0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.33 % Computer : n016.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 960 0.13/0.33 % WCLimit : 120 0.13/0.33 % DateTime : Tue Aug 9 07:23:57 EDT 2022 0.20/0.33 % CPUTime : 4.09/4.18 ============================== Prover9 =============================== 4.09/4.18 Prover9 (32) version 2009-11A, November 2009. 4.09/4.18 Process 20591 was started by sandbox2 on n016.cluster.edu, 4.09/4.18 Tue Aug 9 07:24:01 2022 4.09/4.18 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_20192_n016.cluster.edu". 4.09/4.18 ============================== end of head =========================== 4.09/4.18 4.09/4.18 ============================== INPUT ================================= 4.09/4.18 4.09/4.18 % Reading from file /tmp/Prover9_20192_n016.cluster.edu 4.09/4.18 4.09/4.18 set(prolog_style_variables). 4.09/4.18 set(auto2). 4.09/4.18 % set(auto2) -> set(auto). 4.09/4.18 % set(auto) -> set(auto_inference). 4.09/4.18 % set(auto) -> set(auto_setup). 4.09/4.18 % set(auto_setup) -> set(predicate_elim). 4.09/4.18 % set(auto_setup) -> assign(eq_defs, unfold). 4.09/4.18 % set(auto) -> set(auto_limits). 4.09/4.18 % set(auto_limits) -> assign(max_weight, "100.000"). 4.09/4.18 % set(auto_limits) -> assign(sos_limit, 20000). 4.09/4.18 % set(auto) -> set(auto_denials). 4.09/4.18 % set(auto) -> set(auto_process). 4.09/4.18 % set(auto2) -> assign(new_constants, 1). 4.09/4.18 % set(auto2) -> assign(fold_denial_max, 3). 4.09/4.18 % set(auto2) -> assign(max_weight, "200.000"). 4.09/4.18 % set(auto2) -> assign(max_hours, 1). 4.09/4.18 % assign(max_hours, 1) -> assign(max_seconds, 3600). 4.09/4.18 % set(auto2) -> assign(max_seconds, 0). 4.09/4.18 % set(auto2) -> assign(max_minutes, 5). 4.09/4.18 % assign(max_minutes, 5) -> assign(max_seconds, 300). 4.09/4.18 % set(auto2) -> set(sort_initial_sos). 4.09/4.18 % set(auto2) -> assign(sos_limit, -1). 4.09/4.18 % set(auto2) -> assign(lrs_ticks, 3000). 4.09/4.18 % set(auto2) -> assign(max_megs, 400). 4.09/4.18 % set(auto2) -> assign(stats, some). 4.09/4.18 % set(auto2) -> clear(echo_input). 4.09/4.18 % set(auto2) -> set(quiet). 4.09/4.18 % set(auto2) -> clear(print_initial_clauses). 4.09/4.18 % set(auto2) -> clear(print_given). 4.09/4.18 assign(lrs_ticks,-1). 4.09/4.18 assign(sos_limit,10000). 4.09/4.18 assign(order,kbo). 4.09/4.18 set(lex_order_vars). 4.09/4.18 clear(print_given). 4.09/4.18 4.09/4.18 % formulas(sos). % not echoed (3506 formulas) 4.09/4.18 4.09/4.18 ============================== end of input ========================== 4.09/4.18 4.09/4.18 % From the command line: assign(max_seconds, 960). 4.09/4.18 4.09/4.18 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 4.09/4.18 4.09/4.18 % Formulas that are not ordinary clauses: 4.09/4.18 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 3 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 5 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 6 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 8 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 11 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 13 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 15 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 16 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 19 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 21 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 24 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 26 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 27 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 29 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 30 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 31 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 43 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 44 (all A ((all B -r2_hidden(B,A)) <-> k1_xboole_0 = A)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 47 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 51 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 55 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 56 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 58 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 61 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 62 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 65 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 66 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 67 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 68 (all A all B -(v1_xboole_0(A) & B != A & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.18 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 77 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 95 (all A k1_xboole_0 = k5_xboole_0(A,A)) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 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]. 4.09/4.19 100 (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]. 4.09/4.19 101 (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]. 4.09/4.19 102 (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]. 4.09/4.19 103 (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]. 4.09/4.19 104 (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]. 4.09/4.19 105 (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]. 4.09/4.19 106 (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]. 4.09/4.19 107 (all A all B (r1_tarski(A,B) -> k3_xboole_0(A,B) = A)) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 108 (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]. 4.09/4.19 109 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 110 (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]. 4.09/4.19 111 (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]. 4.09/4.19 112 (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]. 4.09/4.19 113 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 114 (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]. 4.09/4.19 115 (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]. 4.09/4.19 116 (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]. 4.09/4.19 117 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 118 (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]. 4.09/4.19 119 (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]. 4.09/4.19 120 (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]. 4.09/4.19 121 (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]. 4.09/4.19 122 (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]. 4.09/4.19 123 (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]. 4.09/4.19 124 (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]. 4.09/4.19 125 (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]. 4.09/4.19 126 (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]. 4.09/4.19 127 (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]. 4.09/4.19 128 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,B))) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 129 (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]. 4.09/4.19 130 (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]. 4.09/4.19 131 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 132 (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]. 4.09/4.19 133 (all A all B A = k2_xboole_0(A,k3_xboole_0(A,B))) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 134 (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]. 4.09/4.19 135 (all A all B -(r1_tarski(A,B) & r2_xboole_0(B,A))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 136 (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]. 4.09/4.19 137 (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]. 4.09/4.19 138 (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]. 4.09/4.19 139 (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]. 4.09/4.19 140 (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]. 4.09/4.19 141 (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]. 4.09/4.19 142 (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]. 4.09/4.19 143 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 144 (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]. 4.09/4.19 145 (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]. 4.09/4.19 146 (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]. 4.09/4.19 147 (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]. 4.09/4.19 148 (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]. 4.09/4.19 149 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 150 (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]. 4.09/4.19 151 (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]. 4.09/4.19 152 (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]. 4.09/4.19 153 (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]. 4.09/4.19 154 (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]. 4.09/4.19 155 (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]. 4.09/4.19 156 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 157 (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]. 4.09/4.19 158 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 159 (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]. 4.09/4.19 160 (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]. 4.09/4.19 161 (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]. 4.09/4.19 162 (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]. 4.09/4.19 163 (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]. 4.09/4.19 164 (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]. 4.09/4.19 165 (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]. 4.09/4.19 166 (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]. 4.09/4.19 167 (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]. 4.09/4.19 168 (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]. 4.09/4.19 169 (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]. 4.09/4.19 170 (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]. 4.09/4.19 171 (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]. 4.09/4.19 172 (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]. 4.09/4.19 173 (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]. 4.09/4.19 174 (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]. 4.09/4.19 175 (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]. 4.09/4.19 176 (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]. 4.09/4.19 177 (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]. 4.09/4.19 178 (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]. 4.09/4.19 179 (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]. 4.09/4.19 180 (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]. 4.09/4.19 181 (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]. 4.09/4.19 182 (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]. 4.09/4.19 183 (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]. 4.09/4.19 184 (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]. 4.09/4.19 185 (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]. 4.09/4.19 186 (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]. 4.09/4.19 187 (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]. 4.09/4.19 188 (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]. 4.09/4.19 189 (all A k3_enumset1(A,A,A,A,A) = k1_tarski(A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 190 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 191 (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]. 4.09/4.19 192 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 193 (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]. 4.09/4.19 194 (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]. 4.09/4.19 195 (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]. 4.09/4.19 196 (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]. 4.09/4.19 197 (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]. 4.09/4.19 198 (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]. 4.09/4.19 199 (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]. 4.09/4.19 200 (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]. 4.09/4.19 201 (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]. 4.09/4.19 202 (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]. 4.09/4.19 203 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 204 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 205 (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]. 4.09/4.19 206 (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]. 4.09/4.19 207 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 208 (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]. 4.09/4.19 209 (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]. 4.09/4.19 210 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 211 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 212 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 213 (all A k1_tarski(A) = k6_enumset1(A,A,A,A,A,A,A,A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 214 (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]. 4.09/4.19 215 (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]. 4.09/4.19 216 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 217 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 218 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 219 (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]. 4.09/4.19 220 (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]. 4.09/4.19 221 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 222 (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]. 4.09/4.19 223 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 224 (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]. 4.09/4.19 225 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 226 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 227 (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]. 4.09/4.19 228 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 229 (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]. 4.09/4.19 230 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 231 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 232 (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]. 4.09/4.19 233 (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]. 4.09/4.19 234 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 235 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 236 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 237 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 238 (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]. 4.09/4.19 239 (all A k1_tarski(A) = k2_tarski(A,A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 240 (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]. 4.09/4.19 241 (all A k1_tarski(A) = k4_enumset1(A,A,A,A,A,A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 242 (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]. 4.09/4.19 243 (all A all B k3_enumset1(A,A,A,A,B) = k2_tarski(A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 244 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 245 (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]. 4.09/4.19 246 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 247 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 248 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 249 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 250 (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]. 4.09/4.19 251 (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]. 4.09/4.19 252 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 253 (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]. 4.09/4.19 254 (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]. 4.09/4.19 255 (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]. 4.09/4.19 256 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 257 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 258 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 259 (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]. 4.09/4.19 260 (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]. 4.09/4.19 261 (all A all B k2_tarski(A,B) = k2_enumset1(A,A,A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 262 (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]. 4.09/4.19 263 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 264 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 265 (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]. 4.09/4.19 266 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 267 (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]. 4.09/4.19 268 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 269 (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]. 4.09/4.19 270 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 271 (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]. 4.09/4.19 272 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 273 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 274 (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]. 4.09/4.19 275 (all A all B k2_tarski(A,B) = k1_enumset1(A,A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 276 (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]. 4.09/4.19 277 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 278 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 279 (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]. 4.09/4.19 280 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 281 (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]. 4.09/4.19 282 (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]. 4.09/4.19 283 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 284 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 285 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 286 (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]. 4.09/4.19 287 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 288 (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]. 4.09/4.19 289 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 290 (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]. 4.09/4.19 291 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 292 (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]. 4.09/4.19 293 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 294 (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]. 4.09/4.19 295 (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]. 4.09/4.19 296 (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]. 4.09/4.19 297 (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]. 4.09/4.19 298 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 299 (all A k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 300 (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]. 4.09/4.19 301 (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]. 4.09/4.19 302 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 303 (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]. 4.09/4.19 304 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 305 (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]. 4.09/4.19 306 (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]. 4.09/4.19 307 (all A k2_enumset1(A,A,A,A) = k1_tarski(A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 308 (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]. 4.09/4.19 309 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 310 (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]. 4.09/4.19 311 (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]. 4.09/4.19 312 (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]. 4.09/4.19 313 (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]. 4.09/4.19 314 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 315 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 316 (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]. 4.09/4.19 317 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 318 (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]. 4.09/4.19 319 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 320 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 321 (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]. 4.09/4.19 322 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 323 (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]. 4.09/4.19 324 (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]. 4.09/4.19 325 (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]. 4.09/4.19 326 (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]. 4.09/4.19 327 (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]. 4.09/4.19 328 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 329 (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]. 4.09/4.19 330 (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]. 4.09/4.19 331 (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]. 4.09/4.19 332 (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]. 4.09/4.19 333 (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]. 4.09/4.19 334 (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]. 4.09/4.19 335 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 336 (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]. 4.09/4.19 337 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 338 (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]. 4.09/4.19 339 (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]. 4.09/4.19 340 (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]. 4.09/4.19 341 (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]. 4.09/4.19 342 (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]. 4.09/4.19 343 (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]. 4.09/4.19 344 (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]. 4.09/4.19 345 (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]. 4.09/4.19 346 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 347 (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]. 4.09/4.19 348 (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]. 4.09/4.19 349 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(t79_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.19 350 (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]. 4.09/4.19 351 (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]. 4.09/4.19 352 (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]. 4.09/4.20 353 (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]. 4.09/4.20 354 (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]. 4.09/4.20 355 (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]. 4.09/4.20 356 (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]. 4.09/4.20 357 (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]. 4.09/4.20 358 (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]. 4.09/4.20 359 (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]. 4.09/4.20 360 (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]. 4.09/4.20 361 (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]. 4.09/4.20 362 (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]. 4.09/4.20 363 (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]. 4.09/4.20 364 (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]. 4.09/4.20 365 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 366 (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]. 4.09/4.20 367 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 368 (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]. 4.09/4.20 369 (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]. 4.09/4.20 370 (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]. 4.09/4.20 371 (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]. 4.09/4.20 372 (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]. 4.09/4.20 373 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 374 (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]. 4.09/4.20 375 (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]. 4.09/4.20 376 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 377 (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]. 4.09/4.20 378 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 379 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 380 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 381 (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]. 4.09/4.20 382 (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]. 4.09/4.20 383 (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]. 4.09/4.20 384 (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]. 4.09/4.20 385 (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]. 4.09/4.20 386 (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]. 4.09/4.20 387 (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]. 4.09/4.20 388 (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]. 4.09/4.20 389 (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]. 4.09/4.20 390 (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]. 4.09/4.20 391 (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]. 4.09/4.20 392 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 393 (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]. 4.09/4.20 394 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 395 (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]. 4.09/4.20 396 (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]. 4.09/4.20 397 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 398 (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]. 4.09/4.20 399 (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]. 4.09/4.20 400 (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]. 4.09/4.20 401 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 402 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 403 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 404 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 405 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 406 (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]. 4.09/4.20 407 (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]. 4.09/4.20 408 (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]. 4.09/4.20 409 (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]. 4.09/4.20 410 (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]. 4.09/4.20 411 (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]. 4.09/4.20 412 (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]. 4.09/4.20 413 (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]. 4.09/4.20 414 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 415 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 416 (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]. 4.09/4.20 417 (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]. 4.09/4.20 418 (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]. 4.09/4.20 419 (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]. 4.09/4.20 420 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 421 (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]. 4.09/4.20 422 (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]. 4.09/4.20 423 (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]. 4.09/4.20 424 (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]. 4.09/4.20 425 (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]. 4.09/4.20 426 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 427 (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]. 4.09/4.20 428 (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]. 4.09/4.20 429 (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]. 4.09/4.20 430 (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]. 4.09/4.20 431 (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]. 4.09/4.20 432 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 433 (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]. 4.09/4.20 434 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 435 (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]. 4.09/4.20 436 (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]. 4.09/4.20 437 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 438 (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]. 4.09/4.20 439 (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]. 4.09/4.20 440 (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]. 4.09/4.20 441 (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]. 4.09/4.20 442 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 443 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 444 (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]. 4.09/4.20 445 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 446 (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]. 4.09/4.20 447 (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]. 4.09/4.20 448 (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]. 4.09/4.20 449 (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]. 4.09/4.20 450 (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]. 4.09/4.20 451 (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]. 4.09/4.20 452 (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]. 4.09/4.20 453 (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]. 4.09/4.20 454 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 455 (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]. 4.09/4.20 456 (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]. 4.09/4.20 457 (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]. 4.09/4.20 458 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 459 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 460 (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]. 4.09/4.20 461 (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]. 4.09/4.20 462 (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]. 4.09/4.20 463 (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]. 4.09/4.20 464 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 465 (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]. 4.09/4.20 466 (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]. 4.09/4.20 467 (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]. 4.09/4.20 468 (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]. 4.09/4.20 469 (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]. 4.09/4.20 470 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 471 (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]. 4.09/4.20 472 (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]. 4.09/4.20 473 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 474 (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]. 4.09/4.20 475 (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]. 4.09/4.20 476 (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]. 4.09/4.20 477 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 478 (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]. 4.09/4.20 479 (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]. 4.09/4.20 480 (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]. 4.09/4.20 481 (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]. 4.09/4.20 482 (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]. 4.09/4.20 483 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 484 (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]. 4.09/4.20 485 (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]. 4.09/4.20 486 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 487 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 488 (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]. 4.09/4.20 489 (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]. 4.09/4.20 490 (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]. 4.09/4.20 491 (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]. 4.09/4.20 492 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 493 (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]. 4.09/4.20 494 (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]. 4.09/4.20 495 (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]. 4.09/4.20 496 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 497 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 498 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 499 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k3_subset_1(A,k3_subset_1(A,B)))) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 500 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 501 (all A (-$T -> (all B (m1_subset_1(B,A) -> B = k8_subset_1(A))))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 502 (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]. 4.09/4.20 503 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 504 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 505 (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]. 4.09/4.20 506 (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]. 4.09/4.20 507 (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]. 4.09/4.20 508 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 509 (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]. 4.09/4.20 510 (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]. 4.09/4.20 511 (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]. 4.09/4.20 512 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 513 (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]. 4.09/4.20 514 (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]. 4.09/4.20 515 (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]. 4.09/4.20 516 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 517 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 518 (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]. 4.09/4.20 519 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 520 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 521 (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]. 4.09/4.20 522 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 523 (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]. 4.09/4.20 524 (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]. 4.09/4.20 525 (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]. 4.09/4.20 526 (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]. 4.09/4.20 527 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 528 (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]. 4.09/4.20 529 (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]. 4.09/4.20 530 (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]. 4.09/4.20 531 (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]. 4.09/4.20 532 (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]. 4.09/4.20 533 (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]. 4.09/4.20 534 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 535 (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]. 4.09/4.20 536 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 537 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 538 (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]. 4.09/4.20 539 (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]. 4.09/4.20 540 (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]. 4.09/4.20 541 (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]. 4.09/4.20 542 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 543 (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]. 4.09/4.20 544 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 545 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 546 (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]. 4.09/4.20 547 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 548 (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]. 4.09/4.20 549 (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]. 4.09/4.20 550 (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]. 4.09/4.20 551 (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]. 4.09/4.20 552 (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]. 4.09/4.20 553 (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]. 4.09/4.20 554 (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]. 4.09/4.20 555 (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]. 4.09/4.20 556 (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]. 4.09/4.20 557 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 558 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 559 (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]. 4.09/4.20 560 (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]. 4.09/4.20 561 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 562 (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]. 4.09/4.20 563 (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]. 4.09/4.20 564 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 565 (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]. 4.09/4.20 566 (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]. 4.09/4.20 567 (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]. 4.09/4.20 568 (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]. 4.09/4.20 569 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 570 (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]. 4.09/4.20 571 (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]. 4.09/4.20 572 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,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]. 4.09/4.20 573 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 574 (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]. 4.09/4.20 575 (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]. 4.09/4.20 576 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 577 (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]. 4.09/4.20 578 (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]. 4.09/4.20 579 (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]. 4.09/4.20 580 (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]. 4.09/4.20 581 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 582 (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]. 4.09/4.20 583 (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]. 4.09/4.20 584 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.20 585 (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]. 4.09/4.20 586 (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]. 4.09/4.21 587 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k1_relat_1(A),k1_relat_1(B)),k1_relat_1(k4_xboole_0(A,B))))))) # label(t15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 588 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_relat_1(A),k3_relat_1(B))))))) # label(t31_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 589 (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]. 4.09/4.21 590 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))) # label(t14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 591 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 = k9_relat_1(B,A)))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 592 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 593 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k3_relat_1(A),k3_relat_1(B))))))) # label(t34_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 594 (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]. 4.09/4.21 595 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k1_relat_1(B))) & r2_hidden(A,k2_relat_1(B))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 596 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 597 (all A (v1_relat_1(A) -> k8_relat_1(k2_relat_1(A),A) = A)) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 598 (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]. 4.09/4.21 599 (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]. 4.09/4.21 600 (exists A ((all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C) & r2_hidden(B,f1_s1_relat_1))) & v1_relat_1(A))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 601 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k9_relat_1(B,k2_relat_1(A)) = k2_relat_1(k5_relat_1(A,B)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 602 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 603 (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]. 4.09/4.21 604 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 605 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 606 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t118_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 607 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 608 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 609 (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]. 4.09/4.21 610 (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]. 4.09/4.21 611 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 612 (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]. 4.09/4.21 613 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 614 (all A all B (v1_relat_1(B) -> k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)) = k10_relat_1(B,A))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 615 (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]. 4.09/4.21 616 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t157_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 617 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 618 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 619 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A))))))) # label(t105_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 620 (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]. 4.09/4.21 621 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k5_relat_1(A,B)) = k5_relat_1(k4_relat_1(B),k4_relat_1(A)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 622 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,B))))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 623 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k2_relat_1(B)) -> k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A)))))) # label(t47_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 624 (all A all B (v1_relat_1(B) -> v1_relat_1(k8_relat_1(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 625 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 626 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 627 (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]. 4.09/4.21 628 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 629 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t99_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 630 (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]. 4.09/4.21 631 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k8_relat_1(A,C)),k5_relat_1(B,C)))))) # label(t122_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 632 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 633 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(C,A))))))) # label(t179_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 634 (all A all B (v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 635 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t178_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 636 (all A all B all C all D v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 637 (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]. 4.09/4.21 638 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) <-> (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 639 (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]. 4.09/4.21 640 (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]. 4.09/4.21 641 (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]. 4.09/4.21 642 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 643 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(B,C) -> r1_tarski(k8_relat_1(A,B),k8_relat_1(A,C))))))) # label(t132_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 644 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)),k5_relat_1(A,k4_xboole_0(B,C))))))))) # label(t53_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 645 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 646 (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]. 4.09/4.21 647 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(B,k2_relat_1(B))))) # label(t170_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 648 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 649 (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]. 4.09/4.21 650 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t156_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 651 (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]. 4.09/4.21 652 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 653 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> k1_relat_1(k7_relat_1(B,A)) = A))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 654 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 655 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 656 (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]. 4.09/4.21 657 (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]. 4.09/4.21 658 (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]. 4.09/4.21 659 (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]. 4.09/4.21 660 (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]. 4.09/4.21 661 (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]. 4.09/4.21 662 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_relat_1(A)) = k2_relat_1(A))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 663 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 664 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 665 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 666 (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]. 4.09/4.21 667 (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]. 4.09/4.21 668 (all A (v1_relat_1(A) -> k4_relat_1(k4_relat_1(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 669 (all A k6_relat_1(A) = k4_relat_1(k6_relat_1(A))) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 670 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 671 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 672 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t108_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 673 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k5_relat_1(A,B)),k1_relat_1(A)))))) # label(t44_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 674 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 675 (all A (v1_relat_1(A) -> A = k7_relat_1(A,k1_relat_1(A)))) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 676 (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]. 4.09/4.21 677 (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]. 4.09/4.21 678 (all A all B (v1_relat_1(B) -> r1_tarski(k7_relat_1(B,A),B))) # label(t88_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 679 (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]. 4.09/4.21 680 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 681 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 682 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B))))) # label(t104_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 683 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 684 (all A all B (v1_relat_1(B) -> r1_tarski(k8_relat_1(A,B),B))) # label(t117_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 685 (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]. 4.09/4.21 686 (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]. 4.09/4.21 687 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 688 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 689 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(B,k7_relat_1(C,A)),k5_relat_1(B,C)))))) # label(t93_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 690 (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]. 4.09/4.21 691 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 692 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 693 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B))))))))) # label(t48_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 694 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 695 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k4_xboole_0(A,B)) = k4_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t41_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 696 (exists A (v1_relat_1(A) & v1_xboole_0(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 697 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t21_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 698 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k5_relat_1(A,B)),k2_relat_1(B)))))) # label(t45_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 699 (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]. 4.09/4.21 700 (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]. 4.09/4.21 701 (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]. 4.09/4.21 702 (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]. 4.09/4.21 703 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k5_relat_1(B,k6_relat_1(A))))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 704 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 705 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 706 (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]. 4.09/4.21 707 (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]. 4.09/4.21 708 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t89_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 709 (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]. 4.09/4.21 710 (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]. 4.09/4.21 711 (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]. 4.09/4.21 712 (all A (v1_relat_1(A) -> k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 713 (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]. 4.09/4.21 714 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(k7_relat_1(C,A),B),k9_relat_1(C,B)))) # label(t161_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 715 (all A all B all C (v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t154_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 716 (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]. 4.09/4.21 717 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)),k10_relat_1(C,k4_xboole_0(A,B))))) # label(t177_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 718 (all A all B (v1_relat_1(B) -> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 719 (all A all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),A))) # label(t116_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 720 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k2_xboole_0(A,B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 721 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 722 (all A all B (v1_relat_1(B) -> -(v3_relat_1(B) & -v3_relat_1(k7_relat_1(B,A))))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 723 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k2_relat_1(B)))) # label(t144_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 724 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,C))))))))) # label(t49_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 725 (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]. 4.09/4.21 726 (all A (v1_xboole_0(A) -> v1_relat_1(k4_relat_1(A)) & v1_xboole_0(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 727 (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]. 4.09/4.21 728 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 729 (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]. 4.09/4.21 730 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k1_relat_1(B),A),k9_relat_1(k4_relat_1(B),k9_relat_1(B,A))))) # label(t163_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 731 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 732 (all A all B (v1_relat_1(B) -> r1_tarski(k10_relat_1(B,A),k1_relat_1(B)))) # label(t167_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 733 (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]. 4.09/4.21 734 (all A all B all C (v1_relat_1(C) -> k10_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t175_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 735 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 736 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 737 (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]. 4.09/4.21 738 (all A all B (v1_relat_1(B) -> v1_relat_1(k4_xboole_0(B,A)))) # label(t10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 739 (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]. 4.09/4.21 740 (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]. 4.09/4.21 741 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 742 (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]. 4.09/4.21 743 (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]. 4.09/4.21 744 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 745 (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]. 4.09/4.21 746 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 747 (all A (v1_xboole_0(A) -> v1_relat_1(k2_relat_1(A)) & v1_xboole_0(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 748 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 749 (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]. 4.09/4.21 750 (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]. 4.09/4.21 751 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 752 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 753 (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]. 4.09/4.21 754 (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]. 4.09/4.21 755 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(A,k3_xboole_0(B,C)),k3_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C))))))))) # label(t52_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 756 (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]. 4.09/4.21 757 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 758 (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]. 4.09/4.21 759 (all A (v1_relat_1(A) -> (v2_relat_1(A) <-> -r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(d9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 760 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 761 (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]. 4.09/4.21 762 (all A all B (v1_relat_1(B) -> ((all C (r2_hidden(C,A) -> r2_hidden(k4_tarski(C,C),B))) -> r1_tarski(k6_relat_1(A),B)))) # label(t73_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 763 (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]. 4.09/4.21 764 (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]. 4.09/4.21 765 (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]. 4.09/4.21 766 (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]. 4.09/4.21 767 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 768 (all A all B (v1_relat_1(B) -> k7_relat_1(k7_relat_1(B,A),A) = k7_relat_1(B,A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 769 (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]. 4.09/4.21 770 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 771 (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]. 4.09/4.21 772 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 773 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 774 (all A all B (v1_relat_1(B) -> r1_tarski(k3_xboole_0(k2_relat_1(B),A),k10_relat_1(k4_relat_1(B),k10_relat_1(B,A))))) # label(t183_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 775 (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]. 4.09/4.21 776 (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]. 4.09/4.21 777 (all A all B (v1_relat_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),A))) # label(t87_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 778 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k8_relat_1(A,B),C),k5_relat_1(B,C)))))) # label(t121_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 779 (all A all B all C (v1_relat_1(C) -> r1_tarski(k10_relat_1(C,k3_xboole_0(A,B)),k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B))))) # label(t176_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 780 (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]. 4.09/4.21 781 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 782 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> r1_tarski(k5_relat_1(k7_relat_1(B,A),C),k5_relat_1(B,C)))))) # label(t92_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 783 (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]. 4.09/4.21 784 (all A all B (v1_relat_1(B) -> (r1_tarski(A,B) -> v1_relat_1(A)))) # label(t3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 785 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_xboole_0(A,B)),k3_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t27_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 786 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 787 (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]. 4.09/4.21 788 (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]. 4.09/4.21 789 (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]. 4.09/4.21 790 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 791 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 792 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k2_relat_1(k8_relat_1(A,B)) = A))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 793 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k5_relat_1(k6_relat_1(A),B)))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 794 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> r1_tarski(k4_xboole_0(k2_relat_1(A),k2_relat_1(B)),k2_relat_1(k4_xboole_0(A,B))))))) # label(t28_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 795 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,C))))) # label(t131_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 796 (all A all B (v1_relat_1(B) -> r1_tarski(k9_relat_1(B,A),k9_relat_1(B,k1_relat_1(B))))) # label(t147_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 797 (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]. 4.09/4.21 798 (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]. 4.09/4.21 799 (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]. 4.09/4.21 800 (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]. 4.09/4.21 801 (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]. 4.09/4.21 802 (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]. 4.09/4.21 803 (all A all B all C (v1_relat_1(C) -> r1_tarski(k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)),k9_relat_1(C,k4_xboole_0(A,B))))) # label(t155_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 804 (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]. 4.09/4.21 805 (all A (v1_relat_1(A) -> A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.21 806 (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]. 4.09/4.22 807 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k7_relat_1(B,A),C) = k7_relat_1(k5_relat_1(B,C),A))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 808 (all A all B (v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(t9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 809 (all A all B (v1_relat_1(B) -> k2_relat_1(k8_relat_1(A,B)) = k3_xboole_0(k2_relat_1(B),A))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 810 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(B),A) <-> k1_xboole_0 = k10_relat_1(B,A)))) # label(t173_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 811 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 812 (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]. 4.09/4.22 813 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 814 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 815 (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]. 4.09/4.22 816 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 817 (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]. 4.09/4.22 818 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 819 (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]. 4.09/4.22 820 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 821 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 822 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 823 (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]. 4.09/4.22 824 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 825 (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]. 4.09/4.22 826 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 827 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 828 (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]. 4.09/4.22 829 (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]. 4.09/4.22 830 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 831 (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]. 4.09/4.22 832 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 833 (exists A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 834 (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]. 4.09/4.22 835 (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]. 4.09/4.22 836 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 837 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 838 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 839 (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]. 4.09/4.22 840 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 841 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k9_relat_1(k6_relat_1(A),B))) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 842 (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]. 4.09/4.22 843 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 844 (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]. 4.09/4.22 845 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 846 (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]. 4.09/4.22 847 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 848 (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]. 4.09/4.22 849 (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]. 4.09/4.22 850 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 851 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 852 (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]. 4.09/4.22 853 (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]. 4.09/4.22 854 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 855 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 856 (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]. 4.09/4.22 857 (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]. 4.09/4.22 858 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_relat_1(k5_relat_1(k6_relat_1(A),B)) = k3_xboole_0(k1_relat_1(B),A))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 859 (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]. 4.09/4.22 860 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 861 (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]. 4.09/4.22 862 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 863 (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]. 4.09/4.22 864 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 865 (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]. 4.09/4.22 866 (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]. 4.09/4.22 867 (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]. 4.09/4.22 868 (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]. 4.09/4.22 869 (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]. 4.09/4.22 870 (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]. 4.09/4.22 871 (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]. 4.09/4.22 872 (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]. 4.09/4.22 873 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 874 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 875 (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]. 4.09/4.22 876 (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]. 4.09/4.22 877 (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]. 4.09/4.22 878 (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]. 4.09/4.22 879 (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]. 4.09/4.22 880 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 881 (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]. 4.09/4.22 882 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 883 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 884 (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]. 4.09/4.22 885 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 886 (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]. 4.09/4.22 887 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 888 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & k1_relat_1(B) = k2_relat_1(A) -> k2_funct_1(A) = B))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 889 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 890 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(C,k1_relat_1(A)) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 891 (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]. 4.09/4.22 892 (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]. 4.09/4.22 893 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k10_relat_1(B,k9_relat_1(B,A)))))) # label(t146_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 894 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 895 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 896 (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]. 4.09/4.22 897 (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]. 4.09/4.22 898 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 899 (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]. 4.09/4.22 900 (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]. 4.09/4.22 901 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 902 (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]. 4.09/4.22 903 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 904 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 905 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (C = k10_relat_1(A,B) <-> (all D (r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,C))))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 906 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 907 (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]. 4.09/4.22 908 (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]. 4.09/4.22 909 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 910 (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]. 4.09/4.22 911 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 912 (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]. 4.09/4.22 913 (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]. 4.09/4.22 914 (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]. 4.09/4.22 915 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 916 (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]. 4.09/4.22 917 (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]. 4.09/4.22 918 (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]. 4.09/4.22 919 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 920 (all A (v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 921 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> v2_funct_1(k7_relat_1(B,A))))) # label(t84_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 922 (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]. 4.09/4.22 923 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 924 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 925 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 926 (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]. 4.09/4.22 927 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 928 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 929 (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]. 4.09/4.22 930 (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]. 4.09/4.22 931 (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]. 4.09/4.22 932 (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]. 4.09/4.22 933 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 934 (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]. 4.09/4.22 935 (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]. 4.09/4.22 936 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 937 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 938 (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]. 4.09/4.22 939 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> v2_funct_1(k8_relat_1(A,B))))) # label(t99_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 940 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 941 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 942 (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]. 4.09/4.22 943 (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]. 4.09/4.22 944 (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]. 4.09/4.22 945 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 946 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 947 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 948 (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]. 4.09/4.22 949 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 950 (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]. 4.09/4.22 951 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 952 (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]. 4.09/4.22 953 (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]. 4.09/4.22 954 (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]. 4.09/4.22 955 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 956 (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]. 4.09/4.22 957 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 958 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 959 (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]. 4.09/4.22 960 (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]. 4.09/4.22 961 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 962 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 963 (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]. 4.09/4.22 964 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k9_relat_1(k8_relat_1(A,C),B) = k3_xboole_0(A,k9_relat_1(C,B)))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 965 (all A all B all C (v1_relat_1(C) -> r1_tarski(k3_xboole_0(A,k10_relat_1(C,B)),k10_relat_1(C,k3_xboole_0(k9_relat_1(C,A),B))))) # label(t151_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 966 (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]. 4.09/4.22 967 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 968 (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]. 4.09/4.22 969 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 970 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 971 (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]. 4.09/4.22 972 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 973 (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]. 4.09/4.22 974 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 975 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 976 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 977 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 978 (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]. 4.09/4.22 979 (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]. 4.09/4.22 980 (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]. 4.09/4.22 981 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 982 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 983 (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]. 4.09/4.22 984 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 985 (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]. 4.09/4.22 986 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 987 (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]. 4.09/4.22 988 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 989 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))),k3_xboole_0(k9_relat_1(C,A),B)))) # label(t149_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 990 (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]. 4.09/4.22 991 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 992 (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]. 4.09/4.22 993 (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]. 4.09/4.22 994 (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]. 4.09/4.22 995 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 996 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 997 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(C)) -> r1_tarski(k10_relat_1(B,A),k10_relat_1(k5_relat_1(B,C),k9_relat_1(C,A)))))))) # label(t160_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 998 (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]. 4.09/4.22 999 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1000 (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]. 4.09/4.22 1001 (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]. 4.09/4.22 1002 (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]. 4.09/4.22 1003 (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]. 4.09/4.22 1004 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1005 (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]. 4.09/4.22 1006 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1007 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1008 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1009 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_xboole_0(A,B) -> r2_hidden(A,B)))))) # label(t21_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1010 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1011 (all A all B (r1_tarski(A,B) -> (all C (m1_ordinal1(C,A) -> m1_ordinal1(C,B))))) # label(t47_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1012 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1013 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k3_tarski(A)))) # label(t35_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1014 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1015 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1016 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1017 (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]. 4.09/4.22 1018 (all A -((all B (v3_ordinal1(B) -> -r1_tarski(A,B))) & (all B (r2_hidden(B,A) -> v3_ordinal1(B))))) # label(t36_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1019 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1020 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1021 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1022 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1023 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.22 1024 (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]. 4.09/4.23 1025 (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]. 4.09/4.23 1026 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1027 (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]. 4.09/4.23 1028 (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]. 4.09/4.23 1029 (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]. 4.09/4.23 1030 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1031 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1032 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1033 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1034 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1035 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1036 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> r2_hidden(A,B) | A = B)) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1037 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1038 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1039 (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]. 4.09/4.23 1040 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1041 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r1_tarski(A,B) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1042 (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]. 4.09/4.23 1043 (all A all B -(r1_tarski(B,A) & r2_hidden(A,B))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1044 (all A all B (m1_ordinal1(B,A) -> (all C (v3_ordinal1(C) -> m1_ordinal1(k2_ordinal1(B,C),A))))) # label(t48_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1045 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1046 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1047 (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]. 4.09/4.23 1048 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v1_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1049 (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]. 4.09/4.23 1050 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r2_hidden(B,A) | r1_ordinal1(A,B))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1051 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1052 (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]. 4.09/4.23 1053 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(k1_ordinal1(A),B) <-> r2_hidden(A,B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1054 (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]. 4.09/4.23 1055 (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]. 4.09/4.23 1056 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1057 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1058 (all A exists B (v3_ordinal1(B) & -r2_hidden(B,A) & (all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1059 (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]. 4.09/4.23 1060 (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]. 4.09/4.23 1061 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1062 (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]. 4.09/4.23 1063 (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]. 4.09/4.23 1064 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]. 4.09/4.23 1065 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1066 (all A k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A))) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1067 (all A (v4_ordinal1(A) <-> k3_tarski(A) = A)) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1068 (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]. 4.09/4.23 1069 (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]. 4.09/4.23 1070 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1071 (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]. 4.09/4.23 1072 (all A (v1_xboole_0(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1073 (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]. 4.09/4.23 1074 (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]. 4.09/4.23 1075 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s2_ordinal1(B)))) -> p1_s2_ordinal1(A)))) -> (all A (v3_ordinal1(A) -> p1_s2_ordinal1(A))) # label(s2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1076 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1077 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1078 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1079 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1080 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1081 (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]. 4.09/4.23 1082 (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]. 4.09/4.23 1083 (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]. 4.09/4.23 1084 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1085 (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]. 4.09/4.23 1086 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1087 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v5_ordinal1(A) <-> v3_ordinal1(k1_relat_1(A))))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1088 (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]. 4.09/4.23 1089 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1090 (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]. 4.09/4.23 1091 (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]. 4.09/4.23 1092 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> ((exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1093 (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]. 4.09/4.23 1094 (all A all B all C all D (m1_relset_1(C,A,B) -> m2_relset_1(k8_relset_1(A,B,C,D),A,B))) # label(dt_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1095 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k3_relat_1(C),k2_xboole_0(A,B)))) # label(t19_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1096 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(k6_relat_1(C),D) -> r1_tarski(C,k5_relset_1(A,B,D)) & r1_tarski(C,k4_relset_1(A,B,D))))) # label(t30_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1097 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1098 (all A all B all C (m2_relset_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1099 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & k5_relat_1(B,k6_relat_1(A)) = B)) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1100 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1101 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1102 (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]. 4.09/4.23 1103 (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]. 4.09/4.23 1104 (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]. 4.09/4.23 1105 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(k2_relat_1(D),B) -> m2_relset_1(D,C,B)))) # label(t14_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1106 (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]. 4.09/4.23 1107 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A)))) # label(t10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1108 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1109 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1110 (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]. 4.09/4.23 1111 (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]. 4.09/4.23 1112 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1113 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1114 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> k1_xboole_0 = C))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1115 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k5_relset_1(B,A,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C))))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1116 (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]. 4.09/4.23 1117 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(A,B) -> m2_relset_1(D,B,C)))) # label(t15_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1118 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)))) # label(dt_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1119 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(C,D) & r1_tarski(A,B) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1120 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k11_relset_1(A,B,C,D))) # label(redefinition_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1121 (all A all B all C (m1_relset_1(C,A,B) -> k2_relat_1(C) = k5_relset_1(A,B,C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1122 (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]. 4.09/4.23 1123 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k2_relset_1(A,B,C,D),A,B))) # label(dt_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1124 (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]. 4.09/4.23 1125 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1126 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k10_relset_1(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1127 (all A all B all C all D (m2_relset_1(D,A,C) -> m2_relset_1(k8_relset_1(A,C,D,B),B,C))) # label(t33_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1128 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1129 (all A all B all C all D (m1_relset_1(C,A,B) -> m1_subset_1(k11_relset_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k11_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1130 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1131 (all A all B all C all D (m2_relset_1(D,C,A) -> (r1_tarski(A,B) -> m2_relset_1(D,C,B)))) # label(t16_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1132 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k10_relset_1(C,A,D,B)) <-> (exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D) & m1_subset_1(F,C)))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1133 (all A all B all C (m1_relset_1(C,A,B) -> m2_relset_1(k6_relset_1(A,B,C),B,A))) # label(dt_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1134 (all A all B all C all D (m1_relset_1(D,A,B) -> k9_relset_1(A,B,C,D) = k8_relat_1(C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1135 (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]. 4.09/4.23 1136 (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]. 4.09/4.23 1137 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> B = k5_relset_1(A,B,C) & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1138 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1139 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1140 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1141 (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]. 4.09/4.23 1142 (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]. 4.09/4.23 1143 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1144 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C)) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1145 (all A all B all C (m2_relset_1(C,A,B) -> (m2_relset_1(C,k1_xboole_0,B) -> C = k1_xboole_0))) # label(t26_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1146 (all A all B all C (m1_relset_1(C,A,B) -> k1_relat_1(C) = k4_relset_1(A,B,C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1147 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k4_relset_1(A,B,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C))))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1148 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1149 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1150 (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]. 4.09/4.23 1151 (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]. 4.09/4.23 1152 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1153 (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]. 4.09/4.23 1154 (all A all B all C all D (m2_relset_1(D,A,C) -> (r1_tarski(k1_relat_1(D),B) -> m2_relset_1(D,B,C)))) # label(t13_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1155 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1156 (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]. 4.09/4.23 1157 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> v1_relat_1(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1158 (all A all B all C all D (m2_relset_1(D,C,A) -> m2_relset_1(k9_relset_1(C,A,B,D),C,B))) # label(t35_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1159 (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]. 4.09/4.23 1160 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1161 (exists A ((all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (r2_hidden(k4_tarski(B,C),A) <-> p1_s2_relset_1(B,C)))))) & m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1162 (all A all B all C all D (m2_relset_1(D,B,C) -> (r1_tarski(A,D) -> m2_relset_1(A,B,C)))) # label(t4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1163 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1164 (all A all B all C (m1_relset_1(C,A,B) -> m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1165 (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]. 4.09/4.23 1166 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1167 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1168 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1169 (all A all B all C all D (m1_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B))) # label(dt_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1170 (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]. 4.09/4.23 1171 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1172 (all A all B all C all D (r2_hidden(D,B) & r2_hidden(C,A) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1173 (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]. 4.09/4.23 1174 (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]. 4.09/4.23 1175 (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]. 4.09/4.23 1176 (all A all B all C all D (m1_relset_1(C,A,B) -> k8_relset_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1177 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> k9_relset_1(A,B,C,D) = D))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1178 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> m2_relset_1(B,A,k2_relat_1(B))))) # label(t9_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1179 (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]. 4.09/4.23 1180 (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]. 4.09/4.23 1181 (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]. 4.09/4.23 1182 (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]. 4.09/4.23 1183 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1184 (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]. 4.09/4.23 1185 (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]. 4.09/4.23 1186 (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]. 4.09/4.23 1187 (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]. 4.09/4.23 1188 (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]. 4.09/4.23 1189 (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]. 4.09/4.23 1190 (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]. 4.09/4.23 1191 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1192 (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]. 4.09/4.23 1193 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]. 4.09/4.23 1194 (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]. 4.09/4.23 1195 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) -> (k6_partfun1(A) = k5_funct_2(A,B,C) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1196 (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]. 4.09/4.23 1197 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1198 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1199 (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]. 4.09/4.23 1200 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1201 (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]. 4.09/4.23 1202 (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]. 4.09/4.23 1203 (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]. 4.09/4.23 1204 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1205 (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]. 4.09/4.23 1206 (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]. 4.09/4.23 1207 (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]. 4.09/4.23 1208 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1209 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1210 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1211 (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]. 4.09/4.23 1212 (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]. 4.09/4.23 1213 (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]. 4.09/4.23 1214 (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]. 4.09/4.23 1215 (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]. 4.09/4.23 1216 (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]. 4.09/4.23 1217 (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]. 4.09/4.23 1218 (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]. 4.09/4.23 1219 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1220 (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]. 4.09/4.23 1221 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)) = A)) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1222 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1223 (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]. 4.09/4.23 1224 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1225 (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]. 4.09/4.23 1226 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (B != k1_xboole_0 -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1227 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1228 (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]. 4.09/4.23 1229 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1230 (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]. 4.09/4.23 1231 (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]. 4.09/4.23 1232 (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]. 4.09/4.23 1233 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1234 (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]. 4.09/4.23 1235 (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]. 4.09/4.23 1236 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1237 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1238 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1239 (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]. 4.09/4.23 1240 (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]. 4.09/4.23 1241 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1242 (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]. 4.09/4.23 1243 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1244 (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]. 4.09/4.23 1245 (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]. 4.09/4.23 1246 (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]. 4.09/4.23 1247 (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]. 4.09/4.23 1248 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1249 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1250 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1251 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1252 (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]. 4.09/4.23 1253 (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]. 4.09/4.23 1254 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1255 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.23 1256 (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]. 4.09/4.24 1257 (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]. 4.09/4.24 1258 (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]. 4.09/4.24 1259 (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]. 4.09/4.24 1260 (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]. 4.09/4.24 1261 (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]. 4.09/4.24 1262 (all A (k1_xboole_0 != A -> k1_funct_2(A,k1_xboole_0) = k1_xboole_0)) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1263 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1264 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1265 (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]. 4.09/4.24 1266 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1267 (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]. 4.09/4.24 1268 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1269 (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]. 4.09/4.24 1270 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1271 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1272 (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]. 4.09/4.24 1273 (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]. 4.09/4.24 1274 (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]. 4.09/4.24 1275 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1276 (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]. 4.09/4.24 1277 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1278 (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]. 4.09/4.24 1279 (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]. 4.09/4.24 1280 (all A all B k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B)) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1281 (all A all B (-v1_xboole_0(B) -> -v1_xboole_0(k1_funct_2(A,B)))) # label(fc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1282 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1283 (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]. 4.09/4.24 1284 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1285 (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]. 4.09/4.24 1286 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1287 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1288 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1289 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1290 (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]. 4.09/4.24 1291 (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]. 4.09/4.24 1292 (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]. 4.09/4.24 1293 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1294 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1295 (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]. 4.09/4.24 1296 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1297 (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]. 4.09/4.24 1298 (all A all B r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B))) # label(t141_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1299 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1300 (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]. 4.09/4.24 1301 (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]. 4.09/4.24 1302 (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]. 4.09/4.24 1303 (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]. 4.09/4.24 1304 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1305 (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]. 4.09/4.24 1306 (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]. 4.09/4.24 1307 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1308 (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]. 4.09/4.24 1309 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1310 (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]. 4.09/4.24 1311 (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]. 4.09/4.24 1312 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1313 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1314 (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]. 4.09/4.24 1315 (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]. 4.09/4.24 1316 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1317 (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]. 4.09/4.24 1318 (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]. 4.09/4.24 1319 (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]. 4.09/4.24 1320 (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]. 4.09/4.24 1321 (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]. 4.09/4.24 1322 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1323 (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]. 4.09/4.24 1324 (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]. 4.09/4.24 1325 (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]. 4.09/4.24 1326 (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]. 4.09/4.24 1327 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1328 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1329 (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]. 4.09/4.24 1330 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1331 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1332 (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]. 4.09/4.24 1333 (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]. 4.09/4.24 1334 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1335 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1336 (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]. 4.09/4.24 1337 (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]. 4.09/4.24 1338 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1339 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1340 (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]. 4.09/4.24 1341 (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]. 4.09/4.24 1342 (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]. 4.09/4.24 1343 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1344 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1345 (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]. 4.09/4.24 1346 (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]. 4.09/4.24 1347 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1348 (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]. 4.09/4.24 1349 (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]. 4.09/4.24 1350 (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]. 4.09/4.24 1351 (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]. 4.09/4.24 1352 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1353 (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]. 4.09/4.24 1354 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1355 (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]. 4.09/4.24 1356 (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]. 4.09/4.24 1357 (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]. 4.09/4.24 1358 (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]. 4.09/4.24 1359 (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]. 4.09/4.24 1360 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1361 (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]. 4.09/4.24 1362 (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]. 4.09/4.24 1363 (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]. 4.09/4.24 1364 (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]. 4.09/4.24 1365 (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]. 4.09/4.24 1366 (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]. 4.09/4.24 1367 (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]. 4.09/4.24 1368 (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]. 4.09/4.24 1369 (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]. 4.09/4.24 1370 (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]. 4.09/4.24 1371 (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]. 4.09/4.24 1372 (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]. 4.09/4.24 1373 (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]. 4.09/4.24 1374 (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]. 4.09/4.24 1375 (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]. 4.09/4.24 1376 (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]. 4.09/4.24 1377 (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]. 4.09/4.24 1378 (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]. 4.09/4.24 1379 (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]. 4.09/4.24 1380 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1381 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1382 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1383 (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]. 4.09/4.24 1384 (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]. 4.09/4.24 1385 (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]. 4.09/4.24 1386 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(A,A,k3_partfun1(B,A,A)))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1387 (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]. 4.09/4.24 1388 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.09/4.24 1389 (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]. 4.09/4.24 1390 (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]. 4.29/4.36 1391 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1392 (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]. 4.29/4.36 1393 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_ordinal2(A),k2_ordinal2(B)))) # label(t11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1394 (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]. 4.29/4.36 1395 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1396 (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]. 4.29/4.36 1397 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1398 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1399 (all A all B (r1_tarski(A,B) -> r1_tarski(k3_ordinal2(A),k3_ordinal2(B)))) # label(t14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1400 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1401 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1402 (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]. 4.29/4.36 1403 (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]. 4.29/4.36 1404 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1405 (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]. 4.29/4.36 1406 (all A (v3_ordinal1(A) -> A = k3_tarski(k1_ordinal1(A)))) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1407 (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]. 4.29/4.36 1408 (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]. 4.29/4.36 1409 (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]. 4.29/4.36 1410 (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]. 4.29/4.36 1411 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1412 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1413 (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]. 4.29/4.36 1414 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1415 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1416 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r2_hidden(C,A)))) -> r1_ordinal1(k7_ordinal2(B),A))))) # label(t28_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1417 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1418 (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]. 4.29/4.36 1419 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(A,B) -> r2_hidden(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t49_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1420 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(k6_ordinal2(B),B))))) # label(t25_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1421 (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]. 4.29/4.36 1422 (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]. 4.29/4.36 1423 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(C,A),k15_ordinal2(C,B))))))))) # label(t59_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1424 (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]. 4.29/4.36 1425 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1426 (all A (v3_ordinal1(A) -> (r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.29/4.36 1427 (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]. 4.29/4.38 1428 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(A,k16_ordinal2(A,B)) = k16_ordinal2(A,k1_ordinal1(B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1429 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r1_ordinal1(k6_ordinal2(B),A))))) # label(t22_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1430 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1431 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1432 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B))) -> v3_ordinal1(k1_setfam_1(A)))) # label(t17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1433 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1434 (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]. 4.29/4.38 1435 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(C,A),k14_ordinal2(C,B))))))))) # label(t50_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1436 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k15_ordinal2(A,B)))) # label(dt_k15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1437 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1438 (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]. 4.29/4.38 1439 (all A (v3_ordinal1(A) -> (all B -(r2_hidden(A,k7_ordinal2(B)) & (all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1440 (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]. 4.29/4.38 1441 (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]. 4.29/4.38 1442 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1443 (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]. 4.29/4.38 1444 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1445 (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]. 4.29/4.38 1446 (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]. 4.29/4.38 1447 (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]. 4.29/4.38 1448 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1449 (all A all B (r1_tarski(A,B) -> r1_ordinal1(k7_ordinal2(A),k7_ordinal2(B)))) # label(t30_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1450 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1451 (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]. 4.29/4.38 1452 (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]. 4.29/4.38 1453 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(k1_ordinal1(A),B) = k14_ordinal2(k15_ordinal2(A,B),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.29/4.38 1454 (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]. 4.29/4.38 1455 (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]. 4.29/4.38 1456 (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]. 4.29/4.38 1457 (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]. 4.34/4.44 1458 (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]. 4.34/4.44 1459 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1460 (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]. 4.34/4.44 1461 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1462 (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]. 4.34/4.44 1463 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1464 (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]. 4.34/4.44 1465 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1466 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1467 (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]. 4.34/4.44 1468 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1469 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1470 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1471 (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]. 4.34/4.44 1472 (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]. 4.34/4.44 1473 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.44 1474 (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]. 4.34/4.44 1475 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]. 4.34/4.46 1476 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1477 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1478 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1479 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k14_ordinal2(A,C),k14_ordinal2(B,C))))))))) # label(t51_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1480 (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]. 4.34/4.46 1481 (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]. 4.34/4.46 1482 (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]. 4.34/4.46 1483 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1484 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1485 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) -> r2_hidden(A,k7_ordinal2(B)))))) # label(t27_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1486 (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]. 4.34/4.46 1487 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]. 4.34/4.46 1488 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1489 (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]. 4.34/4.46 1490 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1491 (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]. 4.34/4.46 1492 (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]. 4.34/4.46 1493 (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]. 4.34/4.46 1494 (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]. 4.34/4.46 1495 (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]. 4.34/4.46 1496 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1497 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1498 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1499 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.34/4.46 1500 (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]. 4.34/4.46 1501 (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]. 4.40/4.47 1502 (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]. 4.40/4.47 1503 (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]. 4.40/4.47 1504 (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]. 4.40/4.47 1505 (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]. 4.40/4.47 1506 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1507 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_ordinal1(A,B) -> r1_ordinal1(k15_ordinal2(A,C),k15_ordinal2(B,C))))))))) # label(t58_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1508 (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]. 4.40/4.47 1509 (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]. 4.40/4.47 1510 (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]. 4.40/4.47 1511 (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]. 4.40/4.47 1512 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1513 (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]. 4.40/4.47 1514 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1515 (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]. 4.40/4.47 1516 (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]. 4.40/4.47 1517 (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]. 4.40/4.47 1518 (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]. 4.40/4.47 1519 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1520 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1521 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1522 (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]. 4.40/4.47 1523 (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]. 4.40/4.47 1524 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1525 (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]. 4.40/4.47 1526 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_finset_1(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1527 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1528 (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]. 4.40/4.47 1529 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1530 (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]. 4.40/4.47 1531 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1532 (all A all B (v1_finset_1(k2_tarski(A,B)) & -v1_xboole_0(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1533 (all A all B (v1_finset_1(A) -> v1_finset_1(k4_xboole_0(A,B)))) # label(t16_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1534 (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]. 4.40/4.47 1535 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]. 4.40/4.47 1536 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1537 (all A all B all C all D all E all F all G v1_finset_1(k5_enumset1(A,B,C,D,E,F,G))) # label(fc7_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1538 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1539 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1540 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1541 (all A all B (v1_relat_1(A) & v1_finset_1(B) & v1_funct_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1542 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k2_relat_1(B)) & v1_finset_1(k10_relat_1(B,A)) -> v1_finset_1(A)))) # label(t27_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1543 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1544 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1545 (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]. 4.40/4.47 1546 (all A (v1_finset_1(A) <-> v1_finset_1(k1_zfmisc_1(A)))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1547 (all A all B all C all D all E v1_finset_1(k3_enumset1(A,B,C,D,E))) # label(fc5_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1548 (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]. 4.40/4.47 1549 (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]. 4.40/4.47 1550 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1551 (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]. 4.40/4.47 1552 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1553 (all A all B all C all D all E all F v1_finset_1(k4_enumset1(A,B,C,D,E,F))) # label(fc6_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1554 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1555 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1556 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc11_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.47 1557 (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]. 4.40/4.48 1558 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1559 (all A all B (v1_finset_1(B) & r1_tarski(A,B) -> v1_finset_1(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1560 (all A all B all C all D all E all F all G all H v1_finset_1(k6_enumset1(A,B,C,D,E,F,G,H))) # label(fc8_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1561 (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]. 4.40/4.48 1562 (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]. 4.40/4.48 1563 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1564 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1565 (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]. 4.40/4.48 1566 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1567 (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]. 4.40/4.48 1568 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -((all C -((all D (r2_hidden(D,B) & r1_tarski(C,D) -> D = C)) & r2_hidden(C,B))) & B != k1_xboole_0))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1569 (all A all B (v1_finset_1(B) -> v1_finset_1(k3_xboole_0(A,B)))) # label(fc10_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1570 (all A all B all C all D v1_finset_1(k2_enumset1(A,B,C,D))) # label(fc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1571 (all A all B (v1_finset_1(A) -> v1_finset_1(k3_xboole_0(A,B)))) # label(t15_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1572 (all A ((all B (r2_hidden(B,A) -> v1_finset_1(B))) & v1_finset_1(A) <-> v1_finset_1(k3_tarski(A)))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1573 (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]. 4.40/4.48 1574 (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]. 4.40/4.48 1575 (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]. 4.40/4.48 1576 (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]. 4.40/4.48 1577 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]. 4.40/4.48 1578 (all A (m1_subset_1(A,f1_s12_fraenkel) -> (all B (m1_subset_1(B,f2_s12_fraenkel) -> (p1_s12_fraenkel(A,B) -> p2_s12_fraenkel(f3_s12_fraenkel(A,B))))))) -> (all A (r2_hidden(A,a_0_20_fraenkel) -> p2_s12_fraenkel(A))) # label(s12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1579 (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]. 4.40/4.48 1580 (all A ((exists B (m1_subset_1(B,f3_s13_fraenkel) & p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & B = A)) <-> r2_hidden(A,a_0_21_fraenkel))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1581 (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]. 4.40/4.48 1582 (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]. 4.40/4.48 1583 (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]. 4.40/4.48 1584 (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]. 4.40/4.48 1585 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]. 4.40/4.48 1586 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> ((all D (m1_subset_1(D,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))) <-> m1_fraenkel(C,A,B)))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1587 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1588 (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]. 4.40/4.48 1589 (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]. 4.40/4.48 1590 (all A (r2_hidden(A,a_0_19_fraenkel) -> p2_s11_fraenkel(A))) -> (all A (m1_subset_1(A,f1_s11_fraenkel) -> (all B (m1_subset_1(B,f2_s11_fraenkel) -> (p1_s11_fraenkel(A,B) -> p2_s11_fraenkel(f3_s11_fraenkel(A,B))))))) # label(s11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1591 (all A ((exists B (m1_subset_1(B,f1_s17_fraenkel) & f3_s17_fraenkel(B) = A & p1_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel))) <-> r2_hidden(A,a_0_32_fraenkel))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1592 (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]. 4.40/4.48 1593 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1594 (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]. 4.40/4.48 1595 (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]. 4.40/4.48 1596 (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]. 4.40/4.48 1597 (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]. 4.40/4.48 1598 (all A (m1_subset_1(A,f1_s1_fraenkel) -> (p1_s1_fraenkel(A) -> p2_s1_fraenkel(A)))) -> r1_tarski(a_0_0_fraenkel,a_0_1_fraenkel) # label(s1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1599 (all A all B (-v1_xboole_0(B) -> k1_funct_2(A,B) = k1_fraenkel(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1600 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p2_s4_fraenkel(A,B) <-> p1_s4_fraenkel(A,B)))))) -> a_0_6_fraenkel = a_0_7_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1601 (all A (-v1_xboole_0(A) -> (all B m1_fraenkel(k1_funct_2(B,A),B,A)))) # label(t11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1602 (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]. 4.40/4.48 1603 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1604 (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]. 4.40/4.48 1605 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1606 (all A all B r1_tarski(k1_funct_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B)))) # label(t5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1607 (all A (m1_subset_1(A,f1_s2_fraenkel) -> (all B (m1_subset_1(B,f2_s2_fraenkel) -> (p1_s2_fraenkel(A,B) -> p2_s2_fraenkel(A,B)))))) -> r1_tarski(a_0_2_fraenkel,a_0_3_fraenkel) # label(s2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1608 (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]. 4.40/4.48 1609 v1_finset_1(f3_s22_fraenkel) & v1_finset_1(f4_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1610 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1611 (all A all B (-v1_xboole_0(B) -> m1_fraenkel(k1_fraenkel(A,B),A,B))) # label(dt_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1612 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1613 (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]. 4.40/4.48 1614 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (all D (m1_subset_1(D,C) <-> m2_fraenkel(D,A,B,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1615 (all A (r2_hidden(A,a_0_23_fraenkel) <-> (exists B exists C (A = f4_s13_fraenkel(B,C) & p1_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & m1_subset_1(C,f2_s13_fraenkel) & m1_subset_1(B,f1_s13_fraenkel))))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1616 (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]. 4.40/4.48 1617 (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]. 4.40/4.48 1618 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1619 (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]. 4.40/4.48 1620 (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]. 4.40/4.48 1621 (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]. 4.40/4.48 1622 (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]. 4.40/4.48 1623 (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]. 4.40/4.48 1624 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1625 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1626 (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]. 4.40/4.48 1627 (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]. 4.40/4.48 1628 (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]. 4.40/4.48 1629 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1630 (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]. 4.40/4.48 1631 (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]. 4.40/4.48 1632 (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]. 4.40/4.48 1633 (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]. 4.40/4.48 1634 (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]. 4.40/4.48 1635 (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]. 4.40/4.48 1636 (all A (r2_hidden(A,a_0_9_fraenkel) <-> (exists B (p1_s5_fraenkel(B) & A = f3_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1637 (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]. 4.40/4.48 1638 (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]. 4.40/4.48 1639 (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]. 4.40/4.48 1640 (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]. 4.40/4.48 1641 (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]. 4.40/4.48 1642 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1643 (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]. 4.40/4.48 1644 (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]. 4.40/4.48 1645 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1646 (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]. 4.40/4.48 1647 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1648 (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]. 4.40/4.48 1649 (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]. 4.40/4.48 1650 (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]. 4.40/4.48 1651 (all A all B all C (m1_fraenkel(C,A,B) -> v1_fraenkel(C) & -v1_xboole_0(C))) # label(dt_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1652 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_relat_1(B) & v1_funct_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1653 (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]. 4.40/4.48 1654 (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]. 4.40/4.48 1655 (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]. 4.40/4.48 1656 (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]. 4.40/4.48 1657 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1658 (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]. 4.40/4.48 1659 (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]. 4.40/4.48 1660 (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]. 4.40/4.48 1661 (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]. 4.40/4.48 1662 (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]. 4.40/4.48 1663 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f4_s7_fraenkel(A,B) = f3_s7_fraenkel(A,B))))) -> a_0_13_fraenkel = a_0_12_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1664 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1665 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1666 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1667 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1668 (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]. 4.40/4.48 1669 (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]. 4.40/4.48 1670 (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]. 4.40/4.48 1671 (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]. 4.40/4.48 1672 (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]. 4.40/4.48 1673 (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]. 4.40/4.48 1674 (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]. 4.40/4.48 1675 (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]. 4.40/4.48 1676 (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]. 4.40/4.48 1677 (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]. 4.40/4.48 1678 (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]. 4.40/4.48 1679 (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]. 4.40/4.48 1680 (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]. 4.40/4.48 1681 (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]. 4.40/4.48 1682 (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]. 4.40/4.48 1683 (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]. 4.40/4.48 1684 (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]. 4.40/4.48 1685 (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]. 4.40/4.48 1686 (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]. 4.40/4.48 1687 (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]. 4.40/4.48 1688 (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]. 4.40/4.48 1689 (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]. 4.40/4.48 1690 (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]. 4.40/4.48 1691 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1692 (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]. 4.40/4.48 1693 (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]. 4.40/4.48 1694 (all A (r2_hidden(A,k1_numbers) <-> v1_xreal_0(A))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1695 (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]. 4.40/4.48 1696 (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]. 4.40/4.48 1697 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1698 (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]. 4.40/4.48 1699 (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]. 4.40/4.48 1700 (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]. 4.40/4.48 1701 (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]. 4.40/4.48 1702 (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]. 4.40/4.48 1703 (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]. 4.40/4.48 1704 (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]. 4.40/4.48 1705 (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]. 4.40/4.48 1706 (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]. 4.40/4.48 1707 (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]. 4.40/4.48 1708 (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]. 4.40/4.48 1709 (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]. 4.40/4.48 1710 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1711 (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]. 4.40/4.48 1712 (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]. 4.40/4.48 1713 (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]. 4.40/4.48 1714 (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]. 4.40/4.48 1715 (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]. 4.40/4.48 1716 (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]. 4.40/4.48 1717 (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]. 4.40/4.48 1718 (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]. 4.40/4.48 1719 (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]. 4.40/4.48 1720 (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]. 4.40/4.48 1721 (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]. 4.40/4.48 1722 (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]. 4.40/4.48 1723 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1724 (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]. 4.40/4.48 1725 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1726 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1727 (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]. 4.40/4.48 1728 (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]. 4.40/4.48 1729 (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]. 4.40/4.48 1730 (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]. 4.40/4.48 1731 (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]. 4.40/4.48 1732 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1733 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1734 (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]. 4.40/4.48 1735 (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]. 4.40/4.48 1736 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1737 (all A (v1_int_1(A) <-> r2_hidden(A,k4_numbers))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1738 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1739 (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]. 4.40/4.48 1740 (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]. 4.40/4.48 1741 (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]. 4.40/4.48 1742 (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]. 4.40/4.48 1743 (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]. 4.40/4.48 1744 (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]. 4.40/4.48 1745 (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]. 4.40/4.48 1746 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1747 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1748 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1749 (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]. 4.40/4.48 1750 (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]. 4.40/4.48 1751 (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]. 4.40/4.48 1752 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1753 (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]. 4.40/4.48 1754 (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]. 4.40/4.48 1755 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1756 (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]. 4.40/4.48 1757 (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]. 4.40/4.48 1758 (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]. 4.40/4.48 1759 (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]. 4.40/4.48 1760 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1761 (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]. 4.40/4.48 1762 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1763 (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]. 4.40/4.48 1764 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1765 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1766 (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]. 4.40/4.48 1767 (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]. 4.40/4.48 1768 (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]. 4.40/4.48 1769 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1770 (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]. 4.40/4.48 1771 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1772 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1773 (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]. 4.40/4.48 1774 (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]. 4.40/4.48 1775 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1776 (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]. 4.40/4.48 1777 (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]. 4.40/4.48 1778 (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]. 4.40/4.48 1779 (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]. 4.40/4.48 1780 (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]. 4.40/4.48 1781 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1782 (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]. 4.40/4.48 1783 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1784 (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]. 4.40/4.48 1785 (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]. 4.40/4.48 1786 (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]. 4.40/4.48 1787 (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]. 4.40/4.48 1788 (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]. 4.40/4.48 1789 (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]. 4.40/4.48 1790 (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]. 4.40/4.48 1791 (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]. 4.40/4.48 1792 (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]. 4.40/4.48 1793 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1794 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1795 (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]. 4.40/4.48 1796 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1797 (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]. 4.40/4.48 1798 (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]. 4.40/4.48 1799 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.48 1800 (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]. 4.40/4.49 1801 (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]. 4.40/4.49 1802 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1803 (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]. 4.40/4.49 1804 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1805 (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]. 4.40/4.49 1806 (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]. 4.40/4.49 1807 (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]. 4.40/4.49 1808 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1809 (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]. 4.40/4.49 1810 (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]. 4.40/4.49 1811 (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]. 4.40/4.49 1812 (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]. 4.40/4.49 1813 (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]. 4.40/4.49 1814 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1815 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1816 (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]. 4.40/4.49 1817 (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]. 4.40/4.49 1818 (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]. 4.40/4.49 1819 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1820 (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]. 4.40/4.49 1821 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1822 (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]. 4.40/4.49 1823 (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]. 4.40/4.49 1824 (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]. 4.40/4.49 1825 (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]. 4.40/4.49 1826 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1827 (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]. 4.40/4.49 1828 (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]. 4.40/4.49 1829 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]. 4.40/4.49 1830 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1831 (all A (v1_int_1(A) -> v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1832 (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]. 4.40/4.49 1833 (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]. 4.40/4.49 1834 (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]. 4.40/4.49 1835 (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]. 4.40/4.49 1836 (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]. 4.40/4.49 1837 (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]. 4.40/4.49 1838 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1839 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1840 (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]. 4.40/4.49 1841 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k3_card_1(A),k3_card_1(B))))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1842 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1843 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k4_card_1(A),k4_card_1(B))))))) # label(t80_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1844 (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]. 4.40/4.49 1845 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1846 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1847 (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]. 4.40/4.49 1848 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1849 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1850 (all A all B (v1_finset_1(A) & r2_wellord2(A,B) -> v1_finset_1(B))) # label(t68_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1851 (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]. 4.40/4.49 1852 (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]. 4.40/4.49 1853 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1854 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1855 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> B = A))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1856 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1857 (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]. 4.40/4.49 1858 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1859 (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]. 4.40/4.49 1860 (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]. 4.40/4.49 1861 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1862 (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]. 4.40/4.49 1863 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]. 4.40/4.49 1864 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1865 (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]. 4.40/4.49 1866 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1867 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_card_1(A)) & v1_card_1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1868 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1869 (all A all B (v1_card_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_card_1(A),B)))) # label(t23_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1870 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1871 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s2_card_1(B)))) -> p1_s2_card_1(A)))) -> (all A (v1_card_1(A) -> p1_s2_card_1(A))) # label(s2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1872 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1873 (all A all B all C (r1_tarski(A,B) & r2_wellord2(A,C) & r1_tarski(B,C) -> r2_wellord2(B,C) & r2_wellord2(A,B))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1874 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1875 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1876 (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]. 4.40/4.49 1877 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1878 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) <-> -r1_xreal_0(B,A)))))) # label(t73_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1879 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1880 (all A all B all C all D (r1_xboole_0(A,B) & r1_xboole_0(C,D) & r2_wellord2(A,C) & r2_wellord2(B,D) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1881 (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]. 4.40/4.49 1882 (all A r2_hidden(k1_card_1(A),k1_card_1(k1_zfmisc_1(A)))) # label(t30_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1883 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(A) = k3_card_1(B) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1884 (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]. 4.40/4.49 1885 (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]. 4.40/4.49 1886 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1887 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1888 (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]. 4.40/4.49 1889 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1890 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(k1_nat_1(A,np__1)) = k2_card_1(k1_card_1(A)))) # label(t76_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1891 (all A (v1_finset_1(A) -> k4_card_1(A) = k1_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1892 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1893 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1894 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1895 (all A (v1_finset_1(A) -> m2_subset_1(k4_card_1(A),k1_numbers,k5_numbers))) # label(dt_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1896 (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]. 4.40/4.49 1897 (all A all B (r2_wellord2(A,B) -> k2_card_1(B) = k2_card_1(A))) # label(t35_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1898 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1899 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1900 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1901 (all A all B (v1_card_1(B) -> (B = k1_card_1(A) <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1902 (all A all B (v1_card_1(B) -> (r2_hidden(A,B) -> r2_hidden(k1_card_1(A),B)))) # label(t25_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1903 (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]. 4.40/4.49 1904 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1905 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t27_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1906 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1907 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1908 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) & r2_wellord2(A,B) -> r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))))) # label(t61_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1909 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1910 (all A (v1_card_1(A) & v1_finset_1(A) -> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & A = k1_card_1(B))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1911 (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]. 4.40/4.49 1912 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1913 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1914 (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]. 4.40/4.49 1915 (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]. 4.40/4.49 1916 (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]. 4.40/4.49 1917 (all A (v3_ordinal1(A) -> k2_card_1(k3_card_1(A)) = k3_card_1(k1_ordinal1(A)))) # label(t39_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1918 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_ordinal1(A,B) <-> r1_xreal_0(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1919 (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]. 4.40/4.49 1920 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1921 (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]. 4.40/4.49 1922 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> r2_wellord2(k3_relat_1(A),k2_wellord2(A))))) # label(t22_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1923 (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]. 4.40/4.49 1924 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1925 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(A) = A)) # label(t66_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1926 (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]. 4.40/4.49 1927 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1928 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (-r1_tarski(B,A) <-> r2_hidden(A,B)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1929 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1930 (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]. 4.40/4.49 1931 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> r2_hidden(k1_card_1(A),k1_card_1(B)) & -r2_wellord2(A,B))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1932 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1933 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1934 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1935 (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]. 4.40/4.49 1936 (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]. 4.40/4.49 1937 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1938 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1939 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1940 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1941 (all A (A = k1_xboole_0 <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1942 (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]. 4.40/4.49 1943 (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]. 4.40/4.49 1944 (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]. 4.40/4.49 1945 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1946 (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]. 4.40/4.49 1947 (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]. 4.40/4.49 1948 (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]. 4.40/4.49 1949 (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]. 4.40/4.49 1950 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1951 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1952 (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]. 4.40/4.49 1953 (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]. 4.40/4.49 1954 (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]. 4.40/4.49 1955 (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]. 4.40/4.49 1956 (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]. 4.40/4.49 1957 (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]. 4.40/4.49 1958 (all A all B all C (v1_funct_1(k11_finseq_1(A,B,C)) & v1_relat_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1959 (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]. 4.40/4.49 1960 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1961 (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]. 4.40/4.49 1962 (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]. 4.40/4.49 1963 (all A (v1_funct_1(k9_finseq_1(A)) & v1_relat_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1964 (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]. 4.40/4.49 1965 (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]. 4.40/4.49 1966 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1967 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1968 (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]. 4.40/4.49 1969 (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]. 4.40/4.49 1970 (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]. 4.40/4.49 1971 (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]. 4.40/4.49 1972 (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]. 4.40/4.49 1973 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1974 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1975 (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]. 4.40/4.49 1976 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1977 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> k7_relat_1(B,k2_finseq_1(C)) = k16_finseq_1(A,B,C))))) # label(d15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1978 (all A (v1_relat_1(A) & v1_finset_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1979 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1980 (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]. 4.40/4.49 1981 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1982 (all A (v4_ordinal2(A) -> k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(A))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1983 (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]. 4.40/4.49 1984 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1985 (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]. 4.40/4.49 1986 (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]. 4.40/4.49 1987 (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]. 4.40/4.49 1988 (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]. 4.40/4.49 1989 (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]. 4.40/4.49 1990 (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]. 4.40/4.49 1991 (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]. 4.40/4.49 1992 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1993 (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]. 4.40/4.49 1994 (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]. 4.40/4.49 1995 (all A k9_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1996 (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]. 4.40/4.49 1997 (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]. 4.40/4.49 1998 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 1999 (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]. 4.40/4.49 2000 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2001 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> m2_finseq_1(k8_finseq_1(A,B,C),A))) # label(dt_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2002 (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]. 4.40/4.49 2003 (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]. 4.40/4.49 2004 (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]. 4.40/4.49 2005 (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]. 4.40/4.49 2006 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> k5_relat_1(k14_finseq_1(k1_relat_1(A)),A) = k15_finseq_1(A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2007 (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]. 4.40/4.49 2008 (all A (v4_ordinal2(A) -> (all B all C (m2_finseq_1(C,B) -> m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B))))) # label(t23_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2009 (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]. 4.40/4.49 2010 (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]. 4.40/4.49 2011 (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]. 4.40/4.49 2012 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2013 (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]. 4.40/4.49 2014 (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]. 4.40/4.49 2015 (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]. 4.40/4.49 2016 (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]. 4.40/4.49 2017 (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]. 4.40/4.49 2018 (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]. 4.40/4.49 2019 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2020 (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]. 4.40/4.49 2021 (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]. 4.40/4.49 2022 (all A (v4_ordinal2(A) -> k4_card_1(k2_finseq_1(A)) = A)) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2023 (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]. 4.40/4.49 2024 (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]. 4.40/4.49 2025 (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]. 4.40/4.49 2026 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(B,k2_finseq_1(A)) -> r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C)))))))))) # label(t81_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2027 (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]. 4.40/4.49 2028 (exists A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2029 (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]. 4.40/4.49 2030 (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]. 4.40/4.49 2031 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k3_finseq_1(B),C) -> k16_finseq_1(A,B,C) = B))))) # label(t79_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.49 2032 (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]. 4.40/4.49 2033 (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]. 4.40/4.49 2034 (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]. 4.40/4.49 2035 (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]. 4.40/4.49 2036 (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]. 4.40/4.49 2037 (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]. 4.40/4.49 2038 (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]. 4.40/4.49 2039 (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]. 4.40/4.49 2040 (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]. 4.40/4.49 2041 (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]. 4.40/4.49 2042 (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]. 4.40/4.49 2043 (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]. 4.40/4.49 2044 (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]. 4.40/4.49 2045 (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]. 4.40/4.49 2046 (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]. 4.40/4.50 2047 (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]. 4.40/4.50 2048 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2049 (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]. 4.40/4.50 2050 (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]. 4.40/4.50 2051 (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]. 4.40/4.50 2052 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2053 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> r2_wellord2(k2_finseq_1(A),A))) # label(t75_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2054 (all A (v4_ordinal2(A) -> k2_finseq_1(k2_xcmplx_0(A,np__1)) = k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2055 (all A (v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & -v1_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2056 (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]. 4.40/4.50 2057 (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]. 4.40/4.50 2058 (all A (v4_ordinal2(A) -> r2_hidden(k2_xcmplx_0(A,np__1),k2_finseq_1(k2_xcmplx_0(A,np__1))))) # label(t6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2059 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2060 (all A all B (r1_tarski(A,B) -> r1_tarski(k13_finseq_1(A),k13_finseq_1(B)))) # label(t83_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2061 (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]. 4.40/4.50 2062 (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]. 4.40/4.50 2063 (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]. 4.40/4.50 2064 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2065 (all A exists B (v1_relat_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v1_funct_1(B) & m1_relset_1(B,k5_numbers,A))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2066 (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]. 4.40/4.50 2067 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2068 (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]. 4.40/4.50 2069 (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]. 4.40/4.50 2070 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> k3_finseq_1(k16_finseq_1(A,B,C)) = C))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2071 (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]. 4.40/4.50 2072 (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]. 4.40/4.50 2073 (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]. 4.40/4.50 2074 (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]. 4.40/4.50 2075 (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]. 4.40/4.50 2076 (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]. 4.40/4.50 2077 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2078 (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]. 4.40/4.50 2079 (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]. 4.40/4.50 2080 (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]. 4.40/4.50 2081 (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]. 4.40/4.50 2082 (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]. 4.40/4.50 2083 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k1_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2084 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2085 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2086 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2087 (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]. 4.40/4.50 2088 (all A k1_tarski(k4_tarski(np__1,A)) = k5_finseq_1(A)) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2089 (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]. 4.40/4.50 2090 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2091 p1_s3_finseq_1(k1_xboole_0) & (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) -> (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2092 (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]. 4.40/4.50 2093 (all A (v4_ordinal2(A) -> m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2094 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r1_xreal_0(B,np__0) | r2_hidden(B,k2_finseq_1(A)) & r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C)))))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2095 (exists A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2096 (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]. 4.40/4.50 2097 (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]. 4.40/4.50 2098 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2099 (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]. 4.40/4.50 2100 (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]. 4.40/4.50 2101 (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]. 4.40/4.50 2102 (all A k6_finseq_1(A) = k1_xboole_0) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2103 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2104 (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]. 4.40/4.50 2105 (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]. 4.40/4.50 2106 (exists A (v1_struct_0(A) & l1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2107 (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]. 4.40/4.50 2108 (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]. 4.40/4.50 2109 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2110 (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]. 4.40/4.50 2111 (exists A (v2_struct_0(A) & l2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2112 (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]. 4.40/4.50 2113 (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]. 4.40/4.50 2114 (exists A (l2_struct_0(A) & -v3_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2115 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2116 (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]. 4.40/4.50 2117 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2118 (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]. 4.40/4.50 2119 (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]. 4.40/4.50 2120 (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]. 4.40/4.50 2121 (exists A (-v3_struct_0(A) & l1_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2122 (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]. 4.40/4.50 2123 (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]. 4.40/4.50 2124 (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]. 4.40/4.50 2125 (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]. 4.40/4.50 2126 (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]. 4.40/4.50 2127 (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]. 4.40/4.50 2128 (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]. 4.40/4.50 2129 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2130 (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]. 4.40/4.50 2131 (exists A l1_rlvect_1(A)) # label(existence_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2132 (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]. 4.40/4.50 2133 (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]. 4.40/4.50 2134 (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]. 4.40/4.50 2135 (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]. 4.40/4.50 2136 (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]. 4.40/4.50 2137 (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]. 4.40/4.50 2138 (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]. 4.40/4.50 2139 (exists A (l2_rlvect_1(A) & -v3_struct_0(A))) # label(rc3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2140 (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]. 4.40/4.50 2141 (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]. 4.40/4.50 2142 (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]. 4.40/4.50 2143 $T # label(t2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2144 (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]. 4.40/4.50 2145 (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]. 4.40/4.50 2146 (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]. 4.40/4.50 2147 (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]. 4.40/4.50 2148 $T # label(t53_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2149 (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]. 4.40/4.50 2150 (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]. 4.40/4.50 2151 (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]. 4.40/4.50 2152 (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]. 4.40/4.50 2153 (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]. 4.40/4.50 2154 (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]. 4.40/4.50 2155 (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]. 4.40/4.50 2156 $T # label(t15_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2157 (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]. 4.40/4.50 2158 (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]. 4.40/4.50 2159 (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]. 4.40/4.50 2160 (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]. 4.40/4.50 2161 (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]. 4.40/4.50 2162 (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]. 4.40/4.50 2163 (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]. 4.40/4.50 2164 (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]. 4.40/4.50 2165 (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]. 4.40/4.50 2166 $T # label(t8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2167 (all A (l2_rlvect_1(A) -> l1_rlvect_1(A))) # label(dt_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2168 (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]. 4.40/4.50 2169 (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]. 4.40/4.50 2170 (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]. 4.40/4.50 2171 (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]. 4.40/4.50 2172 (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]. 4.40/4.50 2173 (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]. 4.40/4.50 2174 $T # label(t18_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2175 (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]. 4.40/4.50 2176 (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]. 4.40/4.50 2177 (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]. 4.40/4.50 2178 (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]. 4.40/4.50 2179 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2180 (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]. 4.40/4.50 2181 (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]. 4.40/4.50 2182 (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]. 4.40/4.50 2183 (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]. 4.40/4.50 2184 (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]. 4.40/4.50 2185 (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]. 4.40/4.50 2186 (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]. 4.40/4.50 2187 $T # label(t14_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 4.40/4.50 2188 (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]. 4.40/4.50 2189 (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]. 115.41/115.48 2190 (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]. 115.41/115.48 2191 (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]. 115.41/115.48 2192 (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]. 115.41/115.48 2193 (exists A (v1_rlvect_1(A) & l1_rlvect_1(A))) # label(rc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.48 2194 (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]. 115.41/115.48 2195 (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]. 115.41/115.48 2196 (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]. 115.41/115.48 2197 (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]. 115.41/115.48 2198 (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]. 115.41/115.48 2199 (exists A l2_rlvect_1(A)) # label(existence_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.48 2200 (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_clause). [assumption]. 115.41/115.48 2201 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v1_rlvect_1(g1_rlvect_1(A,B,C)) & l1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(dt_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.48 2202 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) = k3_rlvect_1(A,D,k4_real_1(B,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__1) = B)) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,C))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B)) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B))))) -> v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2203 (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)) -> (exists D (k6_rlvect_1(A,C,D) = B & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t36_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2204 $T # label(t32_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2205 $T # label(t88_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2206 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,k5_rlvect_1(A,B)) = B)))) # label(t30_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2207 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = B -> B = k1_rlvect_1(A)))))) # label(t33_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2208 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C))))))) # label(t5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2209 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> k1_rlvect_1(A) = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),k1_rlvect_1(A))))) # label(t90_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2210 (exists A (-v3_struct_0(A) & v1_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & l1_rlvect_1(A))) # label(rc5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2211 $T # label(t6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2212 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> m2_finseq_1(k7_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2213 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(D,k4_finseq_1(B)) & k1_funct_1(C,D) = E -> k5_rlvect_1(A,E) = k1_funct_1(B,D)))))) & k3_finseq_1(B) = k3_finseq_1(C) -> k9_rlvect_1(A,B) = k5_rlvect_1(A,k9_rlvect_1(A,C))))))))) # label(t57_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2214 (all A (-v3_struct_0(A) & l2_rlvect_1(A) -> (v7_rlvect_1(A) <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_rlvect_1(A,B,np__1))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) = k3_rlvect_1(A,D,k3_real_1(B,C)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B))))))))))) # label(d9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2215 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) = k4_rlvect_1(A,B,B) -> k1_rlvect_1(A) = B))))) # label(t34_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2216 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k3_rlvect_1(B,k6_rlvect_1(B,C,D),A) = k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)))))))))) # label(t48_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2217 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k7_rlvect_1(A,B,C) = k10_finseq_1(B,C))) # label(redefinition_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2218 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,k1_rlvect_1(A),B) = B & B = k2_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2219 (all A (v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,C),B) = k6_rlvect_1(A,k5_rlvect_1(A,B),C))))))) # label(t46_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2220 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2221 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t86_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2222 $T # label(t12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2223 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) -> (all D all E all F (g1_rlvect_1(A,B,C) = g1_rlvect_1(D,E,F) -> A = D & C = F & E = B)))) # label(free_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2224 (exists A (l1_rlvect_1(A) & -v3_struct_0(A) & v1_rlvect_1(A))) # label(rc4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2225 $T # label(t17_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2226 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (k3_finseq_1(B) = np__0 -> k9_rlvect_1(A,B) = k1_rlvect_1(A)))))) # label(t94_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2227 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),np__1) & k1_funct_1(B,k3_finseq_1(B)) = D & k7_relat_1(B,k4_finseq_1(C)) = C -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D)))))))))) # label(t55_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2228 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D) = k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))))))))))) # label(t71_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2229 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,B,C) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)))))))) # label(d11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2230 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2231 (all A all B all C (-v3_struct_0(A) & l2_rlvect_1(A) & m1_subset_1(C,k1_numbers) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2232 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (D = k3_finseq_1(B) & r2_hidden(C,k2_finseq_1(D)) -> m1_subset_1(k1_funct_1(B,C),u1_struct_0(A))))))))))) # label(t54_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2233 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> -(k1_rlvect_1(B) = k3_rlvect_1(B,C,A) & C != k1_rlvect_1(B) & np__0 != A))))))) # label(t24_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2234 (all A all B all C all D (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) -> k8_rlvect_1(A,B,C,D) = k11_finseq_1(B,C,D))) # label(redefinition_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2235 (all A (l2_rlvect_1(A) -> v1_funct_1(u2_rlvect_1(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2236 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v6_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)) = k3_rlvect_1(C,D,k5_real_1(A,B)))))))))) # label(t49_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2237 (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)) -> k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A) & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A))))) # label(t16_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2238 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k5_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C))))))))) # label(t70_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2239 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (np__1 = k3_finseq_1(B) -> k1_funct_1(B,np__1) = k9_rlvect_1(A,B)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2240 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))) <-> v4_rlvect_1(A)))) # label(d6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2241 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2242 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k1_funct_1(B,np__1) = C & D = k1_funct_1(B,np__2) & k1_funct_1(B,np__3) = E & np__3 = k3_finseq_1(B) -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k2_rlvect_1(A,C,D),E)))))))))))) # label(t97_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2243 $T # label(t65_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2244 (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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C))))))))) # label(t41_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2245 (all A (m1_subset_1(A,k1_numbers) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (k1_funct_1(D,E) = F & r2_hidden(E,k4_finseq_1(C)) -> k3_rlvect_1(B,F,A) = k1_funct_1(C,E)))))) & k3_finseq_1(C) = k3_finseq_1(D) -> k9_rlvect_1(B,C) = k3_rlvect_1(B,k9_rlvect_1(B,D),A)))))))))) # label(t56_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2246 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) & k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B)) = C & k1_rlvect_1(A) = k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = k1_funct_1(B,k1_nat_1(E,np__1)) -> k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) = k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) | r1_xreal_0(k3_finseq_1(B),E)))))))) <-> k9_rlvect_1(A,B) = C))))))) # label(d12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2247 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (v2_funct_1(B) & v2_funct_1(C) & k2_relat_1(B) = k2_relat_1(C) -> k9_rlvect_1(A,B) = k9_rlvect_1(A,C)))))))) # label(t59_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2248 (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)) -> k9_rlvect_1(A,k7_rlvect_1(A,C,B)) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t72_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2249 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))) = k5_rlvect_1(A,B))))) # label(t69_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2250 $T # label(t9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2251 (all A (m1_subset_1(A,k1_numbers) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k5_rlvect_1(B,k3_rlvect_1(B,C,A)) = k3_rlvect_1(B,k5_rlvect_1(B,C),A))))))) # label(t39_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2252 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__3) = k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)))))) # label(t93_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2253 (all A all B all C all D (-v1_xboole_0(A) & 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) -> -v3_struct_0(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)))) # label(fc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2254 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v3_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C)))))))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2255 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(B,A) -> l2_rlvect_1(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)))) # label(dt_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2256 (all A (l2_struct_0(A) -> k1_rlvect_1(A) = u2_struct_0(A))) # label(d2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2257 (all A (l1_rlvect_1(A) -> l2_struct_0(A))) # label(dt_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2258 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)))))))))) # label(t87_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2259 $T # label(t11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2260 (exists A (v2_rlvect_1(A) & l2_rlvect_1(A))) # label(rc2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2261 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_rlvect_1(A,B,C) = B | B = k2_rlvect_1(A,C,B) -> C = k1_rlvect_1(A)))))))) # label(t22_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2262 $T # label(t52_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2263 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,B))) = k1_rlvect_1(A) & k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),B)) = k1_rlvect_1(A))))) # label(t76_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2264 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_rlvect_1(A,B,C) = k1_rlvect_1(A) -> B = k5_rlvect_1(A,C)))))))) # label(t19_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2265 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t81_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2266 $T # label(t1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2267 (all A (l2_struct_0(A) -> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)))) # label(dt_k1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2268 (all A all B (l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2269 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k3_rlvect_1(B,C,k1_real_1(A)))))))) # label(t38_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2270 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & l2_rlvect_1(C) & v7_rlvect_1(C) & v6_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k3_rlvect_1(C,D,B) = k3_rlvect_1(C,D,A) -> D = k1_rlvect_1(C) | B = A))))))))) # label(t51_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2271 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) -> m2_finseq_1(k8_rlvect_1(A,B,C,D),u1_struct_0(A)))) # label(dt_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2272 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & v2_rlvect_1(A) & -v3_struct_0(A) -> m1_rlsub_1(A,k2_rlsub_1(A)))) # label(t54_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2273 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) -> r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))))))))))) # label(t75_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2274 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (all F (m1_subset_1(F,u1_struct_0(D)) -> (F = C & E = B -> k6_rlvect_1(A,B,C) = k6_rlvect_1(D,E,F)))))))))))))) # label(t24_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2275 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) <-> k3_rlsub_1(A,B,C) = k3_rlsub_1(A,k5_rlvect_1(A,B),C)))))))) # label(t71_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2276 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> r1_rlvect_1(C,k1_rlvect_1(B)))))))) # label(t26_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2277 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (a_3_0_rlsub_1(A,B,C) = D & v1_rlsub_1(C,A) & v1_rlsub_1(B,A) -> v1_rlsub_1(D,A)))))))))) # label(t9_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2278 $T # label(t53_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2279 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> r1_rlvect_1(A,k1_rlvect_1(B)))))) # label(t27_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2280 $T # label(t11_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2281 $T # label(t44_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2282 (all A (v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (B = E -> k3_rlvect_1(D,E,C) = k3_rlvect_1(A,B,C)))))))))))) # label(t22_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2283 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> ((exists E (m2_rlsub_1(E,A,D) & r2_hidden(C,E) & r2_hidden(B,E))) <-> r1_rlvect_1(D,k6_rlvect_1(A,B,C))))))))))) # label(t97_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2284 (all A (-v3_struct_0(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> v2_rlvect_1(k2_rlsub_1(A)) & m1_rlsub_1(k2_rlsub_1(A),A))) # label(dt_k2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2285 $T # label(t57_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2286 (all A (-v3_struct_0(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) <-> k3_rlsub_1(A,k5_rlvect_1(A,B),C) = u1_struct_0(C)))))))) # label(t67_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2287 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_rlsub_1(A,A))) # label(t33_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2288 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) <-> k3_rlsub_1(A,k6_rlvect_1(A,C,B),D) = k3_rlsub_1(A,C,D)))))))))) # label(t69_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2289 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v2_rlvect_1(A) & -v3_struct_0(A) -> (all B (v2_rlvect_1(B) & v4_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (m1_rlsub_1(B,A) & m1_rlsub_1(A,B) -> B = A))))) # label(t34_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2290 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> k1_rlvect_1(B) = k1_rlvect_1(A))))) # label(t19_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2291 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> k1_rlsub_1(A) = k1_rlsub_1(B))))) # label(t48_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2292 $T # label(t12_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2293 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v2_rlvect_1(B) & m1_rlsub_1(B,A) -> (all C (v2_rlvect_1(C) & m1_rlsub_1(C,A) -> (all D (m2_rlsub_1(D,A,B) -> (all E (m2_rlsub_1(E,A,C) -> (E = D -> C = B))))))))))) # label(t87_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2294 (all A (v2_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) & v2_rlvect_1(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_rlvect_1(A,C) <-> r1_rlvect_1(B,C)))) -> A = B))))) # label(t41_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2295 (all A all B (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & m1_rlsub_1(B,A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all C (m2_rlsub_1(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2296 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) -> r1_rlvect_1(A,B)))))) # label(t17_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2297 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) -> (all B all C (m1_rlsub_1(C,A) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(C,B) & m1_rlsub_1(C,D) -> r1_rlvect_1(D,B)))))))) # label(t16_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2298 (all A (-v3_struct_0(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> k1_rlvect_1(B) = k1_rlvect_1(C))))))) # label(t20_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2299 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_rlvect_1(B,D) -> r1_rlvect_1(C,D)))) -> m1_rlsub_1(B,C)))))))) # label(t37_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2300 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) -> u1_struct_0(D) = k3_rlsub_1(A,k3_rlvect_1(A,B,C),D)))))))))) # label(t65_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2301 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m2_rlsub_1(C,A,B) <-> (exists D (k3_rlsub_1(A,D,B) = C & m1_subset_1(D,u1_struct_0(A))))))))))) # label(d6_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2302 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> -v3_struct_0(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B))))) # label(dt_m1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2303 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (all D (m2_rlsub_1(D,A,C) -> (all E (m2_rlsub_1(E,A,C) -> (r2_hidden(B,D) & r2_hidden(B,E) -> D = E))))))))))) # label(t98_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2304 (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_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) -> r2_hidden(k1_rlvect_1(A),B) | k1_xboole_0 = B))))) # label(t4_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2305 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (all D (m2_rlsub_1(D,A,C) -> (D = k3_rlsub_1(A,B,C) <-> r2_hidden(B,D)))))))))) # label(t94_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2306 (all A all B all C (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & m1_rlsub_1(C,A) & m1_subset_1(B,u1_struct_0(A)) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_rlsub_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2307 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(B,k3_rlsub_1(A,C,D)) <-> k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D)))))))))) # label(t70_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2308 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists B m1_rlsub_1(B,A)))) # label(existence_m1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2309 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,C) & r1_rlvect_1(D,B) -> r1_rlvect_1(D,k6_rlvect_1(A,B,C))))))))))) # label(t31_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2310 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (v2_rlvect_1(B) & m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) & v2_rlvect_1(C) -> (u1_struct_0(C) = u1_struct_0(B) -> C = B))))))) # label(t38_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2311 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> -(k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(C = k4_rlvect_1(A,B,E) & r1_rlvect_1(D,E))))))))))))) # label(t82_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2312 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (all F (m1_subset_1(F,u1_struct_0(D)) -> (B = E & F = C -> k4_rlvect_1(D,E,F) = k4_rlvect_1(A,B,C)))))))))))))) # label(t21_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2313 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k6_rlvect_1(A,C,D),B))))))))))) # label(t6_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2314 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> ((exists E (m1_subset_1(E,u1_struct_0(A)) & r2_hidden(B,k3_rlsub_1(A,E,D)) & r2_hidden(C,k3_rlsub_1(A,E,D)))) <-> r1_rlvect_1(D,k6_rlvect_1(A,B,C))))))))))) # label(t81_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2315 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v2_rlvect_1(C) & m1_rlsub_1(C,A) -> (all D (v2_rlvect_1(D) & m1_rlsub_1(D,A) -> (D = C <-> k3_rlsub_1(A,B,D) = k3_rlsub_1(A,B,C)))))))))) # label(t84_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2316 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m2_rlsub_1(C,A,B) -> (v1_rlsub_1(C,A) <-> C = u1_struct_0(B)))))))) # label(t86_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2317 $T # label(t14_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2318 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m2_rlsub_1(u1_struct_0(A),A,k2_rlsub_1(A)))) # label(t91_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.49 2319 (all A (l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> ((exists E (m1_subset_1(E,u1_struct_0(A)) & r1_rlvect_1(D,E) & B = k6_rlvect_1(A,C,E))) <-> r2_hidden(B,k3_rlsub_1(A,C,D))))))))))) # label(t80_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2320 (all A (v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (B = u1_struct_0(A) -> v1_rlsub_1(B,A)))))) # label(t8_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2321 $T # label(t55_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2322 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) & v2_rlvect_1(B) -> (k1_rlsub_1(A) = B <-> u1_struct_0(B) = k1_struct_0(A,k1_rlvect_1(A))))))) # label(d3_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2323 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> r2_hidden(B,k3_rlsub_1(A,B,C)))))))) # label(t59_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2324 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(B,k3_rlsub_1(A,C,D)) <-> (exists E (r1_rlvect_1(D,E) & B = k4_rlvect_1(A,C,E) & m1_subset_1(E,u1_struct_0(A))))))))))))) # label(t79_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2325 $T # label(t3_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2326 (all A (v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) & v2_rlvect_1(D) -> (all E (m1_rlsub_1(E,A) & v2_rlvect_1(E) -> (k3_rlsub_1(A,C,E) = k3_rlsub_1(A,B,D) -> D = E))))))))))) # label(t85_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2327 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B = D -> k5_rlvect_1(C,D) = k5_rlvect_1(A,B)))))))))) # label(t23_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2328 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> k2_rlsub_1(A) = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)))) # label(d4_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2329 (all A (v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k4_rlvect_1(A,C,D),B)))))) & (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r2_hidden(k3_rlvect_1(A,D,C),B)))))) <-> v1_rlsub_1(B,A)))))) # label(d1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2330 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,B) -> r1_rlvect_1(D,k3_rlvect_1(A,B,C))))))))))) # label(t29_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2331 (all A (v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> u1_struct_0(A) = k3_rlsub_1(A,B,k2_rlsub_1(A)))))) # label(t62_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2332 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> r1_rlvect_1(B,k1_rlvect_1(A)))))) # label(t25_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2333 (all A all B all C all D (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v7_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) -> ((exists E exists F (m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & r2_hidden(F,D) & r2_hidden(E,C) & k4_rlvect_1(B,E,F) = A)) <-> r2_hidden(A,a_3_0_rlsub_1(B,C,D))))) # label(fraenkel_a_3_0_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2334 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> m1_rlsub_1(B,C)))))))) # label(t36_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2335 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(B,k3_rlsub_1(A,C,D)) & r2_hidden(B,k3_rlsub_1(A,k5_rlvect_1(A,C),D)) -> r1_rlvect_1(D,C)))))))))) # label(t73_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2336 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t18_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2337 (all A (v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> m2_rlsub_1(u1_struct_0(B),A,B))))) # label(t90_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2338 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(k4_rlvect_1(A,B,C),k3_rlsub_1(A,C,D)) <-> r1_rlvect_1(D,B)))))))))) # label(t77_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2339 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlsub_1(C,A) -> (B = u1_struct_0(C) -> v1_rlsub_1(B,A)))))))) # label(t42_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2340 $T # label(t1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2341 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (exists B (m1_rlsub_1(B,A) & -v3_struct_0(B) & v2_rlvect_1(B) & v4_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B))))) # label(rc1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2342 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(m2_rlsub_1(B,A,k1_rlsub_1(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> B != k1_struct_0(A,C)))))))) # label(t89_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2343 (all A (l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rlsub_1(k1_rlsub_1(A),A) & v2_rlvect_1(k1_rlsub_1(A)))) # label(dt_k1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2344 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (k3_rlsub_1(A,k4_rlvect_1(A,C,B),D) = k3_rlsub_1(A,C,D) <-> r1_rlvect_1(D,B)))))))))) # label(t68_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2345 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C)) <-> r1_rlvect_1(C,B)))))))) # label(t58_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2346 (all A all B (-v3_struct_0(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & m1_rlsub_1(B,A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (exists C m2_rlsub_1(C,A,B)))) # label(existence_m2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2347 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (u1_struct_0(D) = k3_rlsub_1(A,k3_rlvect_1(A,B,C),D) -> C = np__0 | r1_rlvect_1(D,B)))))))))) # label(t66_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2348 $T # label(t2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2349 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> -(k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r1_rlvect_1(D,E) & k6_rlvect_1(A,B,E) = C)))))))))))) # label(t83_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2350 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> k3_rlsub_1(A,B,C) = a_3_1_rlsub_1(A,B,C))))))) # label(d5_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2351 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> u1_struct_0(B) = k3_rlsub_1(A,k1_rlvect_1(A),B))))) # label(t60_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2352 (all A (-v3_struct_0(A) & v2_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) & v2_rlvect_1(B) -> (u1_struct_0(B) = u1_struct_0(A) -> A = B))))) # label(t40_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2353 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,C) <-> r2_hidden(k6_rlvect_1(A,B,C),k3_rlsub_1(A,B,D))))))))))) # label(t78_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2354 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (r1_rlvect_1(D,C) & r1_rlvect_1(D,B) -> r1_rlvect_1(D,k4_rlvect_1(A,B,C))))))))))) # label(t28_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2355 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> k1_rlsub_1(C) = k1_rlsub_1(B))))))) # label(t49_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2356 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r2_hidden(k5_rlvect_1(A,B),k3_rlsub_1(A,B,C)) <-> r1_rlvect_1(C,B)))))))) # label(t76_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2357 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlsub_1(D,A) -> (r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,B,D)) -> r1_rlvect_1(D,B) | C = np__1))))))))) # label(t74_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2358 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (u2_rlvect_1(B) = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(B))) & u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B)) & u2_struct_0(A) = u2_struct_0(B) & r1_tarski(u1_struct_0(B),u1_struct_0(A)) <-> m1_rlsub_1(B,A)))))) # label(d2_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2359 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r1_rlvect_1(C,B) -> r1_rlvect_1(C,k5_rlvect_1(A,B))))))))) # label(t30_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2360 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l2_rlvect_1(C) & v7_rlvect_1(C) & v6_rlvect_1(C) & -v3_struct_0(C) -> (m1_rlsub_1(B,C) & m1_rlsub_1(A,B) -> m1_rlsub_1(A,C)))))))) # label(t35_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2361 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,C) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(C,C),C) & v1_funct_2(E,k2_zfmisc_1(C,C),C) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(k1_numbers,C),C) & v1_funct_2(F,k2_zfmisc_1(k1_numbers,C),C) -> (C = B & E = k1_realset1(u1_rlvect_1(A),B) & k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,B)) = F & k1_rlvect_1(A) = D -> m1_rlsub_1(g2_rlvect_1(C,D,E,F),A)))))))))))))) # label(t32_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2362 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m2_rlsub_1(E,A,D) -> -(r2_hidden(C,E) & (all F (m1_subset_1(F,u1_struct_0(A)) -> -(r1_rlvect_1(D,F) & k4_rlvect_1(A,B,F) = C))) & r2_hidden(B,E)))))))))))) # label(t95_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2363 $T # label(t56_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2364 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m2_rlsub_1(C,A,B) -> (C = u1_struct_0(B) <-> r2_hidden(k1_rlvect_1(A),C)))))))) # label(t93_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2365 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_struct_0(A,B) = k3_rlsub_1(A,B,k1_rlsub_1(A)))))) # label(t61_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2366 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> m2_rlsub_1(k1_struct_0(A,B),A,k1_rlsub_1(A)))))) # label(t88_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2367 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(B != k1_xboole_0 & (all C (v2_rlvect_1(C) & m1_rlsub_1(C,A) -> B != u1_struct_0(C))) & v1_rlsub_1(B,A)))))) # label(t43_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2368 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (r2_hidden(k1_rlvect_1(A),k3_rlsub_1(A,B,C)) <-> k3_rlsub_1(A,B,C) = u1_struct_0(C)))))))) # label(t63_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2369 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlsub_1(C,A) -> (u1_struct_0(C) = k3_rlsub_1(A,B,C) <-> r1_rlvect_1(C,B)))))))) # label(t64_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2370 $T # label(t47_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2371 (all A all B all C all D (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_rlsub_1(D,B) & v7_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_rlsub_1(B,C,D)) <-> (exists E (r1_rlvect_1(D,E) & A = k4_rlvect_1(B,C,E) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2372 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_rlsub_1(E,A) -> (r2_hidden(B,k3_rlsub_1(A,D,E)) & r2_hidden(B,k3_rlsub_1(A,C,E)) -> k3_rlsub_1(A,C,E) = k3_rlsub_1(A,D,E)))))))))))) # label(t72_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2373 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m2_rlsub_1(B,A,k2_rlsub_1(A)) -> u1_struct_0(A) = B))))) # label(t92_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2374 $T # label(t13_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2375 (all A (v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> v1_rlsub_1(k1_struct_0(A,k1_rlvect_1(A)),A))) # label(t7_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2376 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlsub_1(D,A) -> (all E (m2_rlsub_1(E,A,D) -> -(r2_hidden(B,E) & (all F (m1_subset_1(F,u1_struct_0(A)) -> -(r1_rlvect_1(D,F) & k6_rlvect_1(A,B,F) = C))) & r2_hidden(C,E)))))))))))) # label(t96_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2377 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(C,A) & v1_rlsub_1(B,A) -> v1_rlsub_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t10_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2378 $T # label(t15_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2379 $T # label(t46_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2380 $T # label(t45_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2381 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> (all C (m1_rlsub_1(C,A) -> m1_rlsub_1(k1_rlsub_1(B),C))))))) # label(t52_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2382 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_rlsub_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,B) -> r2_hidden(k5_rlvect_1(A,C),B))))))))) # label(t5_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2383 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_rlsub_1(B,A) -> m1_rlsub_1(k1_rlsub_1(B),A))))) # label(t50_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2384 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) -> m1_rlsub_1(k1_rlsub_1(A),B))))) # label(t51_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2385 (all A (l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlsub_1(B,A) & v2_rlvect_1(B) -> (all C (m1_rlsub_1(C,A) & v2_rlvect_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_rlvect_1(B,D) <-> r1_rlvect_1(C,D)))) -> C = B))))))) # label(t39_rlsub_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2386 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (-r1_xreal_0(np__0,A) -> k6_group_1(B,A,C) = k3_group_1(B,k6_group_1(B,k1_int_2(A),C))))))))) # label(t56_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2387 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v2_group_1(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,C,B) & C = k1_group_1(A,B,C)))))))) # label(d2_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2388 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> k4_group_1(A) = k6_finseqop(u1_struct_0(A),u1_group_1(A)))) # label(t37_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2389 $T # label(t2_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2390 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k6_group_1(A,np__0,B))))) # label(t43_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2391 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> k6_group_1(B,A,k2_group_1(B)) = k2_group_1(B))))) # label(t42_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2392 (all A (l1_struct_0(A) -> (v6_group_1(A) <-> v1_finset_1(u1_struct_0(A))))) # label(d14_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2393 (all A all B all C (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v1_int_1(B) & m1_subset_1(C,u1_struct_0(A)) & v3_group_1(A) -> m1_subset_1(k6_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2394 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) = k1_group_1(A,B,C))))))) # label(d1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2395 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,A,k3_group_1(B,C)))))))) # label(t51_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2396 (all A (l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> v2_binop_1(u1_group_1(A),u1_struct_0(A)))) # label(t31_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2397 $T # label(t13_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2398 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = C & k1_group_1(A,B,C) = C)) <-> B = k2_group_1(A))))))) # label(d5_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2399 $T # label(t83_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2400 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_group_1(A,B) = k6_group_1(A,k7_binop_2(np__1),B))))) # label(t62_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2401 (all A (-v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v5_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v6_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v4_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v3_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))))) # label(t97_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2402 (exists A (-v3_struct_0(A) & v1_group_1(A) & v2_group_1(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) # label(rc3_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2403 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> v1_funct_1(k4_group_1(A)) & m2_relset_1(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k4_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2404 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & v4_group_1(B) & v7_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_group_1(B,A,k10_group_1(B,C,D)) = k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)))))))))) # label(t95_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2405 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> v1_card_1(k8_group_1(A)))) # label(dt_k8_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2406 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v1_finseqop(u1_group_1(A),u1_struct_0(A)))) # label(t36_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2407 $T # label(t89_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2408 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(B,A),D) = k1_group_1(C,k6_group_1(C,B,D),k6_group_1(C,A,D)))))))))) # label(t65_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2409 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k7_group_1(A,B) = np__1 -> B = k2_group_1(A)))))) # label(t85_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2410 $T # label(t76_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2411 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(A,np__0) -> k3_group_1(B,k6_group_1(B,k1_int_2(A),C)) = k6_group_1(B,A,C)))))))) # label(t60_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2412 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k1_group_1(A,C,B) <-> k3_group_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C))))))))) # label(t26_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2413 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = B | B = k1_group_1(A,C,B) -> k2_group_1(A) = C))))))) # label(t15_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2414 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (A = np__0 -> k6_group_1(B,A,C) = k2_group_1(B)))))))) # label(t59_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2415 $T # label(t1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2416 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> r1_xreal_0(np__1,k9_group_1(A))))) # label(t90_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2417 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,B,D) = k1_group_1(A,B,C) | k1_group_1(A,D,B) = k1_group_1(A,C,B) -> C = D))))))))) # label(t14_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2418 (all A (l1_group_1(A) -> v1_funct_1(u1_group_1(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2419 $T # label(t78_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2420 (all A (l1_group_1(A) & -v3_struct_0(A) -> v1_funct_2(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & m2_relset_1(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_1(k5_group_1(A)))) # label(dt_k5_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2421 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (-v5_group_1(B,A) -> (np__0 != C & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k6_group_1(A,D,B) = k2_group_1(A) -> r1_xreal_0(C,D) | D = np__0))) & k6_group_1(A,C,B) = k2_group_1(A) <-> k7_group_1(A,B) = C)) & (v5_group_1(B,A) -> (C = np__0 <-> C = k7_group_1(A,B))))))))) # label(d12_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2422 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> m2_subset_1(k9_group_1(A),k1_numbers,k5_numbers))) # label(dt_k9_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2423 (exists A (v1_group_1(A) & l1_group_1(A))) # label(rc1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2424 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,C,B) & k2_group_1(A) = k1_group_1(A,B,C) <-> C = k3_group_1(A,B)))))))) # label(d6_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2425 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_int_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_xreal_0(np__0,B) -> k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B)) = k6_group_1(A,B,C)) & (-r1_xreal_0(np__0,B) -> k3_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B))) = k6_group_1(A,B,C)))))))) # label(d9_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2426 $T # label(t80_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2427 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,C,B) & k1_group_1(A,B,C) = k2_group_1(A) -> k3_group_1(A,B) = C))))))) # label(t12_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2428 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)))))))) # label(t25_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2429 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k4_xcmplx_0(A),C))))))) # label(t70_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2430 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v5_group_1(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k2_group_1(A) = k6_group_1(A,C,B) -> np__0 = C)))))))) # label(d11_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2431 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,B),B) = k6_group_1(A,np__3,B))))) # label(t46_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2432 $T # label(t9_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2433 $T # label(t3_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2434 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k3_group_1(A,B) = k2_group_1(A) -> B = k2_group_1(A)))))) # label(t18_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2435 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2436 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)))))))) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = C & (exists D (m1_subset_1(D,u1_struct_0(A)) & B = k1_group_1(A,C,D) & B = k1_group_1(A,D,C))) & k1_group_1(A,B,C) = C)))) | -v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A)))) # label(t5_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2437 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> k7_group_1(A,k2_group_1(A)) = np__1)) # label(t84_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2438 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t53_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2439 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,k6_group_1(B,A,D),C) = k1_group_1(B,C,k6_group_1(B,A,D))))))))))) # label(t52_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2440 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,k7_group_1(A,B),B) = k2_group_1(A))))) # label(t82_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2441 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (v1_finset_1(C) & B = k4_card_1(C) & u1_struct_0(A) = C)) <-> k9_group_1(A) = B)))))) # label(d15_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2442 (all A (v2_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)))) # label(t32_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2443 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C all D (g1_group_1(C,D) = g1_group_1(A,B) -> C = A & D = B)))) # label(free_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2444 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,C,B) & (exists D (k1_group_1(A,D,C) = B & k1_group_1(A,C,D) = B & m1_subset_1(D,u1_struct_0(A)))) & C = k1_group_1(A,B,C))) & m1_subset_1(B,u1_struct_0(A)))) <-> v3_group_1(A)))) # label(d3_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2445 (all A all B (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) -> m1_subset_1(k3_group_1(A,B),u1_struct_0(A)))) # label(dt_k3_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2446 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k6_group_1(B,A,C) = k2_group_1(B) -> r1_nat_1(k7_group_1(B,C),A)))))))) # label(t86_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2447 $T # label(t39_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2448 (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) -> l1_group_1(g1_group_1(A,B)) & v1_group_1(g1_group_1(A,B)))) # label(dt_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2449 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,B),D) = C))))))))) # label(t21_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2450 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) -> k10_group_1(A,B,C) = k1_group_1(A,B,C))) # label(redefinition_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2451 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_group_1(A,B) = k3_group_1(A,C) -> C = B))))))) # label(t17_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2452 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v7_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_group_1(B,A,k10_group_1(B,C,D)) = k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)))))))))) # label(t96_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2453 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> r1_finseqop(u1_struct_0(A),k4_group_1(A),u1_group_1(A)))) # label(t35_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2454 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__2,B) = k1_group_1(A,B,B))))) # label(t45_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2455 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C))))))))) # label(t27_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2456 (all A (l1_group_1(A) -> (v1_group_1(A) -> A = g1_group_1(u1_struct_0(A),u1_group_1(A))))) # label(abstractness_v1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2457 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,np__1,B) = B)))) # label(t44_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2458 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & l1_group_1(C) & v4_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,D,E) = k1_group_1(C,E,D) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t75_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2459 $T # label(t81_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2460 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k1_group_1(A,B,D) = C & m1_subset_1(D,u1_struct_0(A)))) & (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,D,B) = C)))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)))))))) -> v4_group_1(A) & v3_group_1(A)))) # label(t6_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2461 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v3_group_1(A) -> -v3_struct_0(A) & v2_group_1(A)))) # label(cc1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2462 $T # label(t57_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2463 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k3_xcmplx_0(B,A),D) = k6_group_1(C,A,k6_group_1(C,B,D)))))))))) # label(t69_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2464 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_group_1(A) -> v1_setwiseo(u1_group_1(A),u1_struct_0(A)))) # label(t34_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2465 (exists A (-v3_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & v2_group_1(A) & l1_group_1(A))) # label(rc4_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2466 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2467 (all A (-v3_struct_0(A) & v7_group_1(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,k10_group_1(A,B,C)) = k10_group_1(A,k3_group_1(A,B),k3_group_1(A,C)))))))) # label(t94_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2468 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,k1_nat_1(A,np__1),C) = k1_group_1(B,k6_group_1(B,A,C),C) & k6_group_1(B,k1_nat_1(A,np__1),C) = k1_group_1(B,C,k6_group_1(B,A,C)))))))) # label(t49_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2469 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_1(B) -> (B = k5_group_1(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,np__0) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,k1_nat_1(D,np__1)) = k1_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,D),C)))))))))) # label(d8_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2470 $T # label(t93_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2471 $T # label(t29_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2472 $T # label(t40_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2473 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> -v5_group_1(k2_group_1(A),A))) # label(t79_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.50 2474 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & C = k1_group_1(A,B,D))))))))) # label(t23_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2475 $T # label(t58_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2476 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,B))))))) # label(d10_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2477 $T # label(t41_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2478 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v7_group_1(A) -> m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2479 (all A all B (-v3_struct_0(A) & v4_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & v3_group_1(A) -> m2_subset_1(k7_group_1(A,B),k1_numbers,k5_numbers))) # label(dt_k7_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2480 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k1_card_1(u1_struct_0(A)) = k8_group_1(A))) # label(d13_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2481 (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_xboole_0(A) -> v1_group_1(g1_group_1(A,B)) & -v3_struct_0(g1_group_1(A,B)))) # label(fc1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2482 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & l1_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k6_group_1(B,A,k1_group_1(B,C,D)) = k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D))))))))))) # label(t54_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2483 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_group_1(A,k3_group_1(A,B)) = B)))) # label(t19_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2484 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(np__0,A) -> k6_group_1(B,k1_int_2(A),C) = k6_group_1(B,A,C)))))))) # label(t55_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2485 (all A (l1_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k2_group_1(A))) # label(t33_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2486 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (B = k4_group_1(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C)))))))) # label(d7_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2487 $T # label(t30_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2488 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k6_group_1(B,A,k1_group_1(B,C,D)) = k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D))))))))))) # label(t73_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2489 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) | k1_group_1(A,C,B) = k2_group_1(A) -> k3_group_1(A,C) = B & k3_group_1(A,B) = C))))))) # label(t20_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2490 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v3_struct_0(C) & v3_group_1(C) & v4_group_1(C) & l1_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)) = k6_group_1(C,k1_nat_1(A,B),D))))))))) # label(t48_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2491 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,B,k6_group_1(C,A,D)) = k6_group_1(C,k3_xcmplx_0(A,B),D))))))))) # label(t67_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2492 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k2_group_1(A) = k3_group_1(A,k2_group_1(A)))) # label(t16_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2493 $T # label(t91_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2494 $T # label(t8_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2495 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,B,k6_group_1(C,A,D)) = k6_group_1(C,k3_xcmplx_0(A,B),D))))))))) # label(t68_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2496 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (B = k1_group_1(A,D,k3_group_1(A,C)) <-> k1_group_1(A,B,C) = D))))))))) # label(t22_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2497 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v7_group_1(A) -> k10_group_1(A,B,C) = k10_group_1(A,C,B))) # label(commutativity_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2498 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k6_group_1(A,np__2,B) = k2_group_1(A) <-> B = k3_group_1(A,B)))))) # label(t47_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2499 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = k1_group_1(A,B,C))))) <-> v7_group_1(A)))) # label(d16_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2500 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,A,k3_group_1(B,C)) = k3_group_1(B,k6_group_1(B,A,C)))))))) # label(t72_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2501 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_group_1(B,C,k6_group_1(B,A,C)) = k6_group_1(B,k2_xcmplx_0(A,np__1),C) & k6_group_1(B,k2_xcmplx_0(A,np__1),C) = k1_group_1(B,k6_group_1(B,A,C),C))))))) # label(t66_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2502 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,k3_group_1(A,C)) = k1_group_1(A,k3_group_1(A,C),B) <-> k1_group_1(A,C,B) = k1_group_1(A,B,C)))))))) # label(t28_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2503 $T # label(t11_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2504 (exists A (l1_group_1(A) & v1_group_1(A) & -v3_struct_0(A))) # label(rc2_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2505 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t64_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2506 (all A all B all C (-v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) -> -v3_struct_0(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(fc2_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2507 $T # label(t38_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2508 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,B,k6_group_1(C,A,D)) = k6_group_1(C,k2_nat_1(A,B),D))))))))) # label(t50_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2509 $T # label(t88_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2510 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) <-> v4_group_1(A)))) # label(d4_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2511 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k1_group_1(A,D,B) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t24_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2512 $T # label(t87_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2513 $T # label(t4_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2514 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k1_group_1(B,k6_group_1(B,A,D),C) = k1_group_1(B,C,k6_group_1(B,A,D))))))))))) # label(t77_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2515 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,D,E) = k1_group_1(C,E,D) -> k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D)) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E))))))))))))) # label(t74_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2516 (all A (l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = C & k1_group_1(A,B,C) = C)) -> k2_group_1(A) = B))))) # label(t10_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2517 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k7_binop_2(A),C))))))) # label(t71_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2518 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t63_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2519 (all A (l1_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k2_group_1(A),u1_struct_0(A)))) # label(dt_k2_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2520 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> k6_group_1(B,A,k2_group_1(B)) = k2_group_1(B))))) # label(t61_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2521 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2522 (all A all B all C (-v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v9_vectsp_1(A) -> m1_subset_1(k5_vectsp_1(A,B,C),u1_struct_0(A)))) # label(dt_k5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2523 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,B,k1_rlvect_1(A)))))) # label(t36_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2524 (all A all B (l1_struct_0(A) & l4_vectsp_1(B,A) -> (v11_vectsp_1(B,A) -> B = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B))))) # label(abstractness_v11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2525 $T # label(t9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2526 $T # label(t51_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2527 (exists A (l3_vectsp_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A))) # label(rc10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2528 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,k6_vectsp_1(A,B,C,D),k6_vectsp_1(A,B,C,E)) = k6_vectsp_1(A,B,C,k6_rlvect_1(B,D,E)))))))))))) # label(t70_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2529 $T # label(t10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2530 (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)) -> k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B) & k6_rlvect_1(A,B,k1_rlvect_1(A)) = B)))) # label(t65_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2531 $T # label(t35_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2532 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k2_rlvect_1(A,C,B),k2_rlvect_1(A,D,B)) = k6_rlvect_1(A,C,D))))))))) # label(t90_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2533 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)))))))))) # label(t43_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2534 $T # label(t57_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2535 $T # label(t17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2536 $T # label(t37_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2537 (exists A (v1_vectsp_1(A) & l1_vectsp_1(A))) # label(rc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2538 $T # label(t30_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2539 $T # label(t27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2540 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> k2_group_1(A) != k1_group_1(A,B,E))) & k1_rlvect_1(A) != B) & k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) & k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D))))))))))) # label(t22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2541 (exists A (-v3_struct_0(A) & v2_vectsp_1(A) & l2_vectsp_1(A))) # label(rc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2542 $T # label(t91_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2543 $T # label(d8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2544 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,B),C)))))))) # label(t92_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2545 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v8_vectsp_1(A) & v6_vectsp_1(A) -> v2_group_1(A) & -v3_struct_0(A)))) # label(cc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2546 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (exists B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) & l4_vectsp_1(B,A))))) # label(rc13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2547 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> v1_funct_2(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k7_vectsp_1(A)))) # label(dt_k7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2548 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_subset_1(D,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & l1_struct_0(A) -> (all F all G all H all I all J (g4_vectsp_1(A,B,C,D,E) = g4_vectsp_1(F,G,H,I,J) -> A = F & H = C & J = E & I = D & G = B)))) # label(free_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2549 $T # label(t61_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2550 $T # label(t55_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2551 $T # label(t11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2552 (exists A l3_vectsp_1(A)) # label(existence_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2553 (all A (l1_vectsp_1(A) -> m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)))) # label(dt_u1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2554 $T # label(d4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2555 (all A (v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k1_group_1(A,B,D),k1_group_1(A,C,D)))))))))) # label(t45_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2556 $T # label(t79_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2557 $T # label(t16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2558 $T # label(t8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2559 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,D),C) = k5_rlvect_1(A,k2_rlvect_1(A,C,D)) & k6_rlvect_1(A,C,D) = k5_rlvect_1(A,k2_rlvect_1(A,D,k5_rlvect_1(A,C))) & k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,B,k2_rlvect_1(A,D,C)) & k5_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,C),D)) = k2_rlvect_1(A,D,C) & k5_rlvect_1(A,k6_rlvect_1(A,C,D)) = k2_rlvect_1(A,D,k5_rlvect_1(A,C)))))))))) # label(t64_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2560 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_vectsp_1(A,B,C) = k10_group_1(A,B,k4_vectsp_1(A,C)))))))) # label(d23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2561 (all A all B all C all D (v1_funct_1(B) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> v2_vectsp_1(g2_vectsp_1(A,B,C,D)) & l2_vectsp_1(g2_vectsp_1(A,B,C,D)))) # label(dt_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2562 (exists A l2_vectsp_1(A)) # label(existence_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2563 (all A all B all C (v1_funct_1(B) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all D all E all F (g1_vectsp_1(A,B,C) = g1_vectsp_1(D,E,F) -> F = C & B = E & A = D)))) # label(free_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2564 (exists A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & v1_rlvect_1(A) & l1_rlvect_1(A))) # label(rc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2565 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l4_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D) = k6_vectsp_1(A,B,C,D))))))))) # label(d24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2566 (exists A (-v3_struct_0(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v2_group_1(A) & l1_vectsp_1(A))) # label(rc9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2567 (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)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) -> C = B) & (B = C -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k1_rlvect_1(A)) & (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> C = B) & (B = C -> k6_rlvect_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t66_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2568 (all A (v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k10_group_1(A,B,D) = k10_group_1(A,B,C) -> D = C | B = k1_rlvect_1(A)))))))))) # label(t33_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2569 $T # label(t83_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2570 $T # label(t48_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2571 $T # label(t4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2572 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)) = k1_group_1(A,B,C))))))) # label(t42_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2573 $T # label(t47_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2574 (exists A (l1_group_1(A) & -v3_struct_0(A) & v7_group_1(A) & v4_group_1(A))) # label(rc8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2575 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (v13_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,B) -> B = k1_rlvect_1(A))))))) # label(d28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2576 (all A (l2_vectsp_1(A) -> l1_vectsp_1(A) & l2_struct_0(A))) # label(dt_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2577 (exists A (-v3_struct_0(A) & v13_vectsp_1(A) & l1_rlvect_1(A))) # label(rc14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2578 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k5_rlvect_1(A,C))) <-> k7_vectsp_1(A) = B))))) # label(d25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2579 (all A (l1_vectsp_1(A) -> m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)))) # label(dt_k2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2580 $T # label(d5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2581 (all A all B all C all D all E (l1_struct_0(A) & 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,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & -v1_xboole_0(B) -> v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & -v3_struct_0(g4_vectsp_1(A,B,C,D,E)))) # label(fc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2582 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C))))))))) # label(t93_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2583 $T # label(t50_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2584 $T # label(d3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2585 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (v13_vectsp_1(A) <-> k1_rlvect_1(A) != k2_rlvect_1(A,k2_group_1(A),k2_group_1(A))))) # label(d29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2586 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l1_vectsp_1(g1_vectsp_1(A,B,C)) & v1_vectsp_1(g1_vectsp_1(A,B,C)))) # label(dt_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2587 (all A (l1_vectsp_1(A) -> (v2_group_1(A) & -v3_struct_0(A) -> v8_vectsp_1(A) & v6_vectsp_1(A) & -v3_struct_0(A)))) # label(cc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2588 (all A (l1_vectsp_1(A) -> (v1_vectsp_1(A) -> A = g1_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A))))) # label(abstractness_v1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2589 $T # label(t28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2590 (all A (m1_subset_1(A,u1_struct_0(k3_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k3_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k3_vectsp_1)) -> A = k4_rlvect_1(k3_vectsp_1,A,k1_rlvect_1(k3_vectsp_1)) & k1_rlvect_1(k3_vectsp_1) = k4_rlvect_1(k3_vectsp_1,A,k5_rlvect_1(k3_vectsp_1,A)) & k10_group_1(k3_vectsp_1,A,k10_group_1(k3_vectsp_1,B,C)) = k10_group_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),C) & k10_group_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,B,C),A) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,B,A),k10_group_1(k3_vectsp_1,C,A)) & k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),k10_group_1(k3_vectsp_1,A,C)) = k10_group_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) & -(k1_rlvect_1(k3_vectsp_1) != A & (all D (m1_subset_1(D,u1_struct_0(k3_vectsp_1)) -> k2_group_1(k3_vectsp_1) != k10_group_1(k3_vectsp_1,A,D)))) & k10_group_1(k3_vectsp_1,k2_group_1(k3_vectsp_1),A) = A & k10_group_1(k3_vectsp_1,B,A) = k10_group_1(k3_vectsp_1,A,B) & k4_rlvect_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) = k4_rlvect_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,A,B),C) & k4_rlvect_1(k3_vectsp_1,A,B) = k4_rlvect_1(k3_vectsp_1,B,A))))))) # label(t21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2591 (all A (l1_struct_0(A) -> (all B (l4_vectsp_1(B,A) -> l1_rlvect_1(B))))) # label(dt_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2592 $T # label(t54_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2593 $T # label(t23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2594 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_subset_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) -> l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(dt_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2595 $T # label(d27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2596 (all A all B all C all D all E (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)))) # label(dt_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2597 (all A (l1_struct_0(A) -> (exists B l4_vectsp_1(B,A)))) # label(existence_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2598 (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)) -> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k6_rlvect_1(A,C,B))))))) # label(t81_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2599 (all A (v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k4_vectsp_1(A,B) = C <-> k2_group_1(A) = k10_group_1(A,B,C))))))))) # label(d22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2600 (all A (l3_vectsp_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l4_vectsp_1(B,A) -> (v12_vectsp_1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,D,E)) = k6_vectsp_1(A,B,k2_rlvect_1(A,C,D),E) & k6_vectsp_1(A,B,k2_group_1(A),E) = E & k6_vectsp_1(A,B,k1_group_1(A,C,D),E) = k6_vectsp_1(A,B,C,k6_vectsp_1(A,B,D,E)) & k6_vectsp_1(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,C,F))))))))))))))) # label(d26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2601 (exists A (v1_vectsp_1(A) & -v3_struct_0(A) & l1_vectsp_1(A))) # label(rc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2602 $T # label(t85_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2603 $T # label(d14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2604 $T # label(t38_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2605 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k4_vectsp_1(A,B) != k1_rlvect_1(A) & k1_rlvect_1(A) != k5_rlvect_1(A,k4_vectsp_1(A,B))))))) # label(t74_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2606 $T # label(t71_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2607 $T # label(t82_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2608 (all A all B (l4_vectsp_1(B,A) & l1_struct_0(A) -> v1_funct_1(u2_vectsp_1(A,B)) & v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)))) # label(dt_u2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2609 $T # label(t62_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2610 $T # label(t15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.41/115.51 2611 (all A (m1_subset_1(A,u1_struct_0(k1_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k1_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_1)) -> k4_rlvect_1(k1_vectsp_1,A,B) = k4_rlvect_1(k1_vectsp_1,B,A) & A = k4_rlvect_1(k1_vectsp_1,A,k1_rlvect_1(k1_vectsp_1)) & k1_rlvect_1(k1_vectsp_1) = k4_rlvect_1(k1_vectsp_1,A,k5_rlvect_1(k1_vectsp_1,A)) & k4_rlvect_1(k1_vectsp_1,k4_rlvect_1(k1_vectsp_1,A,B),C) = k4_rlvect_1(k1_vectsp_1,A,k4_rlvect_1(k1_vectsp_1,B,C)))))))) # label(t6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2612 $T # label(t26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2613 (all A (l3_vectsp_1(A) -> (v5_vectsp_1(A) & v4_vectsp_1(A) & -v3_struct_0(A) -> v7_vectsp_1(A) & -v3_struct_0(A)))) # label(cc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2614 (all A (v5_rlvect_1(A) & l3_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,k5_rlvect_1(A,C)) = k5_rlvect_1(A,k1_group_1(A,B,C)))))))) # label(t40_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2615 (all A all B (-v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k4_vectsp_1(A,B),u1_struct_0(A)))) # label(dt_k4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2616 $T # label(d2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2617 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,k2_group_1(A),B) = B)) <-> v8_vectsp_1(A)))) # label(d19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2618 $T # label(t19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2619 $T # label(t58_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2620 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,k10_group_1(A,B,D),C) -> k10_group_1(A,C,k4_vectsp_1(A,B)) = D | k1_rlvect_1(A) = B) & (k1_rlvect_1(A) = k6_rlvect_1(A,C,k10_group_1(A,D,B)) -> D = k10_group_1(A,C,k4_vectsp_1(A,B)) | k1_rlvect_1(A) = B))))))))) # label(t88_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2621 (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)) -> k2_rlvect_1(A,B,C) = k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B))))))))) # label(t89_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2622 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k2_rlvect_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t63_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2623 $T # label(d17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2624 $T # label(t49_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2625 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v3_vectsp_1(A))) # label(rc7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2626 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> (v9_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(k1_rlvect_1(A) != B & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) != k2_group_1(A))))))))) # label(d20_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2627 (all A (l3_vectsp_1(A) & -v3_struct_0(A) -> (v7_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) = k1_group_1(A,k2_rlvect_1(A,C,D),B) & k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D))))))))))) # label(d18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2628 $T # label(t53_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2629 $T # label(t12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2630 $T # label(t75_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2631 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k10_group_1(A,B,C) <-> k1_rlvect_1(A) = C | B = k1_rlvect_1(A)))))))) # label(t44_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2632 (all A (v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v6_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(A) != B -> k6_vectsp_1(A,C,k4_vectsp_1(A,B),k6_vectsp_1(A,C,B,D)) = D))))))))) # label(t67_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2633 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v5_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_rlvect_1(C) = k6_vectsp_1(A,C,B,k1_rlvect_1(C)) & k6_vectsp_1(A,C,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(C,D) & k6_vectsp_1(A,C,k1_rlvect_1(A),D) = k1_rlvect_1(C))))))))) # label(t59_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2634 $T # label(t34_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2635 $T # label(t13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2636 (all A (l3_vectsp_1(A) -> (v7_vectsp_1(A) & -v3_struct_0(A) -> v4_vectsp_1(A) & v5_vectsp_1(A) & -v3_struct_0(A)))) # label(cc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2637 $T # label(d16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2638 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v7_group_1(A) & v8_vectsp_1(A) -> -v3_struct_0(A) & v6_vectsp_1(A)))) # label(cc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2639 $T # label(t29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2640 $T # label(d1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2641 $T # label(d10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2642 (all A all B all C all D (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all E all F all G all H (g2_vectsp_1(A,B,C,D) = g2_vectsp_1(E,F,G,H) -> G = C & H = D & F = B & E = A)))) # label(free_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2643 $T # label(t31_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2644 $T # label(t2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2645 (all A all B all C all D all E (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & m1_subset_1(E,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all F all G all H all I all J (g3_vectsp_1(F,G,H,I,J) = g3_vectsp_1(A,B,C,D,E) -> B = G & E = J & I = D & H = C & F = A)))) # label(free_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2646 $T # label(t77_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2647 (all A (l3_vectsp_1(A) -> (v3_vectsp_1(A) -> g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) = A))) # label(abstractness_v3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2648 (all A (l2_vectsp_1(A) & -v3_struct_0(A) -> (v10_vectsp_1(A) <-> k2_group_1(A) = k1_rlvect_1(A)))) # label(d21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2649 $T # label(t18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2650 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k5_rlvect_1(A,B),C))))))) # label(t41_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2651 $T # label(t46_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2652 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)))))))) <-> v4_vectsp_1(A)))) # label(d11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2653 $T # label(d7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2654 $T # label(t56_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2655 $T # label(t25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2656 (exists A (l3_vectsp_1(A) & v3_vectsp_1(A))) # label(rc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2657 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(A) = B | k1_rlvect_1(C) = D <-> k1_rlvect_1(C) = k6_vectsp_1(A,C,B,D)))))))))) # label(t60_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2658 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,k1_rlvect_1(A),B))))) # label(t39_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2659 $T # label(t80_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2660 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> B = k4_vectsp_1(A,k4_vectsp_1(A,B))))))) # label(t73_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2661 $T # label(t24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2662 $T # label(t5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2663 (all A (l1_vectsp_1(A) -> k2_vectsp_1(A) = u1_vectsp_1(A))) # label(d9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2664 $T # label(t32_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2665 $T # label(t52_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2666 (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)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> k6_rlvect_1(A,C,B) = k1_rlvect_1(A)))))))) # label(t87_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2667 $T # label(t3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2668 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> v3_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v7_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & l1_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v4_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & -v3_struct_0(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))))) # label(t94_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2669 (exists A (v2_vectsp_1(A) & l2_vectsp_1(A))) # label(rc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2670 $T # label(t14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.51 2671 (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)) -> (k5_rlvect_1(A,B) = k1_rlvect_1(A) -> B = k1_rlvect_1(A)))))) # label(t86_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2672 (all A (l2_vectsp_1(A) -> (v2_vectsp_1(A) -> g2_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) = A))) # label(abstractness_v2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2673 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (v5_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B))))))))))) # label(d12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2674 (all A (l1_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & v11_vectsp_1(B,A))))) # label(rc11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2675 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) & k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) & (exists E (m1_subset_1(E,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,E))) & k2_rlvect_1(A,B,k1_rlvect_1(A)) = B)))))) <-> v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2676 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(A) & -v3_struct_0(B) & l4_vectsp_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) -> m1_subset_1(k6_vectsp_1(A,B,C,D),u1_struct_0(B)))) # label(dt_k6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2677 (all A (l1_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & -v3_struct_0(B) & v11_vectsp_1(B,A))))) # label(rc12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2678 (exists A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v3_vectsp_1(A) & v5_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & v13_vectsp_1(A) & v6_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & l3_vectsp_1(A))) # label(rc15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2679 (exists A l1_vectsp_1(A)) # label(existence_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2680 $T # label(t76_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2681 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k1_rlvect_1(A) -> C = B))))))) # label(t84_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2682 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)))))))))) # label(t69_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2683 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) -> (all B (v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,E,k6_vectsp_1(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_1(A,B,k5_rlvect_1(A,C),D)) & k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)) = k6_vectsp_1(A,B,k5_rlvect_1(A,C),D))))))))))) # label(t68_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2684 (all A (l3_vectsp_1(A) -> l2_vectsp_1(A) & l1_rlvect_1(A))) # label(dt_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2685 (all A (l1_vectsp_1(A) -> l1_group_1(A))) # label(dt_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2686 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> (v6_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,k2_group_1(A)) = B))))) # label(d13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2687 $T # label(t1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2688 $T # label(t72_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2689 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers)) -> ((exists C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,C) -> k8_funct_2(u1_struct_0(A),k1_numbers,B,D) = np__0))))) <-> m1_rlvect_2(B,A)))))) # label(d5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2690 (all A (v3_rlvect_1(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)) -> (C != B -> k6_rlvect_2(A,k8_rlvect_2(A,B,C)) = k4_rlvect_1(A,B,C)))))))) # label(t16_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2691 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_rlvect_2(B,A,k1_subset_1(u1_struct_0(A))) -> k11_rlvect_2(A) = B)))) # label(t35_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2692 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k15_rlvect_2(A,np__1,B),B))))) # label(t71_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2693 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> k17_rlvect_2(A,B,C) = k6_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B),k1_rlvect_2(k23_rlvect_2(A),C)))))))) # label(t99_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2694 $T # label(t25_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2695 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k18_rlvect_2(A)) -> B = k19_rlvect_2(A,B))))) # label(d17_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2696 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m2_rlvect_2(C,A,B) -> r2_hidden(k13_rlvect_2(A,C),B))) <-> k1_xboole_0 != B & v1_rlsub_1(B,A)))))) # label(t47_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2697 (all A all B all C (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> k5_rlvect_2(A,C,B) = k5_rlvect_2(A,B,C))) # label(commutativity_k5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2698 (all A all B all C (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & m1_rlvect_2(C,A) & m1_subset_1(B,k1_numbers) & l2_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k15_rlvect_2(A,B,C),A))) # label(dt_k15_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2699 $T # label(dt_k18_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2700 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlsub_1(C,k23_rlvect_2(A)) & v2_rlvect_1(C) -> (a_2_1_rlvect_2(A,B) = u1_struct_0(C) <-> k24_rlvect_2(A,B) = C))))))) # label(d22_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2701 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) -> k21_rlvect_2(A) = u1_rlvect_1(k23_rlvect_2(A)))) # label(t94_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2702 $T # label(t91_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2703 (all A all B all C all D (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & -v3_struct_0(A) -> k9_rlvect_2(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2704 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> k1_rlvect_1(A) = k13_rlvect_2(A,k11_rlvect_2(A)))) # label(t48_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2705 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & v1_finset_1(B) -> k2_rlvect_2(A,C,B) = k2_rlvect_2(A,B,C))) # label(commutativity_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2706 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m2_rlvect_2(k11_rlvect_2(A),A,B))))) # label(t34_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2707 (all A all B all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & l1_struct_0(A) -> m1_subset_1(k5_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(k5_rlvect_2(A,B,C)))) # label(dt_k5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2708 $T # label(t2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2709 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> k2_rlvect_2(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2710 (all A all B all C (l1_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) & -v3_struct_0(A) -> m1_rlvect_2(k14_rlvect_2(A,B,C),A))) # label(dt_k14_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2711 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlvect_2(C,A) -> k8_funct_2(u1_struct_0(A),k1_numbers,k16_rlvect_2(A,C),B) = k1_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,C,B)))))))) # label(t73_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2712 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> B = k20_rlvect_2(A,B))))) # label(d18_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2713 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> k4_rlvect_2(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2714 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> (m2_rlvect_2(D,A,B) & m2_rlvect_2(C,A,B) -> m2_rlvect_2(k14_rlvect_2(A,C,D),A,B)))))))))) # label(t59_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2715 $T # label(t86_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2716 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m2_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_funct_1(B) -> k6_finseq_1(u1_struct_0(A)) = k12_rlvect_2(A,k6_finseq_1(u1_struct_0(A)),B))))) # label(t41_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2717 $T # label(t72_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2718 $T # label(t45_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2719 $T # label(t84_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2720 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (all E (v1_funct_2(E,u1_struct_0(B),k1_numbers) & m2_relset_1(E,u1_struct_0(B),k1_numbers) & v1_funct_1(E) -> (k1_funct_1(D,A) = C & r2_hidden(A,k1_relat_1(D)) -> k1_funct_1(k12_rlvect_2(B,D,E),A) = k3_rlvect_1(B,C,k8_funct_2(u1_struct_0(B),k1_numbers,E,C))))))))))))) # label(t40_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2721 (all A all B all C (l1_rlvect_1(A) & m1_rlvect_2(C,A) & m1_rlvect_2(B,A) & -v3_struct_0(A) -> (r1_rlvect_2(A,B,C) -> r1_rlvect_2(A,C,B)))) # label(symmetry_r1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2722 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> m2_relset_1(k22_rlvect_2(A),k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_2(k22_rlvect_2(A),k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_1(k22_rlvect_2(A)))) # label(dt_k22_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2723 $T # label(t12_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2724 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_relset_1(C,u1_struct_0(A),k1_numbers) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v1_funct_1(C) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k3_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),k1_numbers,C,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E)))))) & k3_finseq_1(B) = k3_finseq_1(D) <-> k12_rlvect_2(A,B,C) = D))))))))) # label(d9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2725 $T # label(t1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2726 $T # label(t36_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2727 (all A all B all C (-v3_struct_0(B) & l1_rlvect_1(B) & m1_rlvect_2(C,B) -> ((exists D (np__0 != k8_funct_2(u1_struct_0(B),k1_numbers,C,D) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_0_rlvect_2(B,C))))) # label(fraenkel_a_2_0_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2728 (all A (l1_struct_0(A) -> (all B (r1_rlvect_1(A,B) -> k1_rlvect_2(A,B) = B)))) # label(d1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2729 $T # label(t13_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2730 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rlvect_2(D,A) -> (k10_rlvect_2(A,D) = k8_rlvect_2(A,B,C) -> k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))) | C = B))))))))) # label(t54_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2731 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(B)) -> k1_funct_1(D,E) = k6_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E))))) & k3_finseq_1(B) = k3_finseq_1(D) & k3_finseq_1(B) = k3_finseq_1(C) -> k9_rlvect_1(A,D) = k6_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C))))))))))) # label(t7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2732 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> k6_rlvect_2(A,k1_pre_topc(A)) = k1_rlvect_1(A))) # label(t14_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2733 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (m2_rlvect_2(C,A,B) -> m2_rlvect_2(k16_rlvect_2(A,C),A,B)))))))) # label(t76_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2734 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> v3_rlvect_1(k23_rlvect_2(A)) & v6_rlvect_1(k23_rlvect_2(A)) & v7_rlvect_1(k23_rlvect_2(A)) & v5_rlvect_1(k23_rlvect_2(A)) & v4_rlvect_1(k23_rlvect_2(A)) & v2_rlvect_1(k23_rlvect_2(A)) & -v3_struct_0(k23_rlvect_2(A)))) # label(fc2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2735 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & m1_subset_1(B,k18_rlvect_2(A)) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k19_rlvect_2(A,B),A))) # label(dt_k19_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2736 (all A all B (v6_rlvect_1(A) & l2_rlvect_1(A) & m1_rlvect_2(B,A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k13_rlvect_2(A,B),u1_struct_0(A)))) # label(dt_k13_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2737 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),k1_numbers,B,C) = np__0 <-> -r2_hidden(C,k10_rlvect_2(A,B))))))))) # label(t28_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2738 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (B = k11_rlvect_2(A) <-> k10_rlvect_2(A,B) = k1_xboole_0))))) # label(d7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2739 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & m1_rlvect_2(B,A) & l2_rlvect_1(A) & v6_rlvect_1(A) -> m1_subset_1(k20_rlvect_2(A,B),k18_rlvect_2(A)))) # label(dt_k20_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2740 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) -> m2_relset_1(k21_rlvect_2(A),k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_2(k21_rlvect_2(A),k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_1(k21_rlvect_2(A)))) # label(dt_k21_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2741 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rlsub_1(k24_rlvect_2(A,B),k23_rlvect_2(A)) & v2_rlvect_1(k24_rlvect_2(A,B)))) # label(dt_k24_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2742 $T # label(t32_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2743 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k15_rlvect_2(A,np__0,B),k11_rlvect_2(A)))))) # label(t66_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2744 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_relset_1(D,k1_relat_1(B),k1_relat_1(B)) & v3_funct_2(D,k1_relat_1(B),k1_relat_1(B)) & v1_funct_2(D,k1_relat_1(B),k1_relat_1(B)) & v1_funct_1(D) -> (k5_relat_1(D,B) = C -> k9_rlvect_1(A,C) = k9_rlvect_1(A,B)))))))))) # label(t9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2745 $T # label(t55_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2746 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),k1_numbers,B,D) = k8_funct_2(u1_struct_0(A),k1_numbers,C,D))) <-> r1_rlvect_2(A,B,C)))))))) # label(d11_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2747 $T # label(t27_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2748 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> (r1_rlvect_2(A,k14_rlvect_2(A,B,C),k11_rlvect_2(A)) -> r1_rlvect_2(A,C,k16_rlvect_2(A,B))))))))) # label(t74_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2749 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m2_rlvect_2(D,A,B) -> (r1_tarski(B,C) -> m2_rlvect_2(D,A,C)))))))))) # label(t33_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2750 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k2_rlvect_2(A,B,C)) & m1_subset_1(k2_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2751 (all A all B all C all D (m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> v1_finset_1(k9_rlvect_2(A,B,C,D)) & m1_subset_1(k9_rlvect_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k9_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2752 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> k4_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B),k1_rlvect_2(k23_rlvect_2(A),C)) = k14_rlvect_2(A,B,C))))))) # label(t96_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2753 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k2_tarski(B,C) = k8_rlvect_2(A,B,C))) # label(redefinition_k8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2754 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k17_rlvect_2(A,B,B),k11_rlvect_2(A)))))) # label(t82_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2755 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(C != D & B != D & k6_rlvect_2(A,k9_rlvect_2(A,B,C,D)) != k4_rlvect_1(A,k4_rlvect_1(A,B,C),D) & B != C))))))))) # label(t17_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2756 (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) -> v4_rlvect_1(k23_rlvect_2(A)) & v6_rlvect_1(k23_rlvect_2(A)) & v7_rlvect_1(k23_rlvect_2(A)) & l2_rlvect_1(k23_rlvect_2(A)) & v5_rlvect_1(k23_rlvect_2(A)) & v3_rlvect_1(k23_rlvect_2(A)) & -v3_struct_0(k23_rlvect_2(A)))) # label(dt_k23_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2757 $T # label(t56_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2758 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> m1_rlvect_2(k11_rlvect_2(A),A))) # label(dt_k11_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2759 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> v1_finset_1(k7_rlvect_2(A,B)) & m1_subset_1(k7_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2760 $T # label(t64_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2761 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> (m2_rlvect_2(D,A,B) & m2_rlvect_2(C,A,B) -> m2_rlvect_2(k17_rlvect_2(A,C,D),A,B)))))))))) # label(t81_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2762 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_rlvect_2(A,B) = C <-> (exists D (m2_finseq_1(D,u1_struct_0(A)) & C = k9_rlvect_1(A,D) & v2_funct_1(D) & k2_relat_1(D) = B)))))))))) # label(d4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2763 (all A (v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k14_rlvect_2(A,B,k14_rlvect_2(A,C,D)),k14_rlvect_2(A,k14_rlvect_2(A,B,C),D)))))))))) # label(t61_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2764 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k15_rlvect_2(A,B,k15_rlvect_2(A,C,D)),k15_rlvect_2(A,k4_real_1(B,C),D)))))))))) # label(t70_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2765 $T # label(t46_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2766 (all A (v3_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k15_rlvect_2(A,B,k14_rlvect_2(A,C,D)),k14_rlvect_2(A,k15_rlvect_2(A,B,C),k15_rlvect_2(A,B,D))))))))))) # label(t69_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2767 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) -> k6_rlvect_2(A,k4_rlvect_2(A,C,B)) = k6_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,k3_rlvect_2(A,C,B))))))))) # label(t22_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2768 (all A all B all C (l1_struct_0(A) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> k3_xboole_0(B,C) = k3_rlvect_2(A,B,C))) # label(redefinition_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2769 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k16_rlvect_2(A,k16_rlvect_2(A,B)),B))))) # label(t77_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2770 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,B,E),k8_funct_2(u1_struct_0(A),k1_numbers,C,E)))) <-> D = k14_rlvect_2(A,B,C)))))))))) # label(d12_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2771 $T # label(t26_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2772 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2773 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> (k15_rlvect_2(A,B,C) = D <-> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_real_1(B,k8_funct_2(u1_struct_0(A),k1_numbers,C,E)) = k8_funct_2(u1_struct_0(A),k1_numbers,D,E)))))))))))) # label(d13_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2774 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (exists B m1_rlvect_2(B,A)))) # label(existence_m1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2775 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (k10_rlvect_2(A,B) = k1_xboole_0 -> k1_rlvect_1(A) = k13_rlvect_2(A,B)))))) # label(t52_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2776 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) -> k6_rlvect_2(A,k5_rlvect_2(A,C,B)) = k6_rlvect_1(A,k6_rlvect_2(A,k2_rlvect_2(A,C,B)),k6_rlvect_2(A,k3_rlvect_2(A,C,B))))))))) # label(t23_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2777 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> (k3_finseq_1(D) = k3_finseq_1(C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(C)) -> k3_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E),B) = k1_funct_1(D,E)))) -> k9_rlvect_1(A,D) = k3_rlvect_1(A,k9_rlvect_1(A,C),B)))))))))) # label(t5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2778 (all A (l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) & m2_relset_1(B,k2_zfmisc_1(k18_rlvect_2(A),k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_1(B) -> ((all C (m1_subset_1(C,k18_rlvect_2(A)) -> (all D (m1_subset_1(D,k18_rlvect_2(A)) -> k2_binop_1(k18_rlvect_2(A),k18_rlvect_2(A),k18_rlvect_2(A),B,C,D) = k14_rlvect_2(A,k19_rlvect_2(A,C),k19_rlvect_2(A,D)))))) <-> B = k21_rlvect_2(A)))))) # label(d19_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2779 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_relset_1(C,u1_struct_0(A),k1_numbers) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v1_funct_1(C) -> k12_finseq_1(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B))) = k12_rlvect_2(A,k12_finseq_1(u1_struct_0(A),B),C))))))) # label(t42_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2780 $T # label(t37_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2781 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m2_rlvect_2(B,A,k1_subset_1(u1_struct_0(A))) -> k13_rlvect_2(A,B) = k1_rlvect_1(A))))) # label(t49_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2782 (all A (l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlvect_2(C,A) -> (k7_rlvect_2(A,B) = k10_rlvect_2(A,C) -> k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) = k13_rlvect_2(A,C)))))))) # label(t53_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2783 $T # label(t38_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2784 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_rlvect_2(D,A) -> (m2_rlvect_2(D,A,C) -> m2_rlvect_2(k15_rlvect_2(A,B,D),A,C)))))))))) # label(t67_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2785 (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)) -> k6_rlvect_2(A,k7_rlvect_2(A,B)) = B)))) # label(t15_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2786 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & l1_struct_0(A) -> k3_rlvect_2(A,B,C) = k3_rlvect_2(A,C,B))) # label(commutativity_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2787 (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 (B = k18_rlvect_2(A) <-> (all C (m1_rlvect_2(C,A) <-> r2_hidden(C,B))))))) # label(d16_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2788 (all A all B all C (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),k1_numbers) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m2_finseq_1(k12_rlvect_2(A,B,C),u1_struct_0(A)))) # label(dt_k12_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2789 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (v1_funct_2(E,u1_struct_0(A),k1_numbers) & m2_relset_1(E,u1_struct_0(A),k1_numbers) & v1_funct_1(E) -> k12_rlvect_2(A,k3_finseq_4(u1_struct_0(A),B,C,D),E) = k3_finseq_4(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,E,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,E,C)),k3_rlvect_1(A,D,k8_funct_2(u1_struct_0(A),k1_numbers,E,D))))))))))))) # label(t44_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2790 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k8_rlvect_2(A,C,B) = k8_rlvect_2(A,B,C))) # label(commutativity_k8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2791 $T # label(t89_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2792 $T # label(t29_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2793 (all A (-v3_struct_0(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_rlvect_2(C,A,k7_rlvect_2(A,B)) -> k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) = k13_rlvect_2(A,C))))))) # label(t50_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2794 (all A all B all C (l1_rlvect_1(A) & m1_rlvect_2(C,A) & m1_rlvect_2(B,A) & -v3_struct_0(A) -> (r1_rlvect_2(A,B,C) <-> C = B))) # label(redefinition_r1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2795 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> k15_rlvect_2(A,B,C) = k3_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),C),B))))))) # label(t97_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2796 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> k15_rlvect_2(A,k1_real_1(np__1),B) = k16_rlvect_2(A,B))))) # label(d14_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2797 $T # label(t63_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2798 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> k23_rlvect_2(A) = g2_rlvect_1(k18_rlvect_2(A),k20_rlvect_2(A,k11_rlvect_2(A)),k21_rlvect_2(A),k22_rlvect_2(A)))) # label(d21_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2799 $T # label(t83_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2800 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all C (m2_rlvect_2(C,A,B) -> m1_rlvect_2(C,A))))) # label(dt_m2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2801 (all A (v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> k10_rlvect_2(A,B) = k10_rlvect_2(A,k16_rlvect_2(A,B)))))) # label(t75_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2802 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & -v3_struct_0(A) -> u1_struct_0(k23_rlvect_2(A)) = k18_rlvect_2(A))) # label(t92_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2803 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_rlvect_2(C,A) -> (np__0 != B -> k10_rlvect_2(A,k15_rlvect_2(A,B,C)) = k10_rlvect_2(A,C)))))))) # label(t65_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2804 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> r1_rlvect_2(A,k14_rlvect_2(A,B,C),k14_rlvect_2(A,C,B)))))))) # label(t60_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2805 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_rlvect_2(C,A) -> (m2_rlvect_2(C,A,B) <-> r1_tarski(k10_rlvect_2(A,C),B)))))))) # label(d8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2806 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & v1_finset_1(B) -> k3_rlvect_2(A,B,B) = B)) # label(idempotence_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2807 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> k10_rlvect_2(A,B) = a_2_0_rlvect_2(A,B))))) # label(d6_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2808 (all A all B (l1_struct_0(A) -> m1_subset_1(k1_rlvect_2(A,B),u1_struct_0(A)))) # label(dt_k1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2809 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers)))))) # label(dt_m1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2810 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> -v1_xboole_0(k18_rlvect_2(A)))) # label(fc1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2811 (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) -> v1_finset_1(k8_rlvect_2(A,B,C)) & m1_subset_1(k8_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2812 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> r1_tarski(k10_rlvect_2(A,k14_rlvect_2(A,B,C)),k2_rlvect_2(A,k10_rlvect_2(A,B),k10_rlvect_2(A,C))))))))) # label(t58_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2813 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_2(A,B) = B)))) # label(t3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2814 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> v1_finset_1(k4_rlvect_2(A,B,C)) & m1_subset_1(k4_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2815 $T # label(d3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2816 (all A (v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_funct_2(D,u1_struct_0(A),k1_numbers) & m2_relset_1(D,u1_struct_0(A),k1_numbers) & v1_funct_1(D) -> k12_rlvect_2(A,k2_finseq_4(u1_struct_0(A),B,C),D) = k2_finseq_4(u1_struct_0(A),k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C))))))))))) # label(t43_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2817 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(C,B) -> k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)) = k6_rlvect_2(A,k2_rlvect_2(A,C,B))))))))) # label(t18_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2818 (all A all B all C (l1_struct_0(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> B = k2_rlvect_2(A,B,B))) # label(idempotence_k2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2819 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> r1_rlvect_2(A,k14_rlvect_2(A,k11_rlvect_2(A),B),B) & r1_rlvect_2(A,k14_rlvect_2(A,B,k11_rlvect_2(A)),B))))) # label(t62_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2820 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B != C -> (all D (m2_rlvect_2(D,A,k8_rlvect_2(A,B,C)) -> k13_rlvect_2(A,D) = k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,D,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,D,C)))))))))))) # label(t51_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2821 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & m1_rlvect_2(B,A) -> m1_subset_1(k10_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(k10_rlvect_2(A,B)))) # label(dt_k10_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2822 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> k14_rlvect_2(A,B,k16_rlvect_2(A,C)) = k17_rlvect_2(A,B,C))))))) # label(d15_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2823 (all A all B all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & l1_struct_0(A) -> v1_finset_1(k3_rlvect_2(A,B,C)) & m1_subset_1(k3_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2824 $T # label(t10_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2825 (all A (v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> k16_rlvect_2(A,B) = k5_rlvect_1(k23_rlvect_2(A),k1_rlvect_2(k23_rlvect_2(A),B)))))) # label(t98_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.52 2826 (all A all B all C (v4_rlvect_1(B) & v5_rlvect_1(B) & l2_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v7_rlvect_1(B) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> ((exists D (m2_rlvect_2(D,B,C) & A = D)) <-> r2_hidden(A,a_2_1_rlvect_2(B,C))))) # label(fraenkel_a_2_1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2827 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & m1_rlvect_2(B,A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> m1_rlvect_2(k16_rlvect_2(A,B),A))) # label(dt_k16_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2828 $T # label(t57_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2829 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),k1_numbers,k11_rlvect_2(A),B) = np__0)))) # label(t30_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2830 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k5_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,D))))) & k3_finseq_1(C) = k3_finseq_1(B) -> k5_rlvect_1(A,k9_rlvect_1(A,B)) = k9_rlvect_1(A,C)))))))) # label(t6_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2831 $T # label(t88_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2832 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (v3_funct_2(D,k1_relat_1(B),k1_relat_1(B)) & m2_relset_1(D,k1_relat_1(B),k1_relat_1(B)) & v1_funct_2(D,k1_relat_1(B),k1_relat_1(B)) & v1_funct_1(D) -> (k3_finseq_1(C) = k3_finseq_1(B) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(C)) -> k1_funct_1(B,k1_funct_1(D,E)) = k1_funct_1(C,E)))) -> k9_rlvect_1(A,C) = k9_rlvect_1(A,B)))))))))) # label(t8_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2833 $T # label(d2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2834 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> k11_rlvect_2(A) = u2_struct_0(k23_rlvect_2(A)))) # label(t93_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2835 (all A all B all C (v4_rlvect_1(A) & v6_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rlvect_2(k17_rlvect_2(A,B,C),A))) # label(dt_k17_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2836 $T # label(t39_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2837 $T # label(t78_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2838 $T # label(t11_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2839 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_rlvect_2(A,k3_rlvect_2(A,C,B)) = k6_rlvect_1(A,k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)),k6_rlvect_2(A,k2_rlvect_2(A,C,B))))))))) # label(t20_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2840 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) & v1_funct_2(B,k2_zfmisc_1(k1_numbers,k18_rlvect_2(A)),k18_rlvect_2(A)) -> ((all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,k18_rlvect_2(A)) -> k1_funct_1(B,k4_tarski(C,D)) = k15_rlvect_2(A,C,k19_rlvect_2(A,D)))))) <-> k22_rlvect_2(A) = B))))) # label(d20_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2841 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(A)) -> (k3_finseq_1(D) = k3_finseq_1(B) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k1_relat_1(B)) -> k1_funct_1(D,E) = k4_rlvect_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),k4_finseq_4(k5_numbers,u1_struct_0(A),C,E))))) & k3_finseq_1(B) = k3_finseq_1(C) -> k4_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) = k9_rlvect_1(A,D)))))))))) # label(t4_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2842 $T # label(t87_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2843 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_rlvect_2(C,A) -> (all D (m1_rlvect_2(D,A) -> k5_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,C,B),k8_funct_2(u1_struct_0(A),k1_numbers,D,B)) = k8_funct_2(u1_struct_0(A),k1_numbers,k17_rlvect_2(A,C,D),B))))))))) # label(t79_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2844 (all A all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k6_rlvect_2(A,B),u1_struct_0(A)))) # label(dt_k6_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2845 $T # label(t31_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2846 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_rlvect_2(D,A) -> r1_rlvect_2(A,k15_rlvect_2(A,k3_real_1(B,C),D),k14_rlvect_2(A,k15_rlvect_2(A,B,D),k15_rlvect_2(A,C,D))))))))))) # label(t68_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2847 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> k7_rlvect_2(A,B) = k1_tarski(B))) # label(redefinition_k7_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2848 (all A all B all C (-v3_struct_0(A) & l1_rlvect_1(A) & m1_rlvect_2(C,A) & m1_rlvect_2(B,A) -> r1_rlvect_2(A,B,B))) # label(reflexivity_r1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2849 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_rlvect_1(A,k6_rlvect_2(A,k2_rlvect_2(A,C,B)),k6_rlvect_2(A,B)) = k6_rlvect_2(A,k4_rlvect_2(A,C,B)))))))) # label(t21_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2850 $T # label(t90_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2851 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v4_rlvect_1(A) -> u2_rlvect_1(k23_rlvect_2(A)) = k22_rlvect_2(A))) # label(t95_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2852 $T # label(t85_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2853 (all A all B all C (l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_rlvect_2(A,B,C) = k5_xboole_0(B,C))) # label(redefinition_k5_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2854 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) -> k6_rlvect_1(A,k4_rlvect_1(A,k6_rlvect_2(A,C),k6_rlvect_2(A,B)),k6_rlvect_2(A,k3_rlvect_2(A,C,B))) = k6_rlvect_2(A,k2_rlvect_2(A,C,B)))))))) # label(t19_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2855 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_rlvect_2(C,A) -> r1_tarski(k10_rlvect_2(A,k17_rlvect_2(A,B,C)),k2_rlvect_2(A,k10_rlvect_2(A,B),k10_rlvect_2(A,C))))))))) # label(t80_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2856 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_rlvect_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k13_rlvect_2(A,B) = C <-> (exists D (m2_finseq_1(D,u1_struct_0(A)) & v2_funct_1(D) & k9_rlvect_1(A,k12_rlvect_2(A,D,B)) = C & k2_relat_1(D) = k10_rlvect_2(A,B)))))))))) # label(d10_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2857 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) -> k4_rlvect_1(A,k6_rlvect_2(A,k4_rlvect_2(A,C,B)),k6_rlvect_2(A,k4_rlvect_2(A,B,C))) = k6_rlvect_2(A,k5_rlvect_2(A,C,B)))))))) # label(t24_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2858 (all A (l1_struct_0(A) -> (exists B (v1_funct_1(B) & v1_finset_1(B) & v1_membered(B) & v2_membered(B) & v4_membered(B) & v5_membered(B) & v3_membered(B) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc1_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2859 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_rlvect_1(A) & -v3_struct_0(A) -> (exists C m2_rlvect_2(C,A,B)))) # label(existence_m2_rlvect_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2860 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) -> v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & v6_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(t13_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2861 $T # label(t68_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2862 (exists A (v4_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v3_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2863 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (exists C (l2_vectsp_2(C,A,B) & -v3_struct_0(C))))) # label(rc11_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2864 (all A all B all C all D all E all F all G (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(C,C),C) & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & v1_funct_1(G) & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_1(F) & m1_subset_1(E,C) & m1_relset_1(D,k2_zfmisc_1(C,C),C) -> (all H all I all J all K all L all M all N (g2_vectsp_2(H,I,J,K,L,M,N) = g2_vectsp_2(A,B,C,D,E,F,G) -> L = E & F = M & G = N & D = K & J = C & I = B & H = A)))) # label(free_g2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2865 $T # label(t44_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2866 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) -> k1_group_1(A,C,B) = k2_group_1(A)))))))) # label(t41_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2867 $T # label(t4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2868 $T # label(d13_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2869 $T # label(t23_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2870 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v4_group_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)) -> -(k1_rlvect_1(A) != B & C != k1_rlvect_1(A) & k2_vectsp_2(A,k1_group_1(A,D,C),k1_group_1(A,B,C)) != k2_vectsp_2(A,D,B)))))))))) # label(t53_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2871 (all A (l1_struct_0(A) -> (exists B l1_vectsp_2(B,A)))) # label(existence_l1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2872 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v7_group_1(A) & v6_vectsp_1(A) -> -v3_struct_0(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v2_group_1(A)))) # label(cc3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2873 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_group_1(A,k1_vectsp_2(A,B),B) = k2_group_1(A) & k1_group_1(A,B,k1_vectsp_2(A,B)) = k2_group_1(A)))))) # label(t43_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2874 $T # label(t35_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2875 $T # label(d1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2876 $T # label(t27_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2877 $T # label(d3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2878 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k5_vectsp_2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k5_vectsp_2(A))) -> k6_vectsp_2(A,k5_vectsp_2(A),B,k6_vectsp_2(A,k5_vectsp_2(A),C,D)) = k6_vectsp_2(A,k5_vectsp_2(A),k1_group_1(A,C,B),D) & D = k6_vectsp_2(A,k5_vectsp_2(A),k2_group_1(A),D) & k6_vectsp_2(A,k5_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),C,D)) & k4_rlvect_1(k5_vectsp_2(A),k6_vectsp_2(A,k5_vectsp_2(A),B,D),k6_vectsp_2(A,k5_vectsp_2(A),B,E)) = k6_vectsp_2(A,k5_vectsp_2(A),B,k4_rlvect_1(k5_vectsp_2(A),D,E)))))))))))) # label(t77_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2879 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k4_vectsp_2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k4_vectsp_2(A))) -> k6_vectsp_1(A,k4_vectsp_2(A),B,k6_vectsp_1(A,k4_vectsp_2(A),C,D)) = k6_vectsp_1(A,k4_vectsp_2(A),k1_group_1(A,B,C),D) & D = k6_vectsp_1(A,k4_vectsp_2(A),k2_group_1(A),D) & k6_vectsp_1(A,k4_vectsp_2(A),k4_rlvect_1(A,B,C),D) = k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),C,D)) & k6_vectsp_1(A,k4_vectsp_2(A),B,k4_rlvect_1(k4_vectsp_2(A),D,E)) = k4_rlvect_1(k4_vectsp_2(A),k6_vectsp_1(A,k4_vectsp_2(A),B,D),k6_vectsp_1(A,k4_vectsp_2(A),B,E)))))))))))) # label(t71_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2880 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & v3_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v2_vectsp_2(A) & -v10_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v4_group_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A))) # label(rc5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2881 (exists A (l3_vectsp_1(A) & -v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A))) # label(rc1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2882 (all A all B all C all D all E (l1_struct_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & m1_subset_1(D,B) & v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_1(E) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) & -v3_struct_0(g1_vectsp_2(A,B,C,D,E)))) # label(fc1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2883 (all A (l1_vectsp_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,k2_vectsp_1(A)) = B & B = k1_group_1(A,k2_vectsp_1(A),B))) <-> v1_vectsp_2(A)))) # label(d2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2884 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> k3_vectsp_2(A) = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A)))) # label(d9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2885 (exists A (l3_vectsp_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v3_vectsp_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A))) # label(rc7_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2886 (all A all B (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v6_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> v4_rlvect_1(k9_vectsp_2(A,B)) & v5_rlvect_1(k9_vectsp_2(A,B)) & v4_vectsp_2(k9_vectsp_2(A,B),A,B) & l2_vectsp_2(k9_vectsp_2(A,B),A,B) & v6_rlvect_1(k9_vectsp_2(A,B)) & v3_rlvect_1(k9_vectsp_2(A,B)) & -v3_struct_0(k9_vectsp_2(A,B)))) # label(dt_k9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2887 $T # label(d16_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2888 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (all B (l1_vectsp_2(B,A) & -v3_struct_0(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k6_vectsp_2(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,C,F)) & E = k6_vectsp_2(A,B,k2_group_1(A),E) & k6_vectsp_2(A,B,C,k6_vectsp_2(A,B,D,E)) = k6_vectsp_2(A,B,k1_group_1(A,D,C),E) & k6_vectsp_2(A,B,k2_rlvect_1(A,C,D),E) = k2_rlvect_1(B,k6_vectsp_2(A,B,C,E),k6_vectsp_2(A,B,D,E)))))))))) <-> v5_vectsp_2(B,A)))))) # label(d23_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2889 $T # label(t15_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2890 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) <-> C = k1_vectsp_2(A,B))))))))) # label(d7_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2891 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_vectsp_2(A,k1_vectsp_2(A,B)) = B))))) # label(t49_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2892 $T # label(t6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2893 $T # label(t73_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2894 $T # label(t66_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2895 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (exists B (l4_vectsp_1(B,A) & -v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B))))) # label(rc15_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2896 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (exists C l2_vectsp_2(C,A,B)))) # label(existence_l2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2897 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (-v3_struct_0(C) & l2_vectsp_2(C,A,B) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (all H (m1_subset_1(H,u1_struct_0(C)) -> (all I (m1_subset_1(I,u1_struct_0(C)) -> k6_vectsp_1(A,C,D,k2_rlvect_1(C,H,I)) = k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,D,I)) & k6_vectsp_2(B,C,F,k2_rlvect_1(C,H,I)) = k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,F,I)) & k6_vectsp_2(B,C,k2_group_1(B),H) = H & k6_vectsp_2(B,C,F,k6_vectsp_1(A,C,D,H)) = k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,F,H)) & k6_vectsp_2(B,C,k1_group_1(B,G,F),H) = k6_vectsp_2(B,C,F,k6_vectsp_2(B,C,G,H)) & k2_rlvect_1(C,k6_vectsp_2(B,C,F,H),k6_vectsp_2(B,C,G,H)) = k6_vectsp_2(B,C,k4_rlvect_1(B,F,G),H) & H = k6_vectsp_1(A,C,k2_group_1(A),H) & k6_vectsp_1(A,C,D,k6_vectsp_1(A,C,E,H)) = k6_vectsp_1(A,C,k1_group_1(A,D,E),H) & k6_vectsp_1(A,C,k4_rlvect_1(A,D,E),H) = k2_rlvect_1(C,k6_vectsp_1(A,C,D,H),k6_vectsp_1(A,C,E,H)))))))))))))) <-> v5_vectsp_2(C,B) & v6_vectsp_2(C,A,B) & v12_vectsp_1(C,A)))))))) # label(t83_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2898 $T # label(t8_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2899 $T # label(t69_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2900 $T # label(t24_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2901 $T # label(t36_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2902 $T # label(t18_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2903 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_vectsp_2(A,B,C) = k1_group_1(A,B,k1_vectsp_2(A,C)))))))) # label(d8_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2904 $T # label(d6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2905 $T # label(t75_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2906 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,B,D) = k1_group_1(A,B,C) -> k1_rlvect_1(A) = B | C = D))))))))) # label(t42_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2907 $T # label(t63_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2908 (all A (v1_funct_1(A) & v1_funct_2(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) & m2_relset_1(A,k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)) -> A = k7_vectsp_2)) # label(d17_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2909 $T # label(t79_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2910 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k5_vectsp_2(A)) & v4_rlvect_1(k5_vectsp_2(A)) & v6_rlvect_1(k5_vectsp_2(A)) & v5_vectsp_2(k5_vectsp_2(A),A) & v3_vectsp_2(k5_vectsp_2(A),A) & v5_rlvect_1(k5_vectsp_2(A)) & v3_rlvect_1(k5_vectsp_2(A)))) # label(fc4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2911 (all A (l1_struct_0(A) -> (exists B (l1_vectsp_2(B,A) & v3_vectsp_2(B,A))))) # label(rc8_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2912 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k5_rlvect_1(A,k2_vectsp_2(A,C,B)) = k2_vectsp_2(A,C,k5_rlvect_1(A,B)) & k2_vectsp_2(A,k5_rlvect_1(A,C),B) = k5_rlvect_1(A,k2_vectsp_2(A,C,B))))))))) # label(t54_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2913 (all A all B all C all D all E all F all G (l1_struct_0(B) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(C,C),C) & m1_subset_1(E,C) & v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C) & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_1(G) & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & v1_funct_2(D,k2_zfmisc_1(C,C),C) & l1_struct_0(A) -> l2_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) & v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B))) # label(dt_g2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2914 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v6_rlvect_1(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists C (v4_vectsp_2(C,A,B) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) & l2_vectsp_2(C,A,B))))) # label(rc14_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2915 (all A (l1_struct_0(A) -> (all B (l1_vectsp_2(B,A) -> l1_rlvect_1(B))))) # label(dt_l1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2916 $T # label(t5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2917 $T # label(t61_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2918 (all A all B (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v7_vectsp_1(B) & v4_group_1(B) & v3_rlvect_1(B) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> v3_rlvect_1(k9_vectsp_2(A,B)) & v5_rlvect_1(k9_vectsp_2(A,B)) & v6_rlvect_1(k9_vectsp_2(A,B)) & v12_vectsp_1(k9_vectsp_2(A,B),A) & v4_vectsp_2(k9_vectsp_2(A,B),A,B) & v6_vectsp_2(k9_vectsp_2(A,B),A,B) & v5_vectsp_2(k9_vectsp_2(A,B),B) & v4_rlvect_1(k9_vectsp_2(A,B)) & -v3_struct_0(k9_vectsp_2(A,B)))) # label(fc5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2919 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (exists B (l1_vectsp_2(B,A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v3_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B))))) # label(rc16_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2920 (exists A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v7_group_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v4_vectsp_1(A) & v4_group_1(A) & l3_vectsp_1(A))) # label(rc3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.53 2921 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(B != k1_rlvect_1(A) & k1_vectsp_2(A,k1_group_1(A,C,B)) != k1_group_1(A,k1_vectsp_2(A,B),k1_vectsp_2(A,C)) & C != k1_rlvect_1(A)))))))) # label(t46_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2922 $T # label(t19_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2923 (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)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & B = k4_rlvect_1(A,C,D) & B = k4_rlvect_1(A,D,C))))))))) # label(t38_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2924 (all A (l1_vectsp_1(A) -> (v1_vectsp_2(A) & -v3_struct_0(A) -> v2_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(A)))) # label(cc1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2925 $T # label(t29_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2926 $T # label(t12_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2927 (all A (-v3_struct_0(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (exists B (l4_vectsp_1(B,A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A))))) # label(rc12_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2928 $T # label(t30_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2929 (all A all B (l1_struct_0(A) & l1_vectsp_2(B,A) -> (v3_vectsp_2(B,A) -> B = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B))))) # label(abstractness_v3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2930 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> -v3_struct_0(k4_vectsp_2(A)) & v3_rlvect_1(k4_vectsp_2(A)) & v4_rlvect_1(k4_vectsp_2(A)) & v12_vectsp_1(k4_vectsp_2(A),A) & v11_vectsp_1(k4_vectsp_2(A),A) & v6_rlvect_1(k4_vectsp_2(A)) & v5_rlvect_1(k4_vectsp_2(A)))) # label(fc3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2931 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (all C (l2_vectsp_2(C,A,B) -> l4_vectsp_1(C,A) & l1_vectsp_2(C,B))))) # label(dt_l2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2932 $T # label(d10_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2933 $T # label(t25_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2934 $T # label(d20_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2935 $T # label(t2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2936 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k3_vectsp_2(A)) & v1_rlvect_1(k3_vectsp_2(A)) & v3_rlvect_1(k3_vectsp_2(A)) & v6_rlvect_1(k3_vectsp_2(A)) & l1_rlvect_1(k3_vectsp_2(A)) & v5_rlvect_1(k3_vectsp_2(A)) & v4_rlvect_1(k3_vectsp_2(A)))) # label(dt_k3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2937 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v6_rlvect_1(B) & v7_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v6_vectsp_1(B) & v4_group_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> -v3_struct_0(k9_vectsp_2(A,B)) & v4_rlvect_1(k9_vectsp_2(A,B)) & v5_rlvect_1(k9_vectsp_2(A,B)) & l2_vectsp_2(k9_vectsp_2(A,B),A,B) & v6_vectsp_2(k9_vectsp_2(A,B),A,B) & v5_vectsp_2(k9_vectsp_2(A,B),B) & v12_vectsp_1(k9_vectsp_2(A,B),A) & v6_rlvect_1(k9_vectsp_2(A,B)) & v3_rlvect_1(k9_vectsp_2(A,B)))))) # label(t84_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2938 $T # label(d22_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2939 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> k5_vectsp_2(A) = g1_vectsp_2(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)))) # label(d14_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2940 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,B,C) -> k1_vectsp_2(A,C) = B & k1_vectsp_2(A,B) = C))))))) # label(t45_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2941 $T # label(t26_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2942 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v4_group_1(B) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (exists C (l2_vectsp_2(C,A,B) & v4_rlvect_1(C) & v6_rlvect_1(C) & v12_vectsp_1(C,A) & v4_vectsp_2(C,A,B) & v6_vectsp_2(C,A,B) & v5_vectsp_2(C,B) & v5_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C))))) # label(rc17_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2943 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) != k2_group_1(A) & -((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) != k2_group_1(A))) & B != k1_rlvect_1(A)))) -> v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A)))) # label(t16_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2944 $T # label(d19_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2945 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D = k4_rlvect_1(A,B,C) -> k6_rlvect_1(A,D,C) = B) & (k6_rlvect_1(A,D,B) = C -> k4_rlvect_1(A,B,C) = D) & (k4_rlvect_1(A,B,C) = D -> k6_rlvect_1(A,D,B) = C) & (k6_rlvect_1(A,D,C) = B -> D = k4_rlvect_1(A,B,C)))))))))) # label(t22_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2946 $T # label(t31_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2947 (all A all B all C all D all E all F all G (l1_struct_0(A) & -v1_xboole_0(C) & v1_funct_2(D,k2_zfmisc_1(C,C),C) & m1_relset_1(D,k2_zfmisc_1(C,C),C) & v1_funct_1(F) & m1_relset_1(F,k2_zfmisc_1(u1_struct_0(A),C),C) & v1_funct_2(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & m1_relset_1(G,k2_zfmisc_1(C,u1_struct_0(B)),C) & v1_funct_1(G) & v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),C),C) & m1_subset_1(E,C) & v1_funct_1(D) & l1_struct_0(B) -> v4_vectsp_2(g2_vectsp_2(A,B,C,D,E,F,G),A,B) & -v3_struct_0(g2_vectsp_2(A,B,C,D,E,F,G)))) # label(fc2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2948 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(C != k1_rlvect_1(A) & k2_vectsp_2(A,k1_group_1(A,D,C),B) != k2_vectsp_2(A,D,k2_vectsp_2(A,B,C)) & k1_rlvect_1(A) != B))))))))) # label(t56_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2949 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) -> -v3_struct_0(k5_vectsp_2(A)) & v3_rlvect_1(k5_vectsp_2(A)) & v3_vectsp_2(k5_vectsp_2(A),A) & l1_vectsp_2(k5_vectsp_2(A),A) & v6_rlvect_1(k5_vectsp_2(A)) & v5_rlvect_1(k5_vectsp_2(A)) & v4_rlvect_1(k5_vectsp_2(A)))) # label(dt_k5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2950 $T # label(t72_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2951 $T # label(t32_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2952 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != k1_rlvect_1(A) & B != k1_rlvect_1(A) & k1_rlvect_1(A) = k1_group_1(A,B,C)))))) <-> v2_vectsp_2(A)))) # label(d5_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2953 (exists A (-v3_struct_0(A) & v5_rlvect_1(A) & v2_group_1(A) & v3_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & l3_vectsp_1(A))) # label(rc2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2954 (all A (v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(k4_vectsp_2(A)) & v11_vectsp_1(k4_vectsp_2(A),A) & l4_vectsp_1(k4_vectsp_2(A),A) & v6_rlvect_1(k4_vectsp_2(A)) & v5_rlvect_1(k4_vectsp_2(A)) & v4_rlvect_1(k4_vectsp_2(A)) & v3_rlvect_1(k4_vectsp_2(A)))) # label(dt_k4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2955 $T # label(t70_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2956 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v6_vectsp_1(B) & v6_rlvect_1(B) & -v3_struct_0(B) -> g2_vectsp_2(A,B,k1_tarski(k1_xboole_0),k2_midsp_1,k8_vectsp_2,k10_funct_3(u1_struct_0(A),k1_tarski(k1_xboole_0)),k9_funct_3(k1_tarski(k1_xboole_0),u1_struct_0(B))) = k9_vectsp_2(A,B))))) # label(d21_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2957 $T # label(t9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2958 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v7_vectsp_1(B) & v6_vectsp_1(B) & v4_group_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (l2_vectsp_2(C,A,B) & -v3_struct_0(C) -> (v6_vectsp_2(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(C)) -> k6_vectsp_1(A,C,D,k6_vectsp_2(B,C,E,F)) = k6_vectsp_2(B,C,E,k6_vectsp_1(A,C,D,F))))))))))))))) # label(d24_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2959 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l1_vectsp_2(B,A) & l1_struct_0(A) & -v3_struct_0(A) -> m1_subset_1(k6_vectsp_2(A,B,C,D),u1_struct_0(B)))) # label(dt_k6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2960 $T # label(t76_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2961 (all A (l1_vectsp_1(A) -> (-v3_struct_0(A) & v7_group_1(A) & v8_vectsp_1(A) -> -v3_struct_0(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v2_group_1(A)))) # label(cc2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2962 $T # label(t28_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2963 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> (v1_vectsp_2(A) -> k2_vectsp_1(A) = k2_group_1(A)))) # label(t85_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2964 (all A (v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> g4_vectsp_1(A,u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A),u1_group_1(A)) = k4_vectsp_2(A))) # label(d11_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2965 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,B,C) = k2_group_1(A) -> k1_rlvect_1(A) != B & k1_rlvect_1(A) != C))))))) # label(t39_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2966 $T # label(t3_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2967 $T # label(t74_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2968 $T # label(t33_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2969 $T # label(t62_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2970 $T # label(d4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2971 (all A all B all C (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v9_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k2_vectsp_2(A,B,C),u1_struct_0(A)))) # label(dt_k2_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2972 $T # label(t58_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2973 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k6_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B)) = k2_vectsp_2(A,k6_rlvect_1(A,C,D),B) & k2_vectsp_2(A,k4_rlvect_1(A,C,D),B) = k4_rlvect_1(A,k2_vectsp_2(A,C,B),k2_vectsp_2(A,D,B))))))))))) # label(t55_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2974 (all A (l1_struct_0(A) -> (exists B (-v3_struct_0(B) & l1_vectsp_2(B,A))))) # label(rc9_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2975 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & 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)) -> -(B != k1_rlvect_1(A) & C != k1_rlvect_1(A) & k1_group_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t47_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2976 $T # label(t82_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2977 $T # label(t64_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2978 (all A (m1_subset_1(A,k1_tarski(k1_xboole_0)) -> k8_vectsp_2 = A)) # label(d18_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2979 (all A all B all C (l1_struct_0(B) & l2_vectsp_2(C,A,B) & l1_struct_0(A) -> (v4_vectsp_2(C,A,B) -> g2_vectsp_2(A,B,u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C),u2_vectsp_1(B,C),u1_vectsp_2(B,C)) = C))) # label(abstractness_v4_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2980 $T # label(t37_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2981 (all A all B (l1_struct_0(A) & l1_struct_0(B) -> (exists C (v4_vectsp_2(C,A,B) & l2_vectsp_2(C,A,B))))) # label(rc10_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2982 (all A (v3_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_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)) -> -(k1_vectsp_2(A,B) = k1_rlvect_1(A) & k1_rlvect_1(A) != B))))) # label(t48_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.45/115.54 2983 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_group_1(A,k2_vectsp_2(A,C,B),B) = C))))))) # label(t57_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2984 $T # label(t80_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2985 $T # label(t65_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2986 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k1_group_1(A,k2_vectsp_2(A,k2_group_1(A),B),B) = k2_group_1(A) & k2_group_1(A) = k1_group_1(A,B,k2_vectsp_2(A,k2_group_1(A),B))))))) # label(t51_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2987 $T # label(t10_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2988 $T # label(t21_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2989 $T # label(t20_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2990 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k2_binop_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_vectsp_2(A,B),D,C) = k6_vectsp_2(A,B,C,D))))))))) # label(d15_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2991 (all A all B all C all D all E (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,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & l1_struct_0(A) -> (all F all G all H all I all J (g1_vectsp_2(F,G,H,I,J) = g1_vectsp_2(A,B,C,D,E) -> H = C & D = I & E = J & B = G & F = A)))) # label(free_g1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2992 (all A (l3_vectsp_1(A) & -v3_struct_0(A) -> (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) & k2_rlvect_1(A,B,k1_rlvect_1(A)) = B & k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,B)) & B = k1_group_1(A,B,k2_group_1(A)) & B = k1_group_1(A,k2_group_1(A),B) & k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D) & k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) & k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) & k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D))))))))))) # label(t1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2993 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k2_group_1(A) = k2_vectsp_2(A,B,B)))))) # label(t52_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2994 (all A (v5_rlvect_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(B != k1_rlvect_1(A) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_group_1(A) != k1_group_1(A,C,B)))))))) # label(t40_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2995 (all A all B (v5_rlvect_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k1_vectsp_2(A,B),u1_struct_0(A)))) # label(dt_k1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2996 $T # label(t14_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2997 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (exists B (v3_rlvect_1(B) & v4_rlvect_1(B) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l1_vectsp_2(B,A))))) # label(rc13_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2998 $T # label(d12_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 2999 $T # label(t11_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3000 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k2_vectsp_2(A,k2_group_1(A),B) = k1_vectsp_2(A,B) & B = k2_vectsp_2(A,k2_group_1(A),k1_vectsp_2(A,B))))))) # label(t50_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3001 $T # label(t17_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3002 $T # label(t7_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3003 (exists A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v2_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc6_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3004 $T # label(t78_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3005 $T # label(t60_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3006 $T # label(t59_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3007 $T # label(t67_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3008 $T # label(t81_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3009 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & m1_relset_1(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & v1_funct_2(E,k2_zfmisc_1(B,u1_struct_0(A)),B) & m1_subset_1(D,B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> l1_vectsp_2(g1_vectsp_2(A,B,C,D,E),A) & v3_vectsp_2(g1_vectsp_2(A,B,C,D,E),A))) # label(dt_g1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3010 (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)) -> (k5_rlvect_1(A,B) = k1_rlvect_1(A) <-> B = k1_rlvect_1(A)))))) # label(t34_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3011 (all A all B (l1_vectsp_2(B,A) & l1_struct_0(A) -> v1_funct_2(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B)) & m2_relset_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)),u1_struct_0(B)) & v1_funct_1(u1_vectsp_2(A,B)))) # label(dt_u1_vectsp_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3012 $T # label(t32_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3013 $T # label(t36_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3014 $T # label(t41_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3015 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (D = k1_rlvect_1(C) | k1_rlvect_1(A) = B <-> k1_rlvect_1(C) = k6_vectsp_1(A,C,B,D)))))))))) # label(t25_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3016 $T # label(t28_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3017 $T # label(t16_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3018 $T # label(t20_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3019 $T # label(t9_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3020 (all A (-v3_struct_0(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_2(A,B,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(B,D) & k6_vectsp_2(A,B,C,k1_rlvect_1(B)) = k1_rlvect_1(B) & k6_vectsp_2(A,B,k1_rlvect_1(A),D) = k1_rlvect_1(B))))))))) # label(t37_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3021 $T # label(t15_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3022 $T # label(t18_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3023 $T # label(t27_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3024 $T # label(t10_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3025 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B != k1_rlvect_1(A) -> D = k6_vectsp_1(A,C,k1_vectsp_2(A,B),k6_vectsp_1(A,C,B,D))))))))))) # label(t26_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3026 $T # label(t34_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3027 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_vectsp_2(A,B,k5_rlvect_1(A,C),D) = k5_rlvect_1(B,k6_vectsp_2(A,B,C,D)) & k2_rlvect_1(B,E,k6_vectsp_2(A,B,k5_rlvect_1(A,C),D)) = k6_rlvect_1(B,E,k6_vectsp_2(A,B,C,D)))))))))))) # label(t38_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3028 $T # label(t1_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3029 (all A (v6_rlvect_1(A) & v5_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k1_group_1(A,k5_rlvect_1(A,k2_group_1(A)),B))))) # label(t14_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3030 $T # label(t7_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3031 $T # label(t24_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3032 $T # label(t5_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3033 $T # label(t4_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3034 $T # label(t30_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3035 $T # label(t22_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3036 $T # label(t6_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3037 $T # label(t3_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3038 $T # label(t11_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3039 $T # label(t35_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3040 $T # label(t8_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3041 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k1_rlvect_1(A) != B -> D = k6_vectsp_2(A,C,k1_vectsp_2(A,B),k6_vectsp_2(A,C,B,D))))))))))) # label(t43_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3042 $T # label(t21_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3043 $T # label(t33_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3044 $T # label(t31_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3045 $T # label(t12_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3046 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k6_vectsp_2(A,C,B,D) = k1_rlvect_1(C) <-> D = k1_rlvect_1(C) | k1_rlvect_1(A) = B))))))))) # label(t42_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3047 $T # label(t17_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3048 $T # label(t23_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3049 $T # label(t19_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3050 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k1_group_1(A,B,k5_rlvect_1(A,k2_group_1(A))))))) # label(t13_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3051 $T # label(t29_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3052 $T # label(t2_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3053 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_2(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_2(A,B,C,D)))))))))) # label(t39_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3054 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_rlvect_1(B,k6_vectsp_2(A,B,C,D),k6_vectsp_2(A,B,C,E)) = k6_vectsp_2(A,B,C,k6_rlvect_1(B,D,E)))))))))))) # label(t40_mod_1) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3055 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m2_rmod_2(D,A,B,C) -> (r2_hidden(k1_rlvect_1(B),D) <-> D = u1_struct_0(C)))))))))) # label(t89_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3056 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k1_rmod_2(A,C) = k1_rmod_2(A,D))))))))) # label(t48_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.54 3057 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & v3_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (u1_struct_0(B) = u1_struct_0(C) -> B = C))))))) # label(t39_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3058 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r2_hidden(C,k3_rmod_2(A,B,D,E)) <-> k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,C,E)))))))))))) # label(t68_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3059 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> r1_rlvect_1(D,k1_rlvect_1(C)))))))))) # label(t26_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3060 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k6_rlvect_1(B,D,E),C))))))))))))) # label(t6_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3061 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -(C != k1_xboole_0 & v1_rmod_2(C,A,B) & (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> C != u1_struct_0(D)))))))))) # label(t42_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3062 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m2_rmod_2(k6_domain_1(u1_struct_0(B),C),A,B,k1_rmod_2(A,B)))))))) # label(t84_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3063 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(D,C) & r2_hidden(E,C) -> r2_hidden(k4_rlvect_1(B,D,E),C)))))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_hidden(k6_vectsp_2(A,B,D,E),C)))))) <-> v1_rmod_2(C,A,B)))))))) # label(d1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3064 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> r1_rlvect_1(B,k1_rlvect_1(C)))))))) # label(t27_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3065 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m2_rmod_2(E,A,B,D) -> (all F (m2_rmod_2(F,A,B,D) -> (r2_hidden(C,F) & r2_hidden(C,E) -> E = F))))))))))))) # label(t94_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3066 $T # label(t13_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3067 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) -> (exists C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v3_vectsp_2(C,A) & v5_vectsp_2(C,A) & v6_rlvect_1(C) & v3_rlvect_1(C) & m1_rmod_2(C,A,B))))) # label(rc1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3068 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) & v3_vectsp_2(E,A) -> (k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,C,D) <-> D = E))))))))))) # label(t79_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3069 $T # label(t45_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3070 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> v1_rmod_2(k6_domain_1(u1_struct_0(B),k1_rlvect_1(B)),A,B))))) # label(t7_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3071 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> -(m2_rmod_2(C,A,B,k1_rmod_2(A,B)) & (all D (m1_subset_1(D,u1_struct_0(B)) -> C != k6_domain_1(u1_struct_0(B),D)))))))))) # label(t85_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3072 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> k3_rmod_2(A,B,k1_rlvect_1(B),C) = u1_struct_0(C))))))) # label(t60_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3073 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (all C (m1_rmod_2(C,A,B) -> -v3_struct_0(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v4_rlvect_1(C) & v3_rlvect_1(C))))) # label(dt_m1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3074 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v3_rlvect_1(C) & v4_rlvect_1(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (r1_rlvect_1(E,D) -> r1_rlvect_1(E,k6_vectsp_2(A,C,B,D))))))))))))) # label(t29_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3075 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) & v1_rmod_2(D,A,B) & E = a_4_0_rmod_2(A,B,C,D) -> v1_rmod_2(E,A,B)))))))))))) # label(t9_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3076 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> m1_rmod_2(k1_rmod_2(A,B),A,C))))))) # label(t50_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3077 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (u1_struct_0(D) = k3_rmod_2(A,B,C,D) <-> r2_hidden(k1_rlvect_1(B),k3_rmod_2(A,B,C,D))))))))))) # label(t63_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3078 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r1_rlvect_1(D,C) <-> k3_rmod_2(A,B,C,D) = u1_struct_0(D)))))))))) # label(t64_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3079 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,D) <-> r2_hidden(k6_rlvect_1(B,C,D),k3_rmod_2(A,B,C,E))))))))))))) # label(t73_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3080 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists C m1_rmod_2(C,A,B)))) # label(existence_m1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3081 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> m2_rmod_2(u1_struct_0(C),A,B,C))))))) # label(t86_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3082 (all A (v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rmod_2(A,B,C,k1_rmod_2(A,B)) = k6_domain_1(u1_struct_0(B),C))))))) # label(t61_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3083 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> r1_rlvect_1(C,k1_rlvect_1(B)))))))) # label(t25_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3084 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> m1_subset_1(D,u1_struct_0(B)))))))))) # label(t18_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3085 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (all F (v3_vectsp_2(F,A) & m1_rmod_2(F,A,B) -> (k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,F) -> E = F))))))))))))) # label(t80_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3086 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) = k2_rmod_2(A,B))))) # label(d4_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3087 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (exists E (r2_hidden(C,E) & m2_rmod_2(E,A,B,D))))))))))) # label(t81_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3088 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v3_vectsp_2(C,A) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) -> (m1_rmod_2(B,A,C) & m1_rmod_2(C,A,B) -> B = C))))))) # label(t33_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3089 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r1_rlvect_1(D,C) <-> r2_hidden(k1_rlvect_1(B),k3_rmod_2(A,B,C,D))))))))))) # label(t58_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3090 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m2_rmod_2(F,A,B,E) -> -(r2_hidden(C,F) & r2_hidden(D,F) & (all G (m1_subset_1(G,u1_struct_0(B)) -> -(k4_rlvect_1(B,C,G) = D & r1_rlvect_1(E,G))))))))))))))))) # label(t91_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3091 $T # label(t1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3092 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,D) & r1_rlvect_1(E,C) -> r1_rlvect_1(E,k4_rlvect_1(B,C,D))))))))))))) # label(t28_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3093 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (r1_rlvect_1(E,D) -> r2_hidden(k6_vectsp_2(A,C,B,D),k3_rmod_2(A,C,D,E))))))))))))) # label(t70_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3094 $T # label(t44_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3095 (all A (v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v3_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (D = F -> k6_vectsp_2(A,C,B,D) = k6_vectsp_2(A,E,B,F)))))))))))))) # label(t22_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3096 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (u1_struct_0(C) = k6_domain_1(u1_struct_0(B),k1_rlvect_1(B)) <-> C = k1_rmod_2(A,B)))))))) # label(d3_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3097 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> (all E (m2_rmod_2(E,A,B,C) -> (all F (m2_rmod_2(F,A,B,D) -> (E = F -> C = D))))))))))))) # label(t83_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3098 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> m2_rmod_2(u1_struct_0(B),A,B,k2_rmod_2(A,B)))))) # label(t87_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3099 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> k1_rlvect_1(B) = k1_rlvect_1(C))))))) # label(t19_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3100 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> v3_vectsp_2(k2_rmod_2(A,B),A) & m1_rmod_2(k2_rmod_2(A,B),A,B))) # label(dt_k2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3101 (all A all B all C all D (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_subset_1(C,u1_struct_0(B)) & m1_rmod_2(D,A,B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_rmod_2(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k3_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3102 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v7_vectsp_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & v6_vectsp_1(B) & v4_group_1(B) & v5_rlvect_1(B) -> (all C (v5_rlvect_1(C) & l1_vectsp_2(C,B) & v5_vectsp_2(C,B) & v6_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_rmod_2(D,B,C) -> (all E (m1_rmod_2(E,B,C) -> (m1_rmod_2(D,B,E) & r1_rlvect_1(D,A) -> r1_rlvect_1(E,A)))))))))) # label(t16_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3103 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,C) <-> r2_hidden(k4_rlvect_1(B,C,D),k3_rmod_2(A,B,D,E))))))))))))) # label(t72_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3104 $T # label(t15_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3105 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> u1_struct_0(B) = k3_rmod_2(A,B,C,k2_rmod_2(A,B)))))))) # label(t62_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3106 $T # label(t43_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3107 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> m1_rmod_2(k1_rmod_2(A,C),A,B))))))) # label(t49_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3108 (all A (v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(D,E) <-> r1_rlvect_1(C,E)))) -> D = C))))))))) # label(t38_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3109 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v3_vectsp_2(B,A) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> m1_rmod_2(B,A,k2_rmod_2(A,B)))))) # label(t53_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3110 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,C) <-> k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,k4_rlvect_1(B,D,C),E)))))))))))) # label(t66_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3111 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(k1_rmod_2(A,C),A,D))))))))) # label(t51_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3112 $T # label(t74_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3113 $T # label(t54_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3114 (all A all B all C all D all E (-v3_struct_0(B) & v4_group_1(B) & v6_vectsp_1(B) & l3_vectsp_1(B) & v4_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,B) & m1_rmod_2(E,B,C) & m1_subset_1(D,u1_struct_0(C)) & l1_vectsp_2(C,B) & v5_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) & v8_vectsp_1(B) & v7_vectsp_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (r2_hidden(A,a_4_1_rmod_2(B,C,D,E)) <-> (exists F (k4_rlvect_1(C,D,F) = A & r1_rlvect_1(E,F) & m1_subset_1(F,u1_struct_0(C))))))) # label(fraenkel_a_4_1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3115 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (-v3_struct_0(C) & v5_vectsp_2(C,A) & l1_vectsp_2(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) -> (all D (-v3_struct_0(D) & v3_rlvect_1(D) & v6_rlvect_1(D) & v5_vectsp_2(D,A) & l1_vectsp_2(D,A) & v5_rlvect_1(D) & v4_rlvect_1(D) -> (m1_rmod_2(C,A,D) & m1_rmod_2(B,A,C) -> m1_rmod_2(B,A,D)))))))))) # label(t34_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3116 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> k1_rmod_2(A,B) = k1_rmod_2(A,C))))))) # label(t47_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3117 (all A all B all C (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_2(C,A,B) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all D (m2_rmod_2(D,A,B,C) -> m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))))) # label(dt_m2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3118 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (u1_struct_0(D) = u1_struct_0(C) -> D = C))))))))) # label(t37_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3119 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> -((all F (m1_subset_1(F,u1_struct_0(B)) -> -(D = k6_rlvect_1(B,C,F) & r1_rlvect_1(E,F)))) & k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,E)))))))))))) # label(t78_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3120 (all A (v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> k3_rmod_2(A,B,C,D) = a_4_1_rmod_2(A,B,C,D))))))))) # label(d5_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3121 (all A (v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (m2_rmod_2(D,A,B,C) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k3_rmod_2(A,B,E,C) = D))))))))))) # label(d6_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3122 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (C = u1_struct_0(B) -> v1_rmod_2(C,A,B)))))))) # label(t8_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3123 $T # label(t3_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3124 $T # label(t2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3125 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> ((exists F (m1_subset_1(F,u1_struct_0(B)) & C = k6_rlvect_1(B,D,F) & r1_rlvect_1(E,F))) <-> r2_hidden(C,k3_rmod_2(A,B,D,E))))))))))))) # label(t75_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3126 (all A (v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v6_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,A,C) -> (r1_rlvect_1(E,D) -> k3_rmod_2(A,C,k6_vectsp_2(A,C,B,D),E) = u1_struct_0(E)))))))))))) # label(t65_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3127 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k1_rlvect_1(C) = k1_rlvect_1(D))))))))) # label(t20_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3128 (all A all B all C all D all E (v4_rlvect_1(B) & v7_vectsp_1(B) & -v3_struct_0(C) & v3_rlvect_1(C) & v6_rlvect_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & l1_vectsp_2(C,B) & v5_vectsp_2(C,B) & v5_rlvect_1(C) & v4_rlvect_1(C) & l3_vectsp_1(B) & v8_vectsp_1(B) & v6_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> ((exists F exists G (r2_hidden(F,D) & r2_hidden(G,E) & k4_rlvect_1(C,F,G) = A & m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(F,u1_struct_0(C)))) <-> r2_hidden(A,a_4_0_rmod_2(B,C,D,E))))) # label(fraenkel_a_4_0_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3129 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,C) <-> k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,k6_rlvect_1(B,D,C),E)))))))))))) # label(t67_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3130 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(C,E) -> r1_rlvect_1(D,E)))) -> m1_rmod_2(C,A,D)))))))))) # label(t36_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3131 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) -> k1_xboole_0 = C | r2_hidden(k1_rlvect_1(B),C)))))))) # label(t4_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3132 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_rmod_2(F,A,B) -> (r2_hidden(C,k3_rmod_2(A,B,D,F)) & r2_hidden(C,k3_rmod_2(A,B,E,F)) -> k3_rmod_2(A,B,E,F) = k3_rmod_2(A,B,D,F)))))))))))))) # label(t69_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.55 3133 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,A) & v5_vectsp_2(C,A) & v4_rlvect_1(C) -> (r1_tarski(u1_struct_0(C),u1_struct_0(B)) & k7_relat_1(u1_vectsp_2(A,B),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(A))) = u1_vectsp_2(A,C) & u1_rlvect_1(C) = k7_relat_1(u1_rlvect_1(B),k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C))) & u2_struct_0(B) = u2_struct_0(C) <-> m1_rmod_2(C,A,B)))))))) # label(d2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3134 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m2_rmod_2(E,A,B,D) -> (E = k3_rmod_2(A,B,C,D) <-> r2_hidden(C,E)))))))))))) # label(t90_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3135 (all A all B all C (-v3_struct_0(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_2(C,A,B) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (exists D m2_rmod_2(D,A,B,C)))) # label(existence_m2_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3136 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(D)) -> (E = C -> k5_rlvect_1(B,C) = k5_rlvect_1(D,E)))))))))))) # label(t23_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3137 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> -(k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,C,E) & (all F (m1_subset_1(F,u1_struct_0(B)) -> -(D = k4_rlvect_1(B,C,F) & r1_rlvect_1(E,F))))))))))))))) # label(t77_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3138 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(D,A,B) & v1_rmod_2(C,A,B) -> v1_rmod_2(k5_subset_1(u1_struct_0(B),C,D),A,B)))))))))) # label(t10_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3139 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (m2_rmod_2(C,A,B,k2_rmod_2(A,B)) -> u1_struct_0(B) = C))))))) # label(t88_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3140 (all A (v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (v1_rmod_2(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(D,C) -> r2_hidden(k5_rlvect_1(B,D),C))))))))))) # label(t5_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3141 $T # label(t11_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3142 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (all G (m1_subset_1(G,u1_struct_0(E)) -> (G = D & C = F -> k4_rlvect_1(E,F,G) = k4_rlvect_1(B,C,D)))))))))))))))) # label(t21_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3143 (all A all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v4_group_1(B) & v6_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_vectsp_2(C,B) & v5_vectsp_2(C,B) -> (k1_rlvect_1(C) = A <-> r1_rlvect_1(k1_rmod_2(B,C),A)))))) # label(t46_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3144 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m1_subset_1(F,u1_struct_0(E)) -> (all G (m1_subset_1(G,u1_struct_0(E)) -> (G = D & C = F -> k6_rlvect_1(E,F,G) = k6_rlvect_1(B,C,D)))))))))))))))) # label(t24_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3145 (all A all B (v4_rlvect_1(B) & v6_vectsp_1(B) & v7_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l1_vectsp_2(C,B) & v5_vectsp_2(C,B) & v6_rlvect_1(C) & v3_rlvect_1(C) -> (all D (m1_rmod_2(D,B,C) -> (r1_rlvect_1(D,A) -> r1_rlvect_1(C,A)))))))) # label(t17_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3146 (all A all B (v5_rlvect_1(B) & v6_vectsp_1(B) & l3_vectsp_1(B) & v8_vectsp_1(B) & v7_vectsp_1(B) & v4_group_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (v6_rlvect_1(C) & v5_vectsp_2(C,B) & l1_vectsp_2(C,B) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_rmod_2(E,B,C) -> ((exists F (r1_rlvect_1(E,F) & A = k4_rlvect_1(C,D,F) & m1_subset_1(F,u1_struct_0(C)))) <-> r2_hidden(A,k3_rmod_2(B,C,D,E))))))))))) # label(t57_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3147 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> ((all D (m1_subset_1(D,u1_struct_0(B)) -> r1_rlvect_1(C,D))) -> B = C))))))) # label(t40_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3148 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r1_rlvect_1(D,C) -> r1_rlvect_1(D,k5_rlvect_1(B,C))))))))))) # label(t30_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3149 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,k6_rlvect_1(B,C,D)) <-> (exists F (r2_hidden(D,F) & r2_hidden(C,F) & m2_rmod_2(F,A,B,E)))))))))))))) # label(t93_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3150 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> r2_hidden(C,k3_rmod_2(A,B,C,D)))))))))) # label(t59_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3151 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m2_rmod_2(D,A,B,C) -> (D = u1_struct_0(C) <-> v1_rmod_2(D,A,B)))))))))) # label(t82_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3152 $T # label(t52_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3153 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> m1_rmod_2(B,A,B))))) # label(t32_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3154 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_rmod_2(k1_rmod_2(A,B),A,B) & v3_vectsp_2(k1_rmod_2(A,B),A))) # label(dt_k1_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3155 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (r1_rlvect_1(D,C) -> r2_hidden(k5_rlvect_1(B,C),k3_rmod_2(A,B,C,D))))))))))) # label(t71_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3156 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,k6_rlvect_1(B,C,D)) <-> (exists F (m1_subset_1(F,u1_struct_0(B)) & r2_hidden(D,k3_rmod_2(A,B,F,E)) & r2_hidden(C,k3_rmod_2(A,B,F,E))))))))))))))) # label(t76_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3157 $T # label(t56_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3158 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (r1_rlvect_1(E,D) & r1_rlvect_1(E,C) -> r1_rlvect_1(E,k6_rlvect_1(B,C,D))))))))))))) # label(t31_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3159 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_2(E,A,B) -> (all F (m2_rmod_2(F,A,B,E) -> -(r2_hidden(C,F) & (all G (m1_subset_1(G,u1_struct_0(B)) -> -(r1_rlvect_1(E,G) & k6_rlvect_1(B,C,G) = D))) & r2_hidden(D,F)))))))))))))) # label(t92_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3160 $T # label(t55_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3161 (all A (v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (r1_tarski(u1_struct_0(C),u1_struct_0(D)) -> m1_rmod_2(C,A,D)))))))))) # label(t35_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3162 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_2(D,A,B) -> (C = u1_struct_0(D) -> v1_rmod_2(C,A,B)))))))))) # label(t41_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3163 $T # label(t14_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3164 $T # label(t12_rmod_2) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3165 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v12_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t67_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3166 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k2_rmod_3(A,B,D,C) = k2_rmod_3(A,B,C,D))))))))) # label(t18_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3167 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> r2_hidden(B,k3_rmod_3(A,B)))))) # label(t44_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3168 $T # label(t59_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3169 (all A all B all C all D all E (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v4_group_1(B) & v8_vectsp_1(B) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_vectsp_2(C,B) & m1_rmod_2(E,B,C) & m1_rmod_2(D,B,C) & l1_vectsp_2(C,B) & v6_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C) & l3_vectsp_1(B) & v7_vectsp_1(B) & v6_vectsp_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (r2_hidden(A,a_4_0_rmod_3(B,C,D,E)) <-> (exists F exists G (m1_subset_1(G,u1_struct_0(C)) & r1_rlvect_1(E,G) & r1_rlvect_1(D,F) & A = k4_rlvect_1(C,F,G) & m1_subset_1(F,u1_struct_0(C))))))) # label(fraenkel_a_4_0_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3170 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_2(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) -> ((all D (m1_subset_1(D,k3_rmod_3(A,B)) -> (all E (m1_subset_1(E,k3_rmod_3(A,B)) -> (all F (m1_rmod_2(F,A,B) -> (all G (m1_rmod_2(G,A,B) -> (F = D & E = G -> k2_binop_1(k3_rmod_3(A,B),k3_rmod_3(A,B),k3_rmod_3(A,B),C,D,E) = k2_rmod_3(A,B,F,G)))))))))) <-> k6_rmod_3(A,B) = C))))))) # label(d7_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3171 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rmod_3(A,B,C,D) -> k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,D,C)) = k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,C,D))))))))))))) # label(t58_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3172 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C ((all D ((exists E (v3_vectsp_2(E,A) & E = D & m1_rmod_2(E,A,B))) <-> r2_hidden(D,C))) <-> k3_rmod_3(A,B) = C)))))) # label(d3_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3173 $T # label(t45_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3174 (all A (v3_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v15_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t66_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3175 $T # label(t43_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3176 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (k2_rmod_3(A,B,C,D) = k1_rmod_2(A,B) & k1_rmod_3(A,B,C,D) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) <-> r1_rmod_3(A,B,C,D)))))))))) # label(d4_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3177 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_2(C,k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) -> (C = k5_rmod_3(A,B) <-> (all D (m1_subset_1(D,k3_rmod_3(A,B)) -> (all E (m1_subset_1(E,k3_rmod_3(A,B)) -> (all F (m1_rmod_2(F,A,B) -> (all G (m1_rmod_2(G,A,B) -> (D = F & E = G -> k2_binop_1(k3_rmod_3(A,B),k3_rmod_3(A,B),k3_rmod_3(A,B),C,D,E) = k1_rmod_3(A,B,F,G))))))))))))))))) # label(d6_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3178 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (exists F ((exists G (m1_subset_1(G,u1_struct_0(B)) & r1_rlvect_1(C,F) & E = k4_rlvect_1(B,F,G) & r1_rlvect_1(D,G))) & m1_subset_1(F,u1_struct_0(B)))))) <-> k1_rmod_3(A,B,C,D) = B))))))))) # label(t50_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3179 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (r1_rlvect_1(C,E) & r1_rlvect_1(D,E) <-> r1_rlvect_1(k2_rmod_3(A,B,C,D),E))))))))))) # label(t7_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3180 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t63_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3181 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> m1_rmod_2(k1_rmod_3(A,B,C,k2_rmod_3(A,B,D,E)),A,k2_rmod_3(A,B,k1_rmod_3(A,B,D,C),k1_rmod_3(A,B,C,E))))))))))))) # label(t34_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3182 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rlvect_1(D,E) | r1_rlvect_1(C,E) -> r1_rlvect_1(k1_rmod_3(A,B,C,D),E)))))))))))) # label(t6_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3183 (all A all B all C all D (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & m1_rmod_2(C,A,B) & m1_rmod_2(D,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> v3_vectsp_2(k2_rmod_3(A,B,C,D),A) & m1_rmod_2(k2_rmod_3(A,B,C,D),A,B))) # label(dt_k2_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3184 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> D = k1_rmod_3(A,B,k2_rmod_3(A,B,C,D),D))))))))) # label(t30_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3185 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v3_rlvect_1(A) -> (all B (l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m2_rmod_2(E,A,B,C) -> (all F (m2_rmod_2(F,A,B,D) -> (-r1_xboole_0(E,F) -> m2_rmod_2(k5_subset_1(u1_struct_0(B),E,F),A,B,k2_rmod_3(A,B,C,D))))))))))))))) # label(t48_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3186 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> k1_rmod_3(A,B,D,C) = k1_rmod_3(A,B,C,D))))))))) # label(t9_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3187 $T # label(t2_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3188 $T # label(t54_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3189 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> k2_rmod_3(A,B,k1_rmod_2(A,B),C) = k1_rmod_2(A,B) & k1_rmod_2(A,B) = k2_rmod_3(A,B,C,k1_rmod_2(A,B)))))))) # label(t25_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3190 (all A all B (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> v1_funct_1(k5_rmod_3(A,B)) & m2_relset_1(k5_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_2(k5_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)))) # label(dt_k5_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3191 $T # label(t4_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3192 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (r1_rmod_3(A,B,D,E) -> (all F (m1_subset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) -> (r1_rlvect_1(E,k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) & r1_rlvect_1(D,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F)) & C = k4_rlvect_1(B,k2_domain_1(u1_struct_0(B),u1_struct_0(B),F),k3_domain_1(u1_struct_0(B),u1_struct_0(B),F)) <-> F = k4_rmod_3(A,B,C,D,E))))))))))))))) # label(d5_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3193 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(k2_rmod_3(A,B,C,D),A,D) & m1_rmod_2(k2_rmod_3(A,B,C,D),A,C))))))))) # label(t20_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3194 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> v1_funct_1(k6_rmod_3(A,B)) & m2_relset_1(k6_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)) & v1_funct_2(k6_rmod_3(A,B),k2_zfmisc_1(k3_rmod_3(A,B),k3_rmod_3(A,B)),k3_rmod_3(A,B)))) # label(dt_k6_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3195 $T # label(t26_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3196 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) & v3_vectsp_2(E,A) -> (m1_rmod_2(E,A,C) -> k2_rmod_3(A,B,k1_rmod_3(A,B,E,D),C) = k1_rmod_3(A,B,E,k2_rmod_3(A,B,D,C))))))))))))) # label(t36_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3197 (all A all B all C all D all E (v6_rlvect_1(A) & v6_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_2(D,A,B) & m1_rmod_2(E,A,B) & m1_subset_1(C,u1_struct_0(B)) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_rmod_3(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))))) # label(dt_k4_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3198 $T # label(t53_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3199 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(E,A,D) & m1_rmod_2(C,A,D) -> m1_rmod_2(k1_rmod_3(A,B,C,E),A,D)))))))))))) # label(t40_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3200 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> k1_rmod_3(A,B,D,k2_rmod_3(A,B,C,E)) = k2_rmod_3(A,B,k1_rmod_3(A,B,C,D),k1_rmod_3(A,B,D,E))))))))))))) # label(t35_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3201 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (k1_rmod_3(A,B,C,D) = B -> r1_rmod_3(A,B,C,D) | (all E (m1_subset_1(E,u1_struct_0(B)) -> (exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G (m1_subset_1(G,u1_struct_0(B)) & (exists H ((exists I (E = k4_rlvect_1(B,F,G) & r1_rlvect_1(C,F) & r1_rlvect_1(C,H) & -(G = I & H = F) & r1_rlvect_1(D,I) & r1_rlvect_1(D,G) & E = k4_rlvect_1(B,H,I) & m1_subset_1(I,u1_struct_0(B)))) & m1_subset_1(H,u1_struct_0(B))))))))))))))))))) # label(t52_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3202 (all A (v5_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> C = k2_rmod_3(A,B,C,C))))))) # label(t17_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3203 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> k2_rmod_3(A,B,C,k2_rmod_2(A,B)) = C & C = k2_rmod_3(A,B,k2_rmod_2(A,B),C))))))) # label(t27_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3204 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(k2_rmod_3(A,B,C,E),A,k2_rmod_3(A,B,D,E))))))))))))) # label(t22_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3205 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (r1_rmod_3(A,B,C,D) -> r1_rmod_3(A,B,D,C)))))))))) # label(t46_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3206 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(k1_rmod_3(A,B,C,E),A,k1_rmod_3(A,B,D,E))))))))))))) # label(t38_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3207 $T # label(t1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3208 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (v3_vectsp_2(E,A) & m1_rmod_2(E,A,B) -> (u1_struct_0(E) = k3_xboole_0(u1_struct_0(C),u1_struct_0(D)) <-> k2_rmod_3(A,B,C,D) = E))))))))))) # label(d2_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3209 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) & v3_vectsp_2(E,A) -> (a_4_0_rmod_3(A,B,C,D) = u1_struct_0(E) <-> E = k1_rmod_3(A,B,C,D)))))))))))) # label(d1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.56 3210 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> m1_rmod_2(k1_rmod_3(A,B,k2_rmod_3(A,B,C,D),k2_rmod_3(A,B,D,E)),A,k2_rmod_3(A,B,D,k1_rmod_3(A,B,C,E))))))))))))) # label(t32_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3211 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E ((exists F (m1_subset_1(F,u1_struct_0(B)) & (exists G (m1_subset_1(G,u1_struct_0(B)) & r1_rlvect_1(C,F) & k4_rlvect_1(B,F,G) = E & r1_rlvect_1(D,G))))) <-> r1_rlvect_1(k1_rmod_3(A,B,C,D),E))))))))))) # label(t5_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3212 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> r1_rmod_3(A,B,k2_rmod_2(A,B),k1_rmod_2(A,B)) & r1_rmod_3(A,B,k1_rmod_2(A,B),k2_rmod_2(A,B)))))) # label(t47_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3213 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) & v3_vectsp_2(C,A) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> (D = k1_rmod_3(A,B,C,D) <-> C = k2_rmod_3(A,B,C,D)))))))))) # label(t37_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3214 $T # label(t60_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3215 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v3_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> B = k1_rmod_3(A,B,k1_rmod_2(A,B),k2_rmod_2(A,B)) & B = k1_rmod_3(A,B,k2_rmod_2(A,B),k1_rmod_2(A,B)))))) # label(t14_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3216 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_vectsp_2(B,A) -> B = k2_rmod_3(A,B,k2_rmod_2(A,B),k2_rmod_2(A,B)))))) # label(t28_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3217 $T # label(t3_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3218 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(k2_rmod_3(A,B,C,E),A,D)))))))))))) # label(t23_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3219 (all A (v3_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> k1_rmod_3(A,B,k2_rmod_3(A,B,C,D),k2_rmod_3(A,B,D,E)) = k2_rmod_3(A,B,D,k1_rmod_3(A,B,C,E))))))))))))) # label(t33_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3220 $T # label(t62_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3221 (all A (v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> k1_rmod_3(A,B,k1_rmod_3(A,B,C,D),E) = k1_rmod_3(A,B,C,k1_rmod_3(A,B,D,E)))))))))))) # label(t10_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3222 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (r1_rmod_3(A,B,C,D) <-> (all E (m2_rmod_2(E,A,B,C) -> (all F (m2_rmod_2(F,A,B,D) -> (exists G (m1_subset_1(G,u1_struct_0(B)) & k5_subset_1(u1_struct_0(B),E,F) = k6_domain_1(u1_struct_0(B),G)))))))))))))))) # label(t49_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3223 $T # label(t56_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3224 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) -> v14_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t65_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3225 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> k1_rmod_3(A,B,C,k1_rmod_2(A,B)) = C & k1_rmod_3(A,B,k1_rmod_2(A,B),C) = C)))))) # label(t13_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3226 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> -((all E (m1_rmod_2(E,A,B) -> k2_xboole_0(u1_struct_0(C),u1_struct_0(D)) != u1_struct_0(E))) & (m1_rmod_2(D,A,C) | m1_rmod_2(C,A,D))) & -(-m1_rmod_2(C,A,D) & -m1_rmod_2(D,A,C) & (exists E (m1_rmod_2(E,A,B) & k2_xboole_0(u1_struct_0(C),u1_struct_0(D)) = u1_struct_0(E)))))))))))) # label(t41_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3227 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(k2_rmod_3(A,B,C,D),A,k1_rmod_3(A,B,C,D)))))))))) # label(t29_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3228 $T # label(t42_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3229 (all A all B all C all D (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & m1_rmod_2(C,A,B) & m1_rmod_2(D,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> v3_vectsp_2(k1_rmod_3(A,B,C,D),A) & m1_rmod_2(k1_rmod_3(A,B,C,D),A,B))) # label(dt_k1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3230 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,D) -> m1_rmod_2(C,A,k1_rmod_3(A,B,D,E))))))))))))) # label(t39_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3231 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> (m1_rmod_2(C,A,E) & m1_rmod_2(C,A,D) -> m1_rmod_2(C,A,k2_rmod_3(A,B,D,E))))))))))))) # label(t24_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3232 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (v3_vectsp_2(D,A) & m1_rmod_2(D,A,B) -> D = k2_rmod_3(A,B,D,k1_rmod_3(A,B,D,C)))))))))) # label(t31_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3233 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_rmod_2(E,A,B) -> k2_rmod_3(A,B,k2_rmod_3(A,B,C,D),E) = k2_rmod_3(A,B,C,k2_rmod_3(A,B,D,E)))))))))))) # label(t19_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3234 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) -> (all C (m1_rmod_2(C,A,B) -> k1_rmod_3(A,B,k2_rmod_2(A,B),C) = g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) & g1_vectsp_2(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u1_vectsp_2(A,B)) = k1_rmod_3(A,B,C,k2_rmod_2(A,B)))))))) # label(t15_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3235 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> -v1_xboole_0(k3_rmod_3(A,B)))) # label(fc1_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3236 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> (m1_rmod_2(D,A,C) -> D = k2_rmod_3(A,B,D,C)))) & (all D (m1_rmod_2(D,A,B) -> (k2_rmod_3(A,B,D,C) = D -> m1_rmod_2(D,A,C)))))))))) # label(t21_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3237 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_rmod_3(A,B,C,D) -> k3_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,D,C)) = k2_domain_1(u1_struct_0(B),u1_struct_0(B),k4_rmod_3(A,B,E,C,D))))))))))))) # label(t57_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3238 (all A (v5_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> m1_rmod_2(C,A,k1_rmod_3(A,B,C,D)) & m1_rmod_2(D,A,k1_rmod_3(A,B,C,D)))))))))) # label(t11_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3239 $T # label(t61_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3240 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) & v3_vectsp_2(D,A) -> (m1_rmod_2(C,A,D) <-> D = k1_rmod_3(A,B,C,D)))))))))) # label(t12_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3241 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> l3_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v13_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & v10_lattices(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))) & -v3_struct_0(g3_lattices(k3_rmod_3(A,B),k5_rmod_3(A,B),k6_rmod_3(A,B))))))) # label(t64_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3242 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_2(C,A,B) -> (all D (m1_rmod_2(D,A,B) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (all H (m1_subset_1(H,u1_struct_0(B)) -> (all I (m1_subset_1(I,u1_struct_0(B)) -> (r1_rlvect_1(C,F) & r1_rlvect_1(D,I) & r1_rlvect_1(D,G) & r1_rlvect_1(C,H) & E = k4_rlvect_1(B,H,I) & k4_rlvect_1(B,F,G) = E & r1_rmod_3(A,B,C,D) -> F = H & I = G))))))))))))))))))) # label(t51_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3243 $T # label(dt_k3_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3244 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v3_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> k1_rmod_3(A,B,k2_rmod_2(A,B),k2_rmod_2(A,B)) = B)))) # label(t16_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3245 $T # label(t55_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3246 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v3_vectsp_2(C,A) & m1_rmod_2(C,A,B) -> C = k1_rmod_3(A,B,C,C))))))) # label(t8_rmod_3) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3247 $T # label(t39_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3248 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & m1_rmod_4(D,A,B) & m1_rmod_4(C,A,B) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v4_rlvect_1(A) -> (r1_rmod_4(A,B,C,D) -> r1_rmod_4(A,B,D,C)))) # label(symmetry_r1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3249 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> -(D != E & C != E & k1_rmod_4(A,B,k9_rlvect_2(B,C,D,E)) != k4_rlvect_1(B,k4_rlvect_1(B,C,D),E) & C != D))))))))))) # label(t8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3250 (all A all B all C (-v3_struct_0(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_rmod_4(C,A,B) & v6_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> k8_rmod_4(A,B,k8_rmod_4(A,B,C)) = C)) # label(involutiveness_k8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3251 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (v1_funct_2(F,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(F) -> k3_finseq_4(u1_struct_0(B),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,D),D),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,E),E)) = k4_rmod_4(A,B,k3_finseq_4(u1_struct_0(B),C,D,E),F))))))))))))) # label(t36_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3252 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> k6_rmod_4(A,B,C,k8_rmod_4(A,B,D)) = k9_rmod_4(A,B,C,D))))))))) # label(d14_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3253 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k1_rmod_4(A,B,k4_rlvect_2(B,C,D)) = k6_rlvect_1(B,k1_rmod_4(A,B,k2_rlvect_2(B,C,D)),k1_rmod_4(A,B,D)))))))))) # label(t12_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3254 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m2_finseq_1(E,u1_struct_0(B)) -> (all F (v1_funct_1(F) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(A)) -> (k1_funct_1(E,C) = D & r2_hidden(C,k1_relat_1(E)) -> k1_funct_1(k4_rmod_4(A,B,E,F),C) = k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,D),D)))))))))))))) # label(t32_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3255 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (all E (m2_finseq_1(E,u1_struct_0(B)) -> (k3_finseq_1(E) = k3_finseq_1(C) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r2_hidden(F,k1_relat_1(E)) -> k1_funct_1(E,F) = k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,k4_finseq_4(k5_numbers,u1_struct_0(B),C,F)),k4_finseq_4(k5_numbers,u1_struct_0(B),C,F))))) <-> k4_rmod_4(A,B,C,D) = E))))))))))) # label(d8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3256 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> k5_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C)) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),k8_rmod_4(A,B,D),C))))))))) # label(t67_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3257 $T # label(t31_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3258 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,D,k7_rmod_4(A,B,C,E)),k7_rmod_4(A,B,k1_group_1(A,C,D),E)))))))))))) # label(t64_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3259 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_4(D,A,B) & m1_rmod_4(C,A,B) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> m1_rmod_4(k6_rmod_4(A,B,C,D),A,B))) # label(dt_k6_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3260 (all A (v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (k3_rmod_4(A,B) = C <-> k1_xboole_0 = k2_rmod_4(A,B,C)))))))) # label(d6_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3261 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> a_3_0_rmod_4(A,B,C) = k2_rmod_4(A,B,C))))))) # label(d5_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3262 $T # label(d1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3263 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & m1_rmod_4(C,A,B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v3_rlvect_1(A) -> m1_rmod_4(k8_rmod_4(A,B,C),A,B))) # label(dt_k8_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3264 $T # label(t57_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3265 (all A (-v3_struct_0(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k4_rlvect_1(B,k4_rlvect_1(B,k6_vectsp_2(A,B,C,D),k6_vectsp_2(A,B,C,E)),k6_vectsp_2(A,B,C,F)) = k6_vectsp_2(A,B,C,k9_rlvect_1(B,k3_finseq_4(u1_struct_0(B),D,E,F))))))))))))))) # label(t4_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3266 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k9_rmod_4(A,B,C,C),k3_rmod_4(A,B)))))))) # label(t76_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3267 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_rmod_4(D,A,B) & m1_rmod_4(C,A,B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (r1_rmod_4(A,B,C,D) <-> C = D))) # label(redefinition_r1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3268 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> k1_rmod_4(A,B,k2_rlvect_2(B,C,D)) = k6_rlvect_1(B,k4_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,D)),k1_rmod_4(A,B,k3_rlvect_2(B,C,D))))))))))) # label(t10_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3269 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all C (m1_rmod_4(C,A,B) -> m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A))))))) # label(dt_m1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3270 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & m1_rmod_4(D,A,B) & m1_subset_1(C,u1_struct_0(A)) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) -> m1_rmod_4(k7_rmod_4(A,B,C,D),A,B))) # label(dt_k7_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3271 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,k4_rlvect_1(A,C,D),E),k6_rmod_4(A,B,k7_rmod_4(A,B,C,E),k7_rmod_4(A,B,D,E))))))))))))) # label(t62_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3272 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k6_rmod_4(A,B,k3_rmod_4(A,B),C),C) & r1_rmod_4(A,B,k6_rmod_4(A,B,C,k3_rmod_4(A,B)),C))))))) # label(t55_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3273 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_rmod_4(E,A,B) -> (k8_rlvect_2(B,C,D) = k2_rmod_4(A,B,E) -> C = D | k4_rlvect_1(B,k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,D),D)) = k5_rmod_4(A,B,E)))))))))))) # label(t47_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3274 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (C != D -> k1_rmod_4(A,B,k8_rlvect_2(B,C,D)) = k4_rlvect_1(B,C,D)))))))))) # label(t7_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3275 $T # label(t17_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3276 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k1_rmod_4(A,B,k4_rlvect_2(B,C,D)) = k6_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,k3_rlvect_2(B,C,D))))))))))) # label(t13_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3277 $T # label(t23_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3278 $T # label(t71_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3279 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_vectsp_2(A,B,C,k9_rlvect_1(B,k6_finseq_1(u1_struct_0(B)))) = k1_rlvect_1(B))))))) # label(t2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3280 $T # label(t48_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3281 $T # label(d2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3282 (all A all B all C (v3_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists D m2_rmod_4(D,A,B,C)))) # label(existence_m2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3283 $T # label(t29_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3284 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_rmod_4(A,B,C) = D <-> (exists E (m2_finseq_1(E,u1_struct_0(B)) & k2_relat_1(E) = C & k9_rlvect_1(B,E) = D & v2_funct_1(E)))))))))))) # label(d3_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3285 $T # label(t24_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3286 (all A (v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> k1_rmod_4(A,B,k5_rlvect_2(B,C,D)) = k6_rlvect_1(B,k1_rmod_4(A,B,k2_rlvect_2(B,C,D)),k1_rmod_4(A,B,k3_rlvect_2(B,C,D))))))))))) # label(t14_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3287 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m2_rmod_4(D,A,B,k7_rlvect_2(B,C)) -> k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),C) = k5_rmod_4(A,B,D))))))))) # label(t43_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3288 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> k5_rmod_4(A,B,k3_rmod_4(A,B)) = k1_rlvect_1(B))))) # label(t41_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3289 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E))) <-> r1_rmod_4(A,B,C,D)))))))))) # label(d10_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3290 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> k1_rmod_4(A,B,k1_pre_topc(B)) = k1_rlvect_1(B))))) # label(t5_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3291 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> r1_rmod_4(A,B,k6_rmod_4(A,B,C,D),k6_rmod_4(A,B,D,C)))))))))) # label(t53_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3292 (all A (-v3_struct_0(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> ((all F (m1_subset_1(F,u1_struct_0(B)) -> k1_group_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F),C) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,F))) <-> k7_rmod_4(A,B,C,D) = E))))))))))) # label(d12_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3293 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D != C -> (all E (m2_rmod_4(E,A,B,k8_rlvect_2(B,C,D)) -> k5_rmod_4(A,B,E) = k4_rlvect_1(B,k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,D),D))))))))))))) # label(t44_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3294 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> (m2_rmod_4(D,A,B,C) & m2_rmod_4(E,A,B,C) -> m2_rmod_4(k9_rmod_4(A,B,D,E),A,B,C)))))))))))) # label(t75_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3295 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m2_rmod_4(k3_rmod_4(A,B),A,B,C))))))) # label(t26_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3296 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & -v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> k5_rmod_4(A,B,k9_rmod_4(A,B,C,D)) = k6_rlvect_1(B,k5_rmod_4(A,B,C),k5_rmod_4(A,B,D)))))))))) # label(t80_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.57 3297 (all A all B all C all D (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & m1_rmod_4(D,A,B) & m1_rmod_4(C,A,B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> m1_rmod_4(k9_rmod_4(A,B,C,D),A,B))) # label(dt_k9_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3298 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> k2_rmod_4(A,B,k8_rmod_4(A,B,C)) = k2_rmod_4(A,B,C))))))) # label(t69_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3299 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (all E (m2_finseq_1(E,u1_struct_0(B)) -> ((all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (k1_funct_1(E,F) = G & r2_hidden(F,k1_relat_1(D)) -> k1_funct_1(D,F) = k6_vectsp_2(A,B,C,G)))))) & k3_finseq_1(D) = k3_finseq_1(E) -> k9_rlvect_1(B,D) = k6_vectsp_2(A,B,C,k9_rlvect_1(B,E))))))))))))) # label(t1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3300 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> k5_rmod_4(A,B,k6_rmod_4(A,B,C,D)) = k4_rlvect_1(B,k5_rmod_4(A,B,C),k5_rmod_4(A,B,D)))))))))) # label(t77_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3301 (all A (v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v2_vectsp_2(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v7_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D != k1_rlvect_1(A) -> k2_rmod_4(A,B,C) = k2_rmod_4(A,B,k7_rmod_4(A,B,D,C))))))))))) # label(t59_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3302 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(C) -> k6_finseq_1(u1_struct_0(B)) = k4_rmod_4(A,B,k6_finseq_1(u1_struct_0(B)),C))))))) # label(t33_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3303 (all A all B all C (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k1_rmod_4(A,B,C),u1_struct_0(B)))) # label(dt_k1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3304 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> (r1_rmod_4(A,B,k6_rmod_4(A,B,C,D),k3_rmod_4(A,B)) -> r1_rmod_4(A,B,D,k8_rmod_4(A,B,C))))))))))) # label(t68_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3305 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> m2_rmod_4(C,A,B,k2_rmod_4(A,B,C)))))))) # label(t28_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3306 $T # label(t66_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3307 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_rmod_4(A,B,k7_rlvect_2(B,C)) = C)))))) # label(t6_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3308 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_4(D,A,B) -> (r1_tarski(k2_rmod_4(A,B,D),C) <-> m2_rmod_4(D,A,B,C)))))))))) # label(d7_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3309 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m2_rmod_4(C,A,B,k1_subset_1(u1_struct_0(B))) -> C = k3_rmod_4(A,B))))))) # label(t27_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3310 $T # label(t56_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3311 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & m1_rmod_4(C,A,B) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> v1_finset_1(k2_rmod_4(A,B,C)) & m1_subset_1(k2_rmod_4(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3312 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,k1_rlvect_1(A),C),k3_rmod_4(A,B)))))))) # label(t60_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3313 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m2_rmod_4(C,A,B,k1_subset_1(u1_struct_0(B))) -> k1_rlvect_1(B) = k5_rmod_4(A,B,C))))))) # label(t42_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3314 $T # label(t38_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3315 (all A all B all C (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_rmod_4(C,A,B) & v5_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k5_rmod_4(A,B,C),u1_struct_0(B)))) # label(dt_k5_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3316 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> (k2_rmod_4(A,B,D) = k7_rlvect_2(B,C) -> k5_rmod_4(A,B,D) = k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),C)))))))))) # label(t46_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3317 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(D) -> (r1_xboole_0(C,D) -> k1_rmod_4(A,B,k2_rlvect_2(B,C,D)) = k4_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,D))))))))))) # label(t9_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3318 (all A (v3_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,k2_group_1(A),C),C))))))) # label(t65_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3319 $T # label(t21_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3320 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> k8_rmod_4(A,B,C) = k7_rmod_4(A,B,k5_rlvect_1(A,k2_group_1(A)),C))))))) # label(d13_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3321 $T # label(t49_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3322 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (all E (m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(E) -> k8_finseq_1(u1_struct_0(B),k4_rmod_4(A,B,C,E),k4_rmod_4(A,B,D,E)) = k4_rmod_4(A,B,k8_finseq_1(u1_struct_0(B),C,D),E))))))))))) # label(t37_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3323 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m2_rmod_4(E,A,B,C) -> (r1_tarski(C,D) -> m2_rmod_4(E,A,B,D)))))))))))) # label(t25_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3324 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v7_group_1(A) & v6_vectsp_1(A) & -v10_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k5_rmod_4(A,B,k7_rmod_4(A,B,D,C)) = k6_vectsp_2(A,B,D,k5_rmod_4(A,B,C)))))))))) # label(t78_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3325 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> (-r2_hidden(C,k2_rmod_4(A,B,D)) <-> k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C) = k1_rlvect_1(A)))))))))) # label(t20_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3326 $T # label(t16_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3327 (all A all B (v3_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> m1_rmod_4(k3_rmod_4(A,B),A,B))) # label(dt_k3_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3328 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) -> k4_rmod_4(A,B,k2_finseq_4(u1_struct_0(B),C,D),E) = k2_finseq_4(u1_struct_0(B),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C),C),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,D),D)))))))))))) # label(t35_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3329 (all A all B all C (v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all D (m2_rmod_4(D,A,B,C) -> m1_rmod_4(D,A,B))))) # label(dt_m2_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3330 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_rmod_4(D,A,B) -> (m2_rmod_4(D,A,B,C) -> m2_rmod_4(k8_rmod_4(A,B,D),A,B,C)))))))))) # label(t70_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3331 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> k4_rmod_4(A,B,k12_finseq_1(u1_struct_0(B),C),D) = k12_finseq_1(u1_struct_0(B),k6_vectsp_2(A,B,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),C)))))))))) # label(t34_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3332 $T # label(t72_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3333 (all A (v3_rlvect_1(A) & v6_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (k1_rlvect_1(A) != k2_group_1(A) -> ((all D (m2_rmod_4(D,A,B,C) -> r2_hidden(k5_rmod_4(A,B,D),C))) <-> k1_xboole_0 != C & v1_rmod_2(C,A,B))))))))) # label(t40_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3334 $T # label(t18_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3335 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k6_rmod_4(A,B,C,k6_rmod_4(A,B,D,E)),k6_rmod_4(A,B,k6_rmod_4(A,B,C,D),E)))))))))))) # label(t54_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3336 (all A all B all C all D (v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) & m1_finseq_1(C,u1_struct_0(B)) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m2_finseq_1(k4_rmod_4(A,B,C,D),u1_struct_0(B)))) # label(dt_k4_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3337 $T # label(t50_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3338 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> ((all F (m1_subset_1(F,u1_struct_0(B)) -> k4_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F)) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,F))) <-> k6_rmod_4(A,B,C,D) = E))))))))))) # label(d11_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3339 $T # label(t30_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3340 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k1_rmod_4(A,B,k3_rlvect_2(B,C,D)) = k6_rlvect_1(B,k4_rlvect_1(B,k1_rmod_4(A,B,C),k1_rmod_4(A,B,D)),k1_rmod_4(A,B,k2_rlvect_2(B,C,D))))))))))) # label(t11_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3341 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v4_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> (k1_xboole_0 = k2_rmod_4(A,B,C) -> k1_rlvect_1(B) = k5_rmod_4(A,B,C)))))))) # label(t45_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3342 (all A all B (v6_rlvect_1(A) & v4_group_1(A) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists C m1_rmod_4(C,A,B)))) # label(existence_m1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3343 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k5_rmod_4(A,B,C) = D <-> (exists E (m2_finseq_1(E,u1_struct_0(B)) & k9_rlvect_1(B,k4_rmod_4(A,B,E,C)) = D & k2_relat_1(E) = k2_rmod_4(A,B,C) & v2_funct_1(E)))))))))))) # label(d9_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3344 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k4_rlvect_1(B,k6_vectsp_2(A,B,C,D),k6_vectsp_2(A,B,C,E)) = k6_vectsp_2(A,B,C,k9_rlvect_1(B,k2_finseq_4(u1_struct_0(B),D,E))))))))))))) # label(t3_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3345 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C all D (m1_rmod_4(D,A,B) -> ((exists E (k1_rlvect_1(A) != k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) & C = E & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(C,k2_rmod_4(A,B,D))))))))) # label(t19_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3346 (all A all B all C all D (-v3_struct_0(B) & v4_rlvect_1(B) & v4_group_1(B) & v8_vectsp_1(B) & l3_vectsp_1(B) & -v3_struct_0(C) & v3_rlvect_1(C) & v6_rlvect_1(C) & v5_vectsp_2(C,B) & l1_vectsp_2(C,B) & m1_rmod_4(D,B,C) & v5_rlvect_1(C) & v4_rlvect_1(C) & v7_vectsp_1(B) & v6_vectsp_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (r2_hidden(A,a_3_0_rmod_4(B,C,D)) <-> (exists E (k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,E) != k1_rlvect_1(B) & A = E & m1_subset_1(E,u1_struct_0(C))))))) # label(fraenkel_a_3_0_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3347 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) -> (all C (m2_fraenkel(C,u1_struct_0(B),u1_struct_0(A),k1_fraenkel(u1_struct_0(B),u1_struct_0(A))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & (all E (m1_subset_1(E,u1_struct_0(B)) -> (-r2_hidden(E,D) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E) = k1_rlvect_1(A)))) & v1_finset_1(D))) <-> m1_rmod_4(C,A,B)))))))) # label(d4_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3348 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rmod_4(D,A,B) -> r1_tarski(k2_rmod_4(A,B,k7_rmod_4(A,B,C,D)),k2_rmod_4(A,B,D)))))))))) # label(t58_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3349 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> r1_rmod_4(A,B,k7_rmod_4(A,B,C,k6_rmod_4(A,B,D,E)),k6_rmod_4(A,B,k7_rmod_4(A,B,C,D),k7_rmod_4(A,B,C,E))))))))))))) # label(t63_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3350 (all A all B all C all D (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v5_rlvect_1(B) & v5_vectsp_2(B,A) & l1_vectsp_2(B,A) & m1_rmod_4(C,A,B) & m1_rmod_4(D,A,B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> r1_rmod_4(A,B,C,C))) # label(reflexivity_r1_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3351 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_rmod_4(C,A,B) -> (all D (m1_rmod_4(D,A,B) -> r1_tarski(k2_rmod_4(A,B,k9_rmod_4(A,B,C,D)),k2_rlvect_2(B,k2_rmod_4(A,B,C),k2_rmod_4(A,B,D))))))))))) # label(t74_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3352 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v2_vectsp_2(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v3_rlvect_1(B) -> (all C (m1_rmod_4(C,A,B) -> k5_rlvect_1(B,k5_rmod_4(A,B,C)) = k5_rmod_4(A,B,k8_rmod_4(A,B,C)))))))) # label(t79_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3353 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) -> (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k4_rlvect_1(B,k1_rmod_4(A,B,k4_rlvect_2(B,C,D)),k1_rmod_4(A,B,k4_rlvect_2(B,D,C))) = k1_rmod_4(A,B,k5_rlvect_2(B,C,D)))))))))) # label(t15_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3354 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k3_rmod_4(A,B),C) = k1_rlvect_1(A))))))) # label(t22_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3355 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v6_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m1_rmod_4(E,A,B) -> (m2_rmod_4(E,A,B,D) -> m2_rmod_4(k7_rmod_4(A,B,C,E),A,B,D)))))))))))) # label(t61_rmod_4) # label(axiom) # label(non_clause). [assumption]. 115.49/115.58 3356 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & l1_vectsp_2(B,A) & v5_vectsp_2(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_rmod_4(D,A,B) -> (all E (m1_rmod_4(E,A,B) -> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k9_rmod_4(A,B,D,E),C) = k6_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,C),k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C)))))))))))) # label(t73_rmod_4) # label(axiom) # labelAlarm clock 120.04/120.07 Prover9 interrupted 120.04/120.07 EOF