(B,k4_pre_topc(A,B,C,D)))) & v2_funct_1(C) & k2_relat_1(C) = k2_pre_topc(B) & k1_relat_1(C) = k2_pre_topc(A) <-> v3_tops_2(C,A,B)))))))) # label(t74_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6856 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k5_setfam_1(u1_struct_0(k3_pre_topc(A,B)),k1_tops_2(A,B,C))) -> r1_tarski(B,k5_setfam_1(u1_struct_0(A),C))))))))) # label(t45_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6857 $T # label(t4_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6858 (all A (l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (l1_struct_0(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) -> (k2_pre_topc(B) = k2_relat_1(D) & k1_relat_1(E) = k2_pre_topc(B) & v2_funct_1(E) & k2_pre_topc(C) = k2_relat_1(E) & v2_funct_1(D) & k1_relat_1(D) = k2_pre_topc(A) -> k2_tops_2(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) = k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),k2_tops_2(B,C,E),k2_tops_2(A,B,D))))))))))))) # label(t66_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6859 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k1_xboole_0 = B & k1_xboole_0 != k7_setfam_1(A,B)) & -(k7_setfam_1(A,B) = k1_xboole_0 & B != k1_xboole_0))) # label(t10_tops_2) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6860 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,B) = k1_rlvect_1(A))))) # label(t28_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6861 (exists A l1_rlvect_1(A)) # label(existence_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6862 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = k5_rlvect_1(A,C) -> B = C))))))) # label(t31_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6863 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_rlvect_1(A,B,C)))))))) # label(t44_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6864 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A))) # label(t74_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6865 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (C = k1_funct_1(B,np__1) & k1_funct_1(B,np__2) = D & np__2 = k3_finseq_1(B) -> k9_rlvect_1(A,B) = k2_rlvect_1(A,C,D)))))))))) # label(t96_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6866 (all A all B all C (v3_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6867 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k2_rlvect_1(A,B,E) = k2_rlvect_1(A,B,D) | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) -> E = D))))))))))) # label(t21_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6868 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A))) = B & B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))) & B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),B)))))) # label(t91_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6869 (exists A (l2_rlvect_1(A) & -v3_struct_0(A))) # label(rc3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6870 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k1_rlvect_1(A))))) # label(t64_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6871 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v8_rlvect_1(B,A) <-> k1_rlvect_1(A) != B))))) # label(d13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6872 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t82_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6873 $T # label(t2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6874 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))) = k3_rlvect_1(A,B,k1_real_1(np__2)))))) # label(t80_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6875 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))) = k5_rlvect_1(A,k2_rlvect_1(A,C,B)))))))) # label(t78_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6876 (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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B))))))))) # label(t84_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6877 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> k1_rlvect_1(A) = k5_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))))) # label(t68_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6878 $T # label(t53_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6879 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (k2_rlvect_1(A,B,C) = k1_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)))))) <-> v6_rlvect_1(A)))) # label(d8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6880 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> B = C))))))) # label(t35_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6881 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B))))))))) # label(t66_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6882 (all A (-v3_struct_0(A) & l2_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) = k3_rlvect_1(A,B,C))))))) # label(d4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6883 (all A all B all C (v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C))) # label(redefinition_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6884 (all A all B all C all D (m1_subset_1(B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(C) -> (all E all F all G all H (g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H) -> E = A & C = G & D = H & B = F)))) # label(free_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6885 (all A (l1_struct_0(A) -> (all B (r1_rlvect_1(A,B) <-> r2_hidden(B,u1_struct_0(A)))))) # label(d1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6886 $T # label(t15_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.76/22.88 6887 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,B,C))))))) # label(t62_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6888 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) = k2_rlvect_1(A,B,C) & k9_rlvect_1(A,k8_rlvect_1(A,B,C,k1_rlvect_1(A))) = k2_rlvect_1(A,B,C) & k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),C)) = k2_rlvect_1(A,B,C))))))) # label(t92_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6889 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)))))))) # label(t58_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6890 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k2_rlvect_1(A,B,C) = k1_rlvect_1(A))))))))) # label(d10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6891 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)))))) # label(t61_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6892 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,B)) = k3_rlvect_1(A,B,np__2))))) # label(t79_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6893 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k1_rlvect_1(A))) # label(t60_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6894 (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)) -> (k1_rlvect_1(B) = C | np__0 = A -> k1_rlvect_1(B) = k3_rlvect_1(B,C,A)))))))) # label(t23_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6895 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k3_rlvect_1(A,B,k1_real_1(np__1)))))) # label(t29_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6896 $T # label(t8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6897 (all A (l2_rlvect_1(A) -> l1_rlvect_1(A))) # label(dt_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6898 (all A (l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k6_rlvect_1(A,C,D)))))))))) # label(t42_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6899 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> 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]. 23.85/22.88 6900 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k6_rlvect_1(A,B,D) = k6_rlvect_1(A,B,C) -> D = C))))))))) # label(t37_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6901 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)))))))) # label(t45_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6902 (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_rlvect_1(A) & v3_rlvect_1(A) -> k4_rlvect_1(A,C,B) = k4_rlvect_1(A,B,C))) # label(commutativity_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6903 (exists A (l2_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A) & -v3_struct_0(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6904 $T # label(t18_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6905 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> k5_rlvect_1(A,k1_rlvect_1(A)) = k1_rlvect_1(A))) # label(t25_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6906 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6907 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & C = k2_rlvect_1(A,B,D))))))))) # label(t20_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6908 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_rlvect_1(A,B))))) # label(t3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6909 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6910 (all A (l1_rlvect_1(A) -> (v1_rlvect_1(A) -> A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A))))) # label(abstractness_v1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6911 (all A (l1_rlvect_1(A) -> v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_rlvect_1(A)))) # label(dt_u1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6912 (all A (m1_subset_1(A,k1_numbers) -> (all B (v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k3_rlvect_1(B,C,A) = k3_rlvect_1(B,D,A) -> C = D | A = np__0))))))))) # label(t50_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6913 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> 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]. 23.85/22.88 6914 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v5_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B))))) # label(d7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6915 (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)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t85_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6916 (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,D,B,C)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t89_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6917 $T # label(t14_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6918 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))) & B = k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)))))) # label(t75_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6919 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B))))) # label(t27_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6920 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)),k3_rlvect_1(A,E,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,C,D,E)),B))))))))))) # label(t67_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6921 (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)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,C))) = k6_rlvect_1(A,B,C))))))) # label(t77_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6922 (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]. 23.85/22.88 6923 (exists A (v1_rlvect_1(A) & l1_rlvect_1(A))) # label(rc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6924 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))))))))) # label(t73_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6925 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)))))))) # label(t47_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6926 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t63_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6927 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k6_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t26_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6928 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6929 (exists A l2_rlvect_1(A)) # label(existence_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 23.85/22.88 6930 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)) = k3_rlvect_1(B,C,A))))))) # label(t40_rlvect_1) # label(axiom) # label(non_Alarm clock 121.02/120.09 Prover9 interrupted 121.02/120.09 EOF