0.12/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.35 % Computer : n019.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 17:26:38 EDT 2019 0.14/0.35 % CPUTime : 4.58/4.67 ============================== Prover9 =============================== 4.58/4.67 Prover9 (32) version 2009-11A, November 2009. 4.58/4.67 Process 32454 was started by sandbox on n019.cluster.edu, 4.58/4.67 Thu Aug 29 17:26:42 2019 4.58/4.67 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_32300_n019.cluster.edu". 4.58/4.67 ============================== end of head =========================== 4.58/4.67 4.58/4.67 ============================== INPUT ================================= 4.58/4.67 4.58/4.67 % Reading from file /tmp/Prover9_32300_n019.cluster.edu 4.58/4.67 4.58/4.67 set(prolog_style_variables). 4.58/4.67 set(auto2). 4.58/4.67 % set(auto2) -> set(auto). 4.58/4.67 % set(auto) -> set(auto_inference). 4.58/4.67 % set(auto) -> set(auto_setup). 4.58/4.67 % set(auto_setup) -> set(predicate_elim). 4.58/4.67 % set(auto_setup) -> assign(eq_defs, unfold). 4.58/4.67 % set(auto) -> set(auto_limits). 4.58/4.67 % set(auto_limits) -> assign(max_weight, "100.000"). 4.58/4.67 % set(auto_limits) -> assign(sos_limit, 20000). 4.58/4.67 % set(auto) -> set(auto_denials). 4.58/4.67 % set(auto) -> set(auto_process). 4.58/4.67 % set(auto2) -> assign(new_constants, 1). 4.58/4.67 % set(auto2) -> assign(fold_denial_max, 3). 4.58/4.67 % set(auto2) -> assign(max_weight, "200.000"). 4.58/4.67 % set(auto2) -> assign(max_hours, 1). 4.58/4.67 % assign(max_hours, 1) -> assign(max_seconds, 3600). 4.58/4.67 % set(auto2) -> assign(max_seconds, 0). 4.58/4.67 % set(auto2) -> assign(max_minutes, 5). 4.58/4.67 % assign(max_minutes, 5) -> assign(max_seconds, 300). 4.58/4.67 % set(auto2) -> set(sort_initial_sos). 4.58/4.67 % set(auto2) -> assign(sos_limit, -1). 4.58/4.67 % set(auto2) -> assign(lrs_ticks, 3000). 4.58/4.67 % set(auto2) -> assign(max_megs, 400). 4.58/4.67 % set(auto2) -> assign(stats, some). 4.58/4.67 % set(auto2) -> clear(echo_input). 4.58/4.67 % set(auto2) -> set(quiet). 4.58/4.67 % set(auto2) -> clear(print_initial_clauses). 4.58/4.67 % set(auto2) -> clear(print_given). 4.58/4.67 assign(lrs_ticks,-1). 4.58/4.67 assign(sos_limit,10000). 4.58/4.67 assign(order,kbo). 4.58/4.67 set(lex_order_vars). 4.58/4.67 clear(print_given). 4.58/4.67 4.58/4.67 % formulas(sos). % not echoed (3845 formulas) 4.58/4.67 4.58/4.67 ============================== end of input ========================== 4.58/4.67 4.58/4.67 % From the command line: assign(max_seconds, 180). 4.58/4.67 4.58/4.67 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 4.58/4.67 4.58/4.67 % Formulas that are not ordinary clauses: 4.58/4.67 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 3 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 4 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 5 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 6 (all A all B k2_tarski(A,B) = k2_tarski(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 7 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 8 (all A all B ((all C ((exists D (r2_hidden(D,A) & r2_hidden(C,D))) <-> r2_hidden(C,B))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 9 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 10 (all A all B -((all C -((all D -(r2_hidden(D,B) & r2_hidden(D,C))) & r2_hidden(C,B))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 11 (all A all B all C (k2_tarski(A,B) = C <-> (all D (r2_hidden(D,C) <-> A = D | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 13 (all A all B ((exists C ((all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(F,G),C) -> (D = F <-> E = G))) & (all D -(r2_hidden(D,A) & (all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))))))) <-> r2_tarski(A,B))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 14 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 15 (all A all B ((all C (A = C <-> r2_hidden(C,B))) <-> k1_tarski(A) = B)) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 16 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 17 (all A all B (r1_tarski(A,B) <-> (all C (r2_hidden(C,A) -> r2_hidden(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 18 (all A exists B (r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 19 (all A all B all C (p1_s1_tarski(A,B) & p1_s1_tarski(A,C) -> C = B)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 20 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 21 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 23 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 24 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 25 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k5_xboole_0(A,B)) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 26 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 27 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 29 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 30 (all A all B all C (-(r2_hidden(A,B) <-> r2_hidden(A,C)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 31 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 32 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 33 (all A all B (r1_tarski(A,B) & A != B <-> r2_xboole_0(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 34 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 35 (all A all B all C -(r1_xboole_0(A,B) & r2_hidden(C,k2_xboole_0(A,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)) & -(r2_hidden(C,B) & -r2_hidden(C,A)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 36 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 37 (all A all B (-(r1_xboole_0(A,B) & (exists C (r2_hidden(C,A) & r2_hidden(C,B)))) & -(-r1_xboole_0(A,B) & (all C -(r2_hidden(C,A) & r2_hidden(C,B)))))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 38 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 39 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 40 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> A = k5_xboole_0(B,C))) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 41 (all A all B all C (C = k3_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 42 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 43 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 44 (exists A all B (r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B) <-> r2_hidden(B,A))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 45 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,A) | r2_hidden(D,B) <-> r2_hidden(D,C))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 46 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 47 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 48 (all A (k1_xboole_0 = A <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 49 (all A all B (k3_xboole_0(A,B) = k1_xboole_0 <-> r1_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 50 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 51 (all A all B (-(-r1_xboole_0(A,B) & (all C -r2_hidden(C,k3_xboole_0(A,B)))) & -(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 52 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 53 (all A all B (B = A <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 54 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 55 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 56 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 57 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (r2_hidden(A,f1_s2_xboole_0) <-> p1_s2_xboole_0(A))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 58 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (r2_hidden(D,A) & -r2_hidden(D,B) <-> r2_hidden(D,C))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 59 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 60 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 61 (all A (v1_xboole_0(A) -> k1_xboole_0 = A)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 62 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 63 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 64 (all A k3_xboole_0(A,k1_xboole_0) = k1_xboole_0) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 65 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 66 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 67 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 68 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 69 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 70 (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]. 4.58/4.67 71 (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]. 4.58/4.67 72 (all A k4_enumset1(A,A,A,A,A,A) = k1_tarski(A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 73 (all A all B all C all D (k1_enumset1(A,B,C) = D <-> (all E (-(E != A & C != E & B != E) <-> r2_hidden(E,D))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 74 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 75 (all A all B k2_tarski(A,B) = k2_enumset1(A,A,A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 76 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 77 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 78 (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]. 4.58/4.67 79 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 80 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D))) # label(t45_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 81 (all A all B all C k1_enumset1(A,B,C) = k3_enumset1(A,A,A,B,C)) # label(t78_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 82 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 83 (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]. 4.58/4.67 84 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 85 (all A all B all C all D all E all F all G all H all I ((all J (r2_hidden(J,I) <-> -(A != J & J != B & J != C & E != J & J != G & J != H & F != J & J != D))) <-> k6_enumset1(A,B,C,D,E,F,G,H) = I)) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 86 (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]. 4.58/4.67 87 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 88 (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]. 4.58/4.67 89 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 90 (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]. 4.58/4.67 91 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 92 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F))) # label(t54_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 93 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 94 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 95 (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]. 4.58/4.67 96 (all A k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 97 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 98 (all A all B all C all D all E all F all G all H k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t64_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 99 (all A all B all C k5_enumset1(A,A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t89_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 100 (all A all B k2_tarski(A,B) = k4_enumset1(A,A,A,A,A,B)) # label(t88_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 101 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k6_enumset1(A,A,B,C,D,E,F,G)) # label(t75_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 102 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 103 (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]. 4.58/4.67 104 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D)) # label(t116_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 105 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 106 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(B,A,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 107 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 108 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 109 (all A all B all C all D k2_enumset1(B,D,A,C) = k2_enumset1(A,B,C,D)) # label(t112_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 110 (all A k1_tarski(A) = k3_enumset1(A,A,A,A,A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 111 (all A all B all C all D k2_enumset1(D,C,B,A) = k2_enumset1(A,B,C,D)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 112 (all A k1_tarski(A) = k5_enumset1(A,A,A,A,A,A,A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 113 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 114 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 115 (all A k1_enumset1(A,A,A) = k1_tarski(A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 116 (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]. 4.58/4.67 117 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 118 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 119 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 120 (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]. 4.58/4.67 121 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E))) # label(t50_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 122 (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]. 4.58/4.67 123 (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]. 4.58/4.67 124 (all A all B all C all D k2_enumset1(A,B,D,C) = k2_enumset1(A,B,C,D)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 125 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 126 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 127 (all A all B all C all D all E all F all G k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t60_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 128 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 129 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H))) # label(t68_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 130 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 131 (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]. 4.58/4.67 132 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 133 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k5_enumset1(A,A,A,B,C,D,E)) # label(t80_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 134 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 135 (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]. 4.58/4.67 136 (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]. 4.58/4.67 137 (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]. 4.58/4.67 138 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 139 (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]. 4.58/4.67 140 (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]. 4.58/4.67 141 (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]. 4.58/4.67 142 (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]. 4.58/4.67 143 (all A all B all C all D all E all F k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F)) = k4_enumset1(A,B,C,D,E,F)) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 144 (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]. 4.58/4.67 145 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 146 (all A all B all C k1_enumset1(A,B,C) = k2_enumset1(A,A,B,C)) # label(t71_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 147 (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]. 4.58/4.67 148 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 149 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B))) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 150 (all A all B all C all D all E (k2_enumset1(A,B,C,D) = E <-> (all F (r2_hidden(F,E) <-> -(F != B & C != F & F != D & A != F))))) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 151 (all A all B all C all D all E k6_enumset1(A,A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E)) # label(t86_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 152 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G))) # label(t61_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 153 (all A all B all C all D all E all F all G (k4_enumset1(A,B,C,D,E,F) = G <-> (all H (r2_hidden(H,G) <-> -(A != H & B != H & H != C & D != H & F != H & E != H))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 154 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 155 (all A k1_tarski(A) = k2_enumset1(A,A,A,A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 156 (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]. 4.58/4.67 157 (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]. 4.58/4.67 158 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,C,D,B)) # label(t105_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 159 (all A all B all C all D all E all F all G all H k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 160 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 161 (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]. 4.58/4.67 162 (all A all B k2_tarski(A,B) = k3_enumset1(A,A,A,A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 163 (all A all B all C all D k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D)) = k2_enumset1(A,B,C,D)) # label(t46_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 164 (all A k2_tarski(A,A) = k1_tarski(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 165 (all A all B all C all D all E all F all G all H k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t62_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 166 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 167 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 168 (all A all B all C k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) = k1_enumset1(A,B,C)) # label(t43_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 169 (all A all B all C all D k2_enumset1(A,D,C,B) = k2_enumset1(A,B,C,D)) # label(t107_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 170 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 171 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 172 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 173 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G))) # label(t57_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 174 (all A all B all C all D k2_enumset1(A,B,C,D) = k5_enumset1(A,A,A,A,B,C,D)) # label(t85_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 175 (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]. 4.58/4.67 176 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 177 (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]. 4.58/4.67 178 (all A all B all C all D k2_enumset1(D,B,C,A) = k2_enumset1(A,B,C,D)) # label(t123_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 179 (all A all B k1_enumset1(A,A,B) = k2_tarski(A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 180 (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]. 4.58/4.67 181 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 182 (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]. 4.58/4.67 183 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 184 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 185 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 186 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 187 (all A all B all C k1_enumset1(A,B,C) = k1_enumset1(A,C,B)) # label(t98_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 188 (all A all B all C all D all E all F all G all H ((all I (r2_hidden(I,H) <-> -(I != B & I != E & I != F & I != G & I != D & C != I & I != A))) <-> H = k5_enumset1(A,B,C,D,E,F,G))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 189 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 190 (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]. 4.58/4.67 191 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 192 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 193 (all A all B all C all D all E all F all G k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G))) # label(t59_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 194 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 195 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 196 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.67 197 (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]. 4.58/4.67 198 (all A all B all C all D all E all F ((all G (-(A != G & G != C & D != G & G != E & B != G) <-> r2_hidden(G,F))) <-> k3_enumset1(A,B,C,D,E) = F)) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 199 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 200 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F))) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 201 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 202 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 203 (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]. 4.58/4.68 204 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 205 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 206 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r2_hidden(C,B) <-> r1_tarski(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 207 (all A all B all C all D -(r1_tarski(k2_tarski(A,B),k2_tarski(C,D)) & A != C & D != A)) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 208 (all A all B all C (k2_zfmisc_1(C,k2_tarski(A,B)) = k2_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(C,k1_tarski(B))) & k2_zfmisc_1(k2_tarski(A,B),C) = k2_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),C)))) # label(t132_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 209 (all A all B -(A != k1_tarski(B) & (all C -(r2_hidden(C,A) & B != C)) & A != k1_xboole_0)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 210 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 211 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) <-> B != A)) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 212 (all A all B all C all D k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D)))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 213 (all A all B (k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0 -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 214 (all A k2_tarski(k1_xboole_0,k1_tarski(A)) = k1_zfmisc_1(k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 215 (all A all B (k1_tarski(A) = k3_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 216 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 217 (all A exists B ((all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C -(r1_tarski(C,B) & -r2_hidden(C,B) & -r2_tarski(C,B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 218 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 219 (all A all B (B != A -> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),k1_tarski(B)))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 220 (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]. 4.58/4.68 221 (all A all B k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t14_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 222 (all A all B all C -(r2_hidden(B,C) & B != A & k1_tarski(A) = k3_xboole_0(k2_tarski(A,B),C))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 223 (all A all B all C all D (B != A -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 224 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 225 (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]. 4.58/4.68 226 (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]. 4.58/4.68 227 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(k1_xboole_0 != A & k1_tarski(B) != A & k1_tarski(C) != A & A != k2_tarski(B,C)))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 228 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) <-> -r2_hidden(B,C) & -r2_hidden(A,C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 229 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & B != C & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 230 (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]. 4.58/4.68 231 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 232 (all A all B (-r2_hidden(A,B) <-> k1_tarski(A) = k4_xboole_0(k1_tarski(A),B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 233 (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]. 4.58/4.68 234 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,B))) & (all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) -> B = A)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 235 (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]. 4.58/4.68 236 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) <-> -r2_hidden(A,C) & (r2_hidden(B,C) | B = A))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 237 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 238 (all A all B all C all D all E -(r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))) & (all F all G -(r2_hidden(F,k3_xboole_0(B,D)) & r2_hidden(G,k3_xboole_0(C,E)) & A = k4_tarski(F,G))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 239 (all A all B (r2_hidden(A,B) -> k1_tarski(A) = k3_xboole_0(B,k1_tarski(A)))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 240 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k2_tarski(B,C) & A != k1_tarski(C) & A != k1_tarski(B) & A != k1_xboole_0))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 241 (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]. 4.58/4.68 242 (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]. 4.58/4.68 243 (all A all B all C k2_zfmisc_1(k2_zfmisc_1(A,B),C) = k3_zfmisc_1(A,B,C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 244 (all A all B all C -(k1_tarski(A) = k2_xboole_0(B,C) & -(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_xboole_0 = C & k1_tarski(A) = B) & -(k1_tarski(A) = B & C = k1_tarski(A)))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 245 (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]. 4.58/4.68 246 (all A all B k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 247 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 248 (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]. 4.58/4.68 249 (all A all B all C ((all D ((exists E exists F (r2_hidden(E,A) & D = k4_tarski(E,F) & r2_hidden(F,B))) <-> r2_hidden(D,C))) <-> k2_zfmisc_1(A,B) = C)) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 250 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 251 (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]. 4.58/4.68 252 (all A all B k2_tarski(A,B) = k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B)))) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 253 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> B = k2_xboole_0(k2_tarski(A,C),B))) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 254 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 255 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 256 (all A all B all C (k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) = k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) & k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) = k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 257 (all A all B all C all D (k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B) -> D = B & A = C | B = k1_xboole_0 | A = k1_xboole_0)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 258 (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]. 4.58/4.68 259 (all A all B all C (k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k4_xboole_0(A,B),C))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 260 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 261 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) | k1_xboole_0 = k4_xboole_0(k1_tarski(A),B))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 262 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 263 (all A all B -(A != k1_tarski(B) & A != k1_xboole_0 & k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 264 (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]. 4.58/4.68 265 (all A all B all C all D (r2_hidden(B,D) & A = C <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 266 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 267 (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]. 4.58/4.68 268 (all A all B all C all D -(k2_tarski(A,B) = k2_tarski(C,D) & A != C & D != A)) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 269 (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]. 4.58/4.68 270 (all A all B (k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 271 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 272 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 273 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 274 (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]. 4.58/4.68 275 (all A all B (A = k1_xboole_0 | k1_xboole_0 = B <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 276 (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]. 4.58/4.68 277 (all A all B all C all D all E all F ((all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 278 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(k4_tarski(E,F) = D & r2_hidden(F,C) & r2_hidden(E,B))) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 279 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 280 (all A all B k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A)) # label(t19_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 281 (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]. 4.58/4.68 282 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 283 (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]. 4.58/4.68 284 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k1_tarski(A),B) = B)) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 285 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 286 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 287 (all A all B -(B = A & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 288 (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]. 4.58/4.68 289 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> k2_zfmisc_1(A,B) = k1_xboole_0 | r1_tarski(A,C) & r1_tarski(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 290 (all A all B all C -(A != B & A != C & r1_tarski(k1_tarski(A),k2_tarski(B,C)))) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 291 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 292 (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]. 4.58/4.68 293 (all A all B (k2_zfmisc_1(B,A) = k2_zfmisc_1(A,B) -> A = B | B = k1_xboole_0 | A = k1_xboole_0)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 294 (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]. 4.58/4.68 295 (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]. 4.58/4.68 296 (all A all B all C -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D all E A != k4_tarski(D,E)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 297 (all A all B (r1_xboole_0(k1_tarski(A),B) | k1_tarski(A) = k3_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 298 (all A all B ((all C all D (r2_hidden(D,k2_xboole_0(A,B)) & r2_hidden(C,k2_xboole_0(A,B)) -> D = C | r1_xboole_0(C,D))) -> k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_xboole_0(A,B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 299 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 300 (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]. 4.58/4.68 301 (all A all B all C -((r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C))) & -r1_tarski(B,C) & k1_xboole_0 != A)) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 302 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 303 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> k1_xboole_0 = A)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 304 (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]. 4.58/4.68 305 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 306 (all A all B (-r2_hidden(B,A) <-> k4_xboole_0(A,k1_tarski(B)) = A)) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 307 (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]. 4.58/4.68 308 (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]. 4.58/4.68 309 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 310 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 311 (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]. 4.58/4.68 312 (all A all B all C (k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 313 (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]. 4.58/4.68 314 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 315 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 316 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 317 (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]. 4.58/4.68 318 (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]. 4.58/4.68 319 (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]. 4.58/4.68 320 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 321 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 322 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 323 (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]. 4.58/4.68 324 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 325 (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]. 4.58/4.68 326 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 327 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 328 (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]. 4.58/4.68 329 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 330 (all A all B all C (k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k3_xboole_0(A,B)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 331 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 332 (all A all B all C k1_xboole_0 != k2_xboole_0(k2_tarski(A,B),C)) # label(t50_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 333 (all A all B k2_xboole_0(A,B) = k3_tarski(k2_tarski(A,B))) # label(t93_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 334 (all A all B (A = k1_xboole_0 | k1_tarski(B) = A <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 335 (all A all B all C (r2_hidden(A,B) -> k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B) | C != A & r2_hidden(C,B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 336 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 337 (all A all B all C all D (k4_tarski(A,B) = k4_tarski(C,D) -> A = C & B = D)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 338 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 339 (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]. 4.58/4.68 340 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(B,C)) & r2_hidden(A,k2_zfmisc_1(D,E)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 341 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 342 (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]. 4.58/4.68 343 (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]. 4.58/4.68 344 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0 <-> r2_hidden(A,C) & r2_hidden(B,C))) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 345 (all A all B all C (k2_tarski(A,B) = k3_xboole_0(k2_tarski(A,B),C) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 346 (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]. 4.58/4.68 347 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 348 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k4_xboole_0(k2_tarski(A,B),C) != k2_tarski(A,B) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 349 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))) <-> C = A & B = D)) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 350 (all A all B k2_xboole_0(k1_tarski(A),B) != k1_xboole_0) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 351 (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]. 4.58/4.68 352 (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]. 4.58/4.68 353 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D)) # label(d4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 354 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (B = k2_subset_1(A) <-> r1_tarski(k3_subset_1(A,B),B)))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 355 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k4_subset_1(A,B,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 356 (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]. 4.58/4.68 357 (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]. 4.58/4.68 358 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 359 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -((all C (m1_subset_1(C,A) -> -r2_hidden(C,B))) & k1_xboole_0 != B))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 360 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 361 (all A all B (m1_subset_1(B,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 362 (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]. 4.58/4.68 363 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,C,B) = k5_subset_1(A,B,C))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 364 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,C) & r2_hidden(E,D)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 365 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 366 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 367 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 368 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 369 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,D) | r2_hidden(E,C) <-> r2_hidden(E,B)))) -> k4_subset_1(A,C,D) = B))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 370 (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]. 4.58/4.68 371 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = k7_subset_1(A,C,B))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 372 (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]. 4.58/4.68 373 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 374 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_xboole_0(A,B) = k3_subset_1(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 375 (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]. 4.58/4.68 376 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_zfmisc_1(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 377 (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]. 4.58/4.68 378 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) <-> r1_tarski(B,C)))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 379 (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]. 4.58/4.68 380 (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]. 4.58/4.68 381 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 382 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r1_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 383 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 384 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 385 (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]. 4.58/4.68 386 (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]. 4.58/4.68 387 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 388 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k3_xboole_0(B,C) = k5_subset_1(A,B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 389 (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]. 4.58/4.68 390 (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]. 4.58/4.68 391 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (B = k1_subset_1(A) <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 392 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 393 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 394 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 395 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) & r1_xboole_0(B,C) -> B = k3_subset_1(A,C)))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 396 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k1_xboole_0 != A -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 397 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 398 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (A != k1_xboole_0 -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 399 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f2_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f3_s4_subset_1)))) -> f3_s4_subset_1 = f2_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 400 (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]. 4.58/4.68 401 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 402 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 403 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 404 (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]. 4.58/4.68 405 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))) = k3_subset_1(A,k7_subset_1(A,B,C)))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 406 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 407 (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]. 4.58/4.68 408 (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]. 4.58/4.68 409 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 410 (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]. 4.58/4.68 411 (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]. 4.58/4.68 412 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 413 (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]. 4.58/4.68 414 (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]. 4.58/4.68 415 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 416 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,k3_subset_1(A,C)) & r2_hidden(B,C)))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 417 (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]. 4.58/4.68 418 (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]. 4.58/4.68 419 (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]. 4.58/4.68 420 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 421 (all A (k1_xboole_0 != A -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 422 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 423 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 424 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 425 (all A (m1_subset_1(A,k1_zfmisc_1(f1_s2_subset_1)) -> (all B (m1_subset_1(B,k1_zfmisc_1(f1_s2_subset_1)) -> ((all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,B)))) & (all C (m1_subset_1(C,f1_s2_subset_1) -> (p1_s2_subset_1(C) <-> r2_hidden(C,A)))) -> B = A))))) # label(s2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 426 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)) & (all B (r2_hidden(B,A) <-> p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1))))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 427 (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]. 4.58/4.68 428 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 429 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_xboole_0(A,B) <-> r2_subset_1(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 430 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 431 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 432 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 433 (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]. 4.58/4.68 434 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 435 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 436 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 437 (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]. 4.58/4.68 438 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 439 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (-r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 440 (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]. 4.58/4.68 441 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 442 (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]. 4.58/4.68 443 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_xboole_0(B,C) = k7_subset_1(A,B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 444 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 445 (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]. 4.58/4.68 446 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(A) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 447 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 448 (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]. 4.58/4.68 449 (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]. 4.58/4.68 450 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 451 (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]. 4.58/4.68 452 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 453 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 454 (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]. 4.58/4.68 455 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,D) <-> r2_hidden(E,C))))) -> B = k7_subset_1(A,C,D)))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 456 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)) & (all B (m1_subset_1(B,f1_s3_subset_1) -> (p1_s3_subset_1(B) <-> r2_hidden(B,A)))))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 457 (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]. 4.58/4.68 458 (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]. 4.58/4.68 459 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,C) & -r2_hidden(E,D)))) -> B = k6_subset_1(A,C,D)))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 460 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 461 (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]. 4.58/4.68 462 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A))) # label(t25_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 463 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 464 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 465 (all A all B (r1_tarski(A,B) <-> m1_subset_1(A,k1_zfmisc_1(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 466 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 467 (all A all B all C -(r2_hidden(A,B) & v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(C)))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 468 (all A all B (m1_subset_1(A,B) -> r2_hidden(A,B) | v1_xboole_0(B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 469 (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]. 4.58/4.68 470 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 471 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 472 (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]. 4.58/4.68 473 (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]. 4.58/4.68 474 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k7_relat_1(A,B) = k1_xboole_0)))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 475 (exists A (-v1_xboole_0(A) & v1_relat_1(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 476 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 477 (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]. 4.58/4.68 478 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 479 (all A all B all C (v1_relat_1(C) -> k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 480 (exists A (v3_relat_1(A) & v1_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 481 (all A (v1_relat_1(A) -> k10_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 482 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 483 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B) <-> r2_hidden(A,k1_relat_1(k7_relat_1(C,B)))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.68 484 (all A k1_xboole_0 = k10_relat_1(k1_xboole_0,A)) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 485 (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]. 4.58/4.69 486 (all A all B (v1_relat_1(B) -> (k9_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 487 (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]. 4.58/4.69 488 (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]. 4.58/4.69 489 (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]. 4.58/4.69 490 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 491 (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]. 4.58/4.69 492 (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]. 4.58/4.69 493 (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]. 4.58/4.69 494 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 495 (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]. 4.58/4.69 496 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 497 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 498 (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]. 4.58/4.69 499 (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]. 4.58/4.69 500 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D)) <-> r2_hidden(k4_tarski(A,B),D) & r2_hidden(A,C)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 501 (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]. 4.58/4.69 502 (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]. 4.58/4.69 503 (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]. 4.58/4.69 504 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 505 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k2_xboole_0(A,B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 506 (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]. 4.58/4.69 507 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k3_relat_1(A)) & r1_tarski(k1_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 508 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 509 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 510 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k9_relat_1(C,B)) <-> (exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(k4_tarski(D,A),C) & r2_hidden(D,B)))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 511 (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]. 4.58/4.69 512 (all A all B (v1_relat_1(B) -> -(r1_tarski(A,k2_relat_1(B)) & k1_xboole_0 = k10_relat_1(B,A) & A != k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 513 (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]. 4.58/4.69 514 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(B)) = k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 515 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 516 (all A (v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B))) <-> r2_hidden(D,C))) <-> k10_relat_1(A,B) = C)))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 517 (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]. 4.58/4.69 518 (all A (v1_relat_1(A) -> k5_relat_1(A,k1_xboole_0) = k1_xboole_0 & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 519 (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]. 4.58/4.69 520 (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]. 4.58/4.69 521 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 522 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 523 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(D,k6_relat_1(C))) <-> r2_hidden(k4_tarski(A,B),D) & r2_hidden(B,C)))) # label(t75_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 524 (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]. 4.58/4.69 525 (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]. 4.58/4.69 526 (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]. 4.58/4.69 527 (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]. 4.58/4.69 528 (all A k1_xboole_0 = k7_relat_1(k1_xboole_0,A)) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 529 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 530 (all A all B all C all D all E (v1_relat_1(E) -> (k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) = E -> k2_relat_1(E) = k2_tarski(B,D) & k1_relat_1(E) = k2_tarski(A,C)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 531 (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]. 4.58/4.69 532 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k1_relat_1(C) = k1_tarski(A) & k2_relat_1(C) = k1_tarski(B)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 533 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 534 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_xboole_0 = A))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 535 (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]. 4.58/4.69 536 (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]. 4.58/4.69 537 (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]. 4.58/4.69 538 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k4_relat_1(A) <-> (all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B)))))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 539 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 540 (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]. 4.58/4.69 541 (all A all B all C (v1_relat_1(C) -> (C = k1_tarski(k4_tarski(A,B)) -> k3_relat_1(C) = k2_tarski(A,B)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 542 (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]. 4.58/4.69 543 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k2_xboole_0(A,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 544 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> r1_tarski(k2_relat_1(A),k1_tarski(k1_xboole_0))))) # label(d15_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 545 (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]. 4.58/4.69 546 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> k7_relat_1(B,A) = B))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 547 (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]. 4.58/4.69 548 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k10_relat_1(C,B)) <-> (exists D (r2_hidden(D,k2_relat_1(C)) & r2_hidden(k4_tarski(A,D),C) & r2_hidden(D,B)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 549 (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]. 4.58/4.69 550 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> B = k1_xboole_0))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 551 (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]. 4.58/4.69 552 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> (k7_relat_1(A,B) = C <-> (all D all E (r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 553 (all A ((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) <-> v1_relat_1(A))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 554 (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]. 4.58/4.69 555 (all A all B (v1_relat_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k7_relat_1(B,A)))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 556 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)) = k7_relat_1(C,k4_xboole_0(A,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 557 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 558 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 559 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 560 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k1_xboole_0 = k5_relat_1(A,B)))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 561 (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]. 4.58/4.69 562 (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]. 4.58/4.69 563 (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]. 4.58/4.69 564 (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]. 4.58/4.69 565 (all A (v1_relat_1(A) -> k2_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k2_relat_1(A) = k1_relat_1(k4_relat_1(A)))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 566 (all A all B (v1_relat_1(B) -> -((all C -r2_hidden(C,k2_relat_1(B))) & r2_hidden(A,k1_relat_1(B))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 567 (all A (v1_relat_1(A) -> k8_relat_1(k1_xboole_0,A) = k1_xboole_0)) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 568 (all A all B (v1_relat_1(B) -> (k7_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 569 (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]. 4.58/4.69 570 (exists A (v1_relat_1(A) & v1_xboole_0(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 571 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 572 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k8_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(B,k8_relat_1(A,C)))))) # label(t139_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 573 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k8_relat_1(B,C))) <-> r2_hidden(A,k2_relat_1(C)) & r2_hidden(A,B)))) # label(t115_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 574 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 575 (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]. 4.58/4.69 576 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E ((exists F (r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B))) <-> r2_hidden(k4_tarski(D,E),C))) <-> C = k5_relat_1(A,B)))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 577 (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]. 4.58/4.69 578 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 579 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 580 (all A (v1_relat_1(A) -> k1_xboole_0 = k7_relat_1(A,k1_xboole_0))) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 581 (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]. 4.58/4.69 582 (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]. 4.58/4.69 583 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (A = k1_relat_1(B) & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k6_relat_1(A) = k5_relat_1(B,D) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 584 (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]. 4.58/4.69 585 (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]. 4.58/4.69 586 (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]. 4.58/4.69 587 (all A (v1_relat_1(A) -> (all B (B = k1_relat_1(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 588 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 589 (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]. 4.58/4.69 590 (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]. 4.58/4.69 591 (all A (v1_relat_1(A) -> k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 592 (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]. 4.58/4.69 593 (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]. 4.58/4.69 594 (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]. 4.58/4.69 595 (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]. 4.58/4.69 596 (all A all B all C (v1_relat_1(C) -> k8_relat_1(A,k7_relat_1(C,B)) = k7_relat_1(k8_relat_1(A,C),B))) # label(t140_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 597 (all A (v1_relat_1(A) -> A = k3_xboole_0(A,k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A))))) # label(t22_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 598 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k4_xboole_0(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 599 (all A (v1_relat_1(A) -> k9_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 600 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 601 (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]. 4.58/4.69 602 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 603 (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]. 4.58/4.69 604 (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]. 4.58/4.69 605 (all A all B (v1_relat_1(A) & v3_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 606 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 607 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 608 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 609 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> A = B))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 610 (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]. 4.58/4.69 611 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k2_relat_1(C))))) # label(t20_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 612 (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]. 4.58/4.69 613 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 614 (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]. 4.58/4.69 615 (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]. 4.58/4.69 616 (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]. 4.58/4.69 617 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 618 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 619 (all A (v1_relat_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))) <-> B = k2_relat_1(A))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 620 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 621 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 622 (all A all B (v1_relat_1(B) -> k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)) = k9_relat_1(B,A))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 623 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k3_relat_1(A),k3_relat_1(B)) = k3_relat_1(k2_xboole_0(A,B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 624 (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]. 4.58/4.69 625 (all A (k1_relat_1(k6_relat_1(A)) = A & k2_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 626 (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]. 4.58/4.69 627 (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]. 4.58/4.69 628 (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]. 4.58/4.69 629 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 630 (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]. 4.58/4.69 631 (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]. 4.58/4.69 632 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_relat_1(A),k2_relat_1(B)) & r1_tarski(k1_relat_1(A),k1_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 633 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 634 (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]. 4.58/4.69 635 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 636 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 637 (all A all B all C (v1_relat_1(C) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 638 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k5_relat_1(A,C),k5_relat_1(B,D))))))))))) # label(t50_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 639 (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]. 4.58/4.69 640 (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]. 4.58/4.69 641 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 642 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C))))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 643 (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]. 4.58/4.69 644 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(C,A) & D = C)) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 645 (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]. 4.58/4.69 646 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 647 (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]. 4.58/4.69 648 (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]. 4.58/4.69 649 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 650 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & k7_relat_1(A,C) = k7_relat_1(B,C) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 651 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(C,B) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 652 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 653 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 654 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 655 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,A))) <-> C = k8_relat_1(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 656 (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]. 4.58/4.69 657 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 658 (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]. 4.58/4.69 659 (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]. 4.58/4.69 660 (all A (v1_relat_1(A) -> (k2_relat_1(A) = k1_xboole_0 | k1_xboole_0 = k1_relat_1(A) -> k1_xboole_0 = A))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 661 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k3_xboole_0(A,B),C) = k8_relat_1(A,k8_relat_1(B,C)))) # label(t127_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 662 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 663 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k8_relat_1(A,B) = B))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 664 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 665 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 666 (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]. 4.58/4.69 667 (all A (v1_relat_1(A) -> (k1_xboole_0 = k1_relat_1(A) <-> k1_xboole_0 = k2_relat_1(A)))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 668 (all A (v1_relat_1(A) -> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 669 (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]. 4.58/4.69 670 (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]. 4.58/4.69 671 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 672 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k10_relat_1(A,k1_relat_1(B)) = k1_relat_1(k5_relat_1(A,B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 673 (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]. 4.58/4.69 674 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(k6_relat_1(A),B),B) & r1_tarski(k5_relat_1(B,k6_relat_1(A)),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 675 (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]. 4.58/4.69 676 (all A all B (v1_relat_1(B) -> k5_relat_1(k6_relat_1(A),B) = k7_relat_1(B,A))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 677 (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]. 4.58/4.69 678 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 679 (all A (v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 680 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 681 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 682 (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]. 4.58/4.69 683 (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]. 4.58/4.69 684 (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]. 4.58/4.69 685 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 686 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 687 (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]. 4.58/4.69 688 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 689 (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]. 4.58/4.69 690 (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]. 4.58/4.69 691 (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]. 4.58/4.69 692 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(B,k10_relat_1(C,A)) = k10_relat_1(k5_relat_1(B,C),A))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 693 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 694 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 695 (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]. 4.58/4.69 696 (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]. 4.58/4.69 697 (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]. 4.58/4.69 698 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 699 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 700 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 701 (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]. 4.58/4.69 702 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k5_relat_1(k6_relat_1(A),C),B) = k1_funct_1(C,B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 703 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 704 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 705 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 706 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 707 (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]. 4.58/4.69 708 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 709 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 710 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 711 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 712 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A))) & k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 713 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_funct_1(k2_funct_1(A)) = A))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 714 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 715 (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]. 4.58/4.69 716 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = C)) <-> B = k6_relat_1(A)))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 717 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 718 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 719 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,A),k2_relat_1(B))))) # label(t12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 720 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 721 (all A all B all C (p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) & r2_hidden(A,f1_s2_funct_1) -> B = C)) & (all A -(r2_hidden(A,f1_s2_funct_1) & (all B -p1_s2_funct_1(A,B)))) -> (exists A (v1_relat_1(A) & f1_s2_funct_1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 722 (all A (k1_xboole_0 != A -> (all B exists C (v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C) & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 723 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 724 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 725 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,D),A))) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> B = k8_relat_1(A,C)))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 726 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_tarski(k1_funct_1(B,A)) = k9_relat_1(B,k1_tarski(A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 727 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 728 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 729 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & A = k5_relat_1(A,B) -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 730 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 731 (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]. 4.58/4.69 732 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 733 (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]. 4.58/4.69 734 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 735 (all A all B k5_relat_1(k6_relat_1(B),k6_relat_1(A)) = k6_relat_1(k3_xboole_0(A,B))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 736 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = B & v2_funct_1(B) & k1_relat_1(B) = A -> C = k6_relat_1(A)))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 737 (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]. 4.58/4.69 738 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k2_relat_1(B)) -> k1_funct_1(k5_relat_1(k2_funct_1(B),B),A) = A & A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A))))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 739 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k1_xboole_0 != k10_relat_1(B,k1_tarski(A))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 740 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & v2_funct_1(C) & r1_tarski(A,k1_relat_1(C)) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 741 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 742 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 743 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(k2_funct_1(A)) = k2_relat_1(A) & k2_relat_1(k2_funct_1(A)) = k1_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 744 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 745 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.69 746 (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]. 4.58/4.69 747 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 748 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 749 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 750 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 751 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A)) & v2_funct_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 752 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 753 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k10_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 754 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 755 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 756 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(D) & k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(C) = A -> C = D))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 757 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 758 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 759 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 760 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 761 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 762 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k2_relat_1(B) & A = k1_relat_1(C) & k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(D) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 763 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k5_relat_1(k2_funct_1(A),A)) & k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 764 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 765 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 766 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 767 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 768 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 769 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 770 (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]. 4.58/4.70 771 (all A (v1_relat_1(A) & v1_funct_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A) & A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 772 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 773 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 774 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 775 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & k5_relat_1(B,A) = k6_relat_1(k2_relat_1(A)) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 776 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),C) <-> r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 777 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k8_relat_1(A,C),B),k9_relat_1(C,B)))) # label(t120_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 778 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 779 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 780 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 781 (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]. 4.58/4.70 782 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(C)) & r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 783 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 784 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))) = k9_relat_1(B,k10_relat_1(B,A)))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 785 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 786 (all A (v1_funct_1(A) <-> (all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> C = D)))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 787 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 788 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 789 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 790 (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]. 4.58/4.70 791 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(A,k10_relat_1(C,B)) = k10_relat_1(k7_relat_1(C,A),B))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 792 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k4_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 793 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 794 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 795 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,A),k1_relat_1(B))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 796 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 797 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 798 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 799 (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]. 4.58/4.70 800 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k2_relat_1(A) <-> (all C (r2_hidden(C,B) <-> (exists D (C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)))))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 801 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 802 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 803 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C)) <-> r2_hidden(B,k1_relat_1(k8_relat_1(A,C)))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 804 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(C = k1_funct_1(B,D) & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 805 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) -> A = B))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 806 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 807 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 808 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 809 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) & k5_relat_1(B,A) = k5_relat_1(C,A) & k1_relat_1(B) = k1_relat_1(C) -> C = B)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 810 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 811 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 812 (exists A (v1_relat_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> f2_s4_funct_1(B) = k1_funct_1(A,B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 813 (all A all B all C (p1_s1_funct_1(A,B) & p1_s1_funct_1(A,C) -> C = B)) -> (exists A ((all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 814 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 815 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 816 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 817 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 818 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 819 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> (r2_hidden(k4_tarski(B,C),A) <-> k1_funct_1(A,B) = C)) & (-r2_hidden(B,k1_relat_1(A)) -> (k1_xboole_0 = C <-> C = k1_funct_1(A,B))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 820 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C all D ((k1_funct_1(A,D) = C & r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(B,C) = D & r2_hidden(C,k2_relat_1(A))) & (r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D -> r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C))) & k2_relat_1(A) = k1_relat_1(B) <-> k2_funct_1(A) = B)))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 821 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 822 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(C) & k1_tarski(A) = k2_relat_1(B) & k2_relat_1(C) = k1_tarski(A) -> C = B))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 823 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_xboole_0(k1_relat_1(C),A) = k1_relat_1(B) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D))) <-> k7_relat_1(C,A) = B))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 824 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 825 (all A all B -(-(k1_xboole_0 != B & k1_xboole_0 = A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> -(B = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 826 (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]. 4.58/4.70 827 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 828 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 829 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(k5_relat_1(B,A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 830 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 831 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 832 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k4_relat_1(A) = k2_funct_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 833 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 834 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(k5_relat_1(B,A)) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 835 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A) = A & k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) = A))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 836 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 837 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 838 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(r2_hidden(B,k2_relat_1(A)) & (all C k10_relat_1(A,k1_tarski(B)) != k1_tarski(C)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 839 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 840 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 841 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 842 (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]. 4.58/4.70 843 (all A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 844 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 845 (all A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A) -> v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 846 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 847 (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]. 4.58/4.70 848 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 849 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 850 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_tarski(A) = k1_relat_1(B) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 851 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 852 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 853 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 854 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k3_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 855 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 856 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 857 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 858 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) & (all D (r2_hidden(D,k1_relat_1(C)) <-> r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)))) -> C = k5_relat_1(A,B)))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 859 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 860 (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]. 4.58/4.70 861 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & k1_relat_1(B) = k2_relat_1(A) & (all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (k1_funct_1(A,C) = D <-> k1_funct_1(B,D) = C))) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 862 (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]. 4.58/4.70 863 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A))))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 864 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) <-> (all B -(v1_xboole_0(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 865 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 866 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 867 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)) & r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 868 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 869 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 870 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 871 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B))))))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 872 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> C = D)) & (all B -(r2_hidden(B,A) & (all C all D k4_tarski(C,D) != B))) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 873 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A))))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 874 (all A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A) -> v1_funct_1(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 875 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k9_relat_1(B,A) = k10_relat_1(k2_funct_1(B),A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 876 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 877 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 878 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 879 (exists A (f1_s3_funct_1 = k1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))) & v1_funct_1(A) & v1_relat_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 880 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 881 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C)) & k8_relat_1(A,C) = k8_relat_1(A,k8_relat_1(B,C))))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 882 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(k5_relat_1(B,A)) & k1_relat_1(A) = k2_relat_1(B) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 883 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 884 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 885 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v1_funct_1(B) & k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,B) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 886 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,A) = k10_relat_1(C,B) -> B = A))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 887 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((all D ((exists E (r2_hidden(E,B) & D = k1_funct_1(A,E) & r2_hidden(E,k1_relat_1(A)))) <-> r2_hidden(D,C))) <-> k9_relat_1(A,B) = C)))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 888 (all A all B (r2_hidden(B,A) -> k1_funct_1(k6_relat_1(A),B) = B)) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 889 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k2_funct_1(B),A) = k10_relat_1(B,A)))) # label(t155_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 890 (all A all B (v1_relat_1(B) -> ((all C -(k1_xboole_0 = k10_relat_1(B,k1_tarski(C)) & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 891 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 892 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,k10_relat_1(C,B))) = k3_xboole_0(k9_relat_1(C,A),B))) # label(t150_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 893 (all A ((all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = A & A = k1_relat_1(C) -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 894 (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]. 4.58/4.70 895 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v1_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 896 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 897 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 898 (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]. 4.58/4.70 899 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 900 (all A all B (k1_ordinal1(B) = k1_ordinal1(A) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 901 (all A (v1_xboole_0(A) -> v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 902 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 903 (exists A (v3_ordinal1(A) & p1_s1_ordinal1(A))) -> (exists A (v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 904 (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]. 4.58/4.70 905 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,B) | r1_ordinal1(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 906 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 907 (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]. 4.58/4.70 908 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 909 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 910 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A))) <-> v1_ordinal1(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 911 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & A != k1_xboole_0))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 912 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 913 (all A ((all B (r2_hidden(B,A) -> r1_tarski(B,A) & v3_ordinal1(B))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 914 (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]. 4.58/4.70 915 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 916 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 917 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 918 (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]. 4.58/4.70 919 k1_relat_1(f3_s3_ordinal1) = f1_s3_ordinal1 & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (B = k2_ordinal1(f3_s3_ordinal1,A) & r2_hidden(A,f1_s3_ordinal1) -> k1_funct_1(f3_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) -> f3_s3_ordinal1 = f4_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 920 (all A (v6_ordinal1(A) & (all B (r2_hidden(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) -> v1_relat_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 921 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 922 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 923 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 924 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 925 (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]. 4.58/4.70 926 (all A (v6_ordinal1(A) <-> (all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r3_xboole_0(B,C))))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 927 (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f2_s5_ordinal1(A)))) & (all A (v3_ordinal1(A) -> (all B (f2_s5_ordinal1(A) = B <-> (exists C (v1_relat_1(C) & f3_s5_ordinal1(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = f3_s5_ordinal1(k2_ordinal1(C,D))))) & A = k1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C))))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> k1_funct_1(f1_s5_ordinal1,A) = f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A))))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 928 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 929 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 930 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(A,B) & B != A & -r2_hidden(B,A)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 931 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 932 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 933 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 934 (exists A (v2_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 935 (all A all B all C all D -(r2_hidden(C,D) & r2_hidden(D,A) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 936 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_funct_1(A) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 937 (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_s4_ordinal1 & (all B (v3_ordinal1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) -> (C = k2_ordinal1(A,B) & r2_hidden(B,f1_s4_ordinal1) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & v5_ordinal1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 938 (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]. 4.58/4.70 939 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 940 (all A all B all C -(r2_hidden(B,C) & r2_hidden(C,A) & r2_hidden(A,B))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 941 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 942 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 943 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(B,A) & r2_hidden(C,A) & -r2_hidden(B,C) & B != C & -r2_hidden(C,B))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 944 (all A (v4_ordinal1(A) <-> k3_tarski(A) = A)) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 945 (all A all B all C all D all E all F -(r2_hidden(F,A) & r2_hidden(E,F) & r2_hidden(D,E) & r2_hidden(C,D) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 946 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v1_ordinal1(C) -> (r2_hidden(C,A) & r2_hidden(A,B) -> r2_hidden(C,B)))))))) # label(t19_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 947 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 948 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_tarski(A,B) <-> r1_ordinal1(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 949 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 950 (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]. 4.58/4.70 951 (exists A (v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 952 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 953 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 954 (all A all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) <-> m1_ordinal1(B,A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 955 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) <-> (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A))))))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 956 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(E,A) & r2_hidden(D,E) & r2_hidden(C,D))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 957 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(A,B) & -r2_xboole_0(B,A) & A != B))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 958 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 959 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 960 (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]. 4.58/4.70 961 (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]. 4.58/4.70 962 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 963 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,k1_ordinal1(B)) <-> r1_ordinal1(A,B)))))) # label(t34_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 964 (all A all B (m1_ordinal1(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 965 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_funct_1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 966 (all A (v3_ordinal1(A) -> -(v4_ordinal1(A) & (exists B (A = k1_ordinal1(B) & v3_ordinal1(B)))) & -((all B (v3_ordinal1(B) -> A != k1_ordinal1(B))) & -v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 967 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 968 (exists A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 969 (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]. 4.58/4.70 970 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 971 (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]. 4.58/4.70 972 (exists A (v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 973 (all A (v2_ordinal1(A) & v1_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 974 (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]. 4.58/4.70 975 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 976 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 977 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 978 (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]. 4.58/4.70 979 (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]. 4.58/4.70 980 (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]. 4.58/4.70 981 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 982 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 983 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(E,D),C))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 984 (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]. 4.58/4.70 985 (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]. 4.58/4.70 986 (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]. 4.58/4.70 987 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 988 (all A all B all C (m2_relset_1(C,B,A) -> k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) = k5_relset_1(B,A,C) & k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 989 (all A all B all C (m2_relset_1(C,A,B) -> (k5_relset_1(A,B,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(E,D),C))))))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.70 990 (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]. 4.58/4.70 991 (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]. 4.58/4.71 992 (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]. 4.58/4.71 993 (all A all B all C (m1_relset_1(C,A,B) -> k4_relat_1(C) = k6_relset_1(A,B,C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 994 (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]. 4.58/4.71 995 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (p1_s1_relset_1(B,C) & r2_hidden(C,f2_s1_relset_1) & r2_hidden(B,f1_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 996 (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]. 4.58/4.71 997 (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]. 4.58/4.71 998 (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]. 4.58/4.71 999 (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]. 4.58/4.71 1000 (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]. 4.58/4.71 1001 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> (r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E)) <-> (exists H (r2_hidden(k4_tarski(H,G),E) & r2_hidden(k4_tarski(F,H),D) & m1_subset_1(H,B)))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1002 (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]. 4.58/4.71 1003 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1004 (all A all B all C (m2_relset_1(C,A,B) -> k10_relset_1(A,B,C,A) = k5_relset_1(A,B,C) & k4_relset_1(A,B,C) = k11_relset_1(A,B,C,B))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1005 (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]. 4.58/4.71 1006 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1007 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1008 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1009 (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]. 4.58/4.71 1010 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1011 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1012 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1013 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> r1_tarski(B,k5_relset_1(B,A,C)) & k4_relset_1(B,A,C) = B))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1014 (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]. 4.58/4.71 1015 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1016 (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]. 4.58/4.71 1017 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,D) = k2_relset_1(A,B,D,C))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1018 (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]. 4.58/4.71 1019 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k11_relset_1(A,C,D,B)) <-> (exists F (r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D) & m1_subset_1(F,C)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1020 (all A all B all C (m2_relset_1(C,B,A) -> (k4_relset_1(B,A,C) = B <-> (all D -(r2_hidden(D,B) & (all E -r2_hidden(k4_tarski(D,E),C))))))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1021 (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]. 4.58/4.71 1022 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1023 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1024 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k1_relset_1(A,B,C,D),A,B))) # label(dt_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1025 (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]. 4.58/4.71 1026 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1027 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1028 (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]. 4.58/4.71 1029 (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]. 4.58/4.71 1030 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1031 (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]. 4.58/4.71 1032 (all A all B all C (m2_relset_1(C,A,B) -> k4_relset_1(B,A,k6_relset_1(A,B,C)) = k5_relset_1(A,B,C) & k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1033 (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]. 4.58/4.71 1034 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1035 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1036 (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]. 4.58/4.71 1037 (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]. 4.58/4.71 1038 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1039 (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]. 4.58/4.71 1040 (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]. 4.58/4.71 1041 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1042 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1043 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1044 (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]. 4.58/4.71 1045 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relset_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1046 (all A all B all C all D (m2_relset_1(D,B,A) -> (r1_tarski(B,C) -> k8_relset_1(B,A,D,C) = D))) # label(t34_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1047 (all A all B all C (m2_relset_1(C,A,B) <-> m1_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1048 (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]. 4.58/4.71 1049 (all A all B all C (r1_tarski(C,k2_zfmisc_1(A,B)) <-> m1_relset_1(C,A,B))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1050 (all A all B all C (m2_relset_1(C,A,B) -> r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A))) # label(t12_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1051 (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]. 4.58/4.71 1052 (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]. 4.58/4.71 1053 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1054 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k3_relset_1(A,B,C,D) = k4_xboole_0(C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1055 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,D) = k1_relset_1(A,B,D,C))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1056 (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]. 4.58/4.71 1057 (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]. 4.58/4.71 1058 (all A all B all C all D (m2_relset_1(D,A,B) -> -(r2_hidden(C,D) & (all E all F -(r2_hidden(F,B) & r2_hidden(E,A) & C = k4_tarski(E,F)))))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1059 (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]. 4.58/4.71 1060 (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]. 4.58/4.71 1061 (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]. 4.58/4.71 1062 (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]. 4.58/4.71 1063 (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]. 4.58/4.71 1064 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k3_xboole_0(C,D) = k2_relset_1(A,B,C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1065 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1066 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> k3_partfun1(D,B,k3_xboole_0(A,C)) = k9_relset_1(B,C,A,k3_partfun1(D,B,C)))) # label(t97_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1067 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1068 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1069 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1070 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & C = k2_xboole_0(A,B))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1071 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1072 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1073 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1074 (all A all B all C (r2_hidden(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t120_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1075 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1076 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1077 (all A all B (m2_relset_1(k1_xboole_0,A,B) & v1_funct_1(k1_xboole_0))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1078 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_tarski(A,C) & r1_tarski(B,D) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1079 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1080 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1081 (all A all B all C (C = k4_partfun1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E (v1_funct_1(E) & r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_relat_1(E))))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1082 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1083 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1084 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k8_relat_1(A,B),B))) # label(t145_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1085 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(k1_funct_1(D,E) = C & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1086 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(C,A),k4_partfun1(C,B)))) # label(t127_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1087 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1088 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1089 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1090 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1091 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1092 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1093 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1094 (all A all B all C (m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) <-> k4_relset_1(A,B,C) = A))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1095 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),C) = k4_relset_1(A,k1_tarski(B),D) -> D = C))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1096 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1097 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1098 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1099 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1100 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1101 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1102 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1103 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1104 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k1_tarski(k1_xboole_0) = k5_partfun1(k1_xboole_0,A,B))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1105 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> (all D (m2_relset_1(D,B,k1_xboole_0) & v1_funct_1(D) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1106 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k3_partfun1(D,k3_xboole_0(A,C),B) = k2_partfun1(A,B,k3_partfun1(D,A,B),C))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1107 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1108 (all A (v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1109 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (v1_relat_1(C) & v1_funct_1(C) -> k2_xboole_0(A,B) != C)) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1110 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k9_relset_1(A,B,C,D)) & m2_relset_1(k9_relset_1(A,B,C,D),A,C))) # label(t45_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1111 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1112 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> k5_relat_1(E,F) = k1_partfun1(A,B,C,D,E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.58/4.71 1113 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k3_partfun1(C,A,B),C))) # label(t76_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1114 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D)) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1115 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & r1_partfun1(C,D) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1116 (all A k6_relat_1(A) = k6_partfun1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1117 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)) & m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1118 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),C,B))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1119 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> k3_partfun1(C,A,B) = C))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1120 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k3_partfun1(E,A,C),k3_partfun1(E,B,D))))) # label(t84_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1121 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E (r2_hidden(E,D) <-> (exists F (v1_funct_1(F) & E = F & v1_partfun1(F,A,B) & r1_partfun1(C,F) & m2_relset_1(F,A,B))))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1122 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1123 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1124 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1125 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) <-> k1_tarski(C) = k5_partfun1(A,B,C)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1126 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1127 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1128 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1129 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1130 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1131 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1132 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & C = k1_funct_1(D,E))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1133 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1134 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k1_xboole_0 = k2_relat_1(B))) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1135 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1136 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_1(k8_relset_1(A,B,D,C)) & m2_relset_1(k8_relset_1(A,B,D,C),A,B))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1137 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1138 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (r1_tarski(B,C) & r1_tarski(A,C) & v1_funct_1(C) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1139 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1140 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1141 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1142 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1143 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1144 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> k1_funct_1(D,C) = B))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1145 (all A all B all C all D (r2_hidden(A,f1_s4_partfun1) & r2_hidden(B,f2_s4_partfun1) & p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) -> D = C)) & (all A all B all C (r2_hidden(B,f2_s4_partfun1) & p1_s4_partfun1(A,B,C) & r2_hidden(A,f1_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) <-> (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(C,f2_s4_partfun1) & r2_hidden(B,f1_s4_partfun1))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1146 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (k4_relset_1(A,B,C) = k4_relset_1(A,B,D) & (all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E)))) -> C = D))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1147 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1148 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1149 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1150 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,D) -> m2_relset_1(C,A,B) & v1_funct_1(C)))))) # label(t33_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1151 (all A all B exists C (m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1152 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> v2_funct_1(B))) # label(t59_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1153 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1154 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (m2_relset_1(D,k1_xboole_0,B) & v1_funct_1(D) -> D = C)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1155 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1156 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1157 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1158 (exists A (v2_funct_1(A) & v1_xboole_0(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1159 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1160 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1161 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1162 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1163 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1164 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1165 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1166 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1167 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s1_partfun1) -> (-p1_s1_partfun1(B) -> k1_funct_1(A,B) = f3_s1_partfun1(B)) & (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)))) & f1_s1_partfun1 = k1_relat_1(A) & v1_funct_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1168 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(C,k6_relat_1(B)))) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1169 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1170 (all A (v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1171 (all A all B all C (p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> C = B)) & (all A all B (p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> r2_hidden(B,f2_s2_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) <-> (exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1))))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1172 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_partfun1(k2_funct_1(C),B,A) = k2_funct_1(k3_partfun1(C,A,B))))) # label(t95_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1173 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1174 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1175 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1176 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k2_xboole_0(A,B) -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,D) = k1_funct_1(B,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1177 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1178 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1179 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1180 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1181 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1182 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1183 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1184 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A ((all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s5_partfun1(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & v1_funct_1(A))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1185 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1186 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1187 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1188 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> B = k1_xboole_0)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1189 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1190 (all A (v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1191 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & r1_tarski(D,k2_zfmisc_1(E,F)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1192 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1193 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(k6_relat_1(A),C))) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1194 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1195 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1196 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1197 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1198 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1199 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1200 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,C)))) # label(t125_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.71 1201 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1202 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1203 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> B = k1_xboole_0)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1204 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1205 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1206 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) & r2_hidden(E,k4_relset_1(A,B,C)) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1207 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1208 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1209 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1210 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t80_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1211 (all A all B k1_xboole_0 = k3_partfun1(k1_xboole_0,A,B)) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1212 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1213 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1214 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t116_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1215 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1216 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1217 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1218 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k1_xboole_0 = B & v1_partfun1(C,A,B) -> k1_xboole_0 = A))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1219 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1220 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1221 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1222 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(v1_partfun1(E,A,B) & r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1223 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1224 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1225 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1226 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1227 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1228 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1229 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1230 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1231 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> (k1_xboole_0 != A -> k5_partfun1(A,k1_xboole_0,B) = k1_xboole_0))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1232 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1233 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1234 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(B,C) & r1_tarski(A,C) -> r1_partfun1(A,B)))))))) # label(t139_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1235 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B)))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1236 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> k1_xboole_0 = A)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1237 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1238 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (v1_partfun1(D,A,B) & r1_partfun1(C,D) & v1_partfun1(C,A,B) -> D = C))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1239 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1240 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1241 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1242 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1243 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1244 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1245 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_tarski(A) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1246 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1247 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1248 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1249 (all A all B r1_tarski(k4_partfun1(k1_xboole_0,A),k4_partfun1(B,A))) # label(t126_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1250 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B))) # label(dt_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1251 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k7_relat_1(k8_relat_1(C,A),B) = k3_partfun1(A,B,C)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1252 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1253 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1254 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(C,A,B),C))) # label(t147_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1255 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1256 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1257 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k2_partfun1(A,B,C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1258 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1259 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1260 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) & r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1261 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1262 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B) & k2_relat_1(B) = k1_xboole_0)) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1263 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1264 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1265 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1266 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> f3_s3_partfun1(B) = k1_funct_1(A,B))) & (all B (r2_hidden(B,f1_s3_partfun1) & p1_s3_partfun1(B) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1267 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1268 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1269 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) <-> r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B)))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1270 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1271 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1272 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1273 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1274 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1275 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1276 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1277 (all A exists B (v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_1(B) & m1_relset_1(B,A,A))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1278 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1279 (all A all B all C all D k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1280 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1281 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D)) = k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1282 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> G = E))))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k8_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | A = k1_xboole_0))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1283 (all A all B all C all D k4_mcart_1(A,B,C,D) = k3_mcart_1(k4_tarski(A,B),C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1284 (all A all B (B = k2_mcart_1(k4_tarski(A,B)) & A = k1_mcart_1(k4_tarski(A,B)))) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1285 (all A all B all C all D -(k1_xboole_0 != B & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> H = F)) <-> F = k9_mcart_1(A,B,C,D,E)))))) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1286 (all A all B all C all D all E k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E)) = k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1287 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k11_mcart_1(A,B,C,D,E),D))) # label(dt_k11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1288 (all A all B all C all D all E all F all G all H (m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(A)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1289 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> I = E))))))))) -> A = k1_xboole_0 | k1_xboole_0 = C | k10_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | B = k1_xboole_0))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1290 (all A -((all B -(r2_hidden(B,A) & (all C all D (r2_hidden(C,D) & r2_hidden(D,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1291 (all A -(k1_xboole_0 != A & (all B -((all C all D all E all F (r2_hidden(C,D) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(D,E) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1292 (all A all B all C -(-(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (k7_mcart_1(A,B,C,D) = E <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> E = H))))))) & k1_xboole_0 != C & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1293 (all A ((exists B exists C A = k4_tarski(B,C)) -> A != k2_mcart_1(A) & k1_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1294 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1295 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1296 (all A all B -(A != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) = C)) & k1_xboole_0 != B)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1297 (all A all B all C (-(-r1_tarski(A,k3_zfmisc_1(A,B,C)) & -r1_tarski(A,k3_zfmisc_1(B,C,A)) & -r1_tarski(A,k3_zfmisc_1(C,A,B))) -> k1_xboole_0 = A)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1298 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1299 (all A all B all C all D -(k1_xboole_0 != A & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) = E)) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1300 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1301 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> k1_xboole_0 = A | F = C & B = E & A = D | k1_xboole_0 = C | k1_xboole_0 = B)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1302 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k10_mcart_1(A,B,C,D,E),C))) # label(dt_k10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1303 (all A all B all C all D all E all F all G all H (r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) <-> r2_hidden(A,E) & r2_hidden(C,G) & r2_hidden(D,H) & r2_hidden(B,F))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1304 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D all E all F -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k4_mcart_1(C,D,E,F))))))) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1305 (all A all B all C k4_tarski(k4_tarski(A,B),C) = k3_mcart_1(A,B,C)) # label(d3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1306 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1307 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> (D = k2_mcart_1(A) | C = k2_mcart_1(A)) & r2_hidden(k1_mcart_1(A),B))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1308 (all A all B all C all D all E all F (r1_tarski(E,F) & r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1309 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> ((all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> I = F)) <-> F = k10_mcart_1(A,B,C,D,E)))))) & D != k1_xboole_0 & k1_xboole_0 != B)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1310 (all A all B all C all D -(A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> E != k8_mcart_1(A,B,C,D,E) & E != k9_mcart_1(A,B,C,D,E) & k10_mcart_1(A,B,C,D,E) != E & k11_mcart_1(A,B,C,D,E) != E)) & D != k1_xboole_0)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1311 (all A all B -(A != k1_xboole_0 & k1_xboole_0 != B & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) != C & k2_mcart_1(C) != C)))) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1312 (all A all B all C all D -(A != k1_xboole_0 & B != k1_xboole_0 & (exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (-(k8_mcart_1(A,B,C,D,E) = F & H = k10_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = I & k9_mcart_1(A,B,C,D,E) = G) & E = k4_mcart_1(F,G,H,I))))) & D != k1_xboole_0 & C != k1_xboole_0)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1313 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k15_mcart_1(A)) & v1_funct_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1314 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) -> k13_mcart_1(A,B,C,D,E,F) = k3_zfmisc_1(D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1315 (all A all B all C -(A != k1_xboole_0 & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k1_mcart_1(k1_mcart_1(D)) = k5_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k2_mcart_1(k1_mcart_1(D)) & k7_mcart_1(A,B,C,D) = k2_mcart_1(D))) & k1_xboole_0 != B)) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1316 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> B = k1_xboole_0 | C = k1_xboole_0 | k1_xboole_0 = D | A = E & F = B & C = G & D = H | A = k1_xboole_0)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1317 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1318 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(k1_xboole_0 != C & (exists E exists F exists G (-(k7_mcart_1(A,B,C,D) = G & F = k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = E) & D = k3_mcart_1(E,F,G))) & B != k1_xboole_0 & k1_xboole_0 != A))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1319 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D),k3_mcart_1(A,C,E),k3_mcart_1(B,C,E)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,E))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1320 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1321 (all A all B all C all D (C != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != B & k1_xboole_0 != A <-> k1_xboole_0 != k4_zfmisc_1(A,B,C,D))) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1322 (all A ((exists B exists C k4_tarski(B,C) = A) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1323 (all A all B all C all D k4_tarski(k3_mcart_1(A,B,C),D) = k4_mcart_1(A,B,C,D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1324 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1325 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> C = k2_mcart_1(A) & r2_hidden(k1_mcart_1(A),B))) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1326 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> (F = k11_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> J = F))))))) & k1_xboole_0 != D & k1_xboole_0 != C)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1327 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k9_mcart_1(A,B,C,D,E),B))) # label(dt_k9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1328 (all A all B all C all D all E k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E)) = k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1329 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1330 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(k1_xboole_0 != B & k1_xboole_0 != D & (exists F exists G exists H exists I (-(k8_mcart_1(A,B,C,D,E) = F & G = k9_mcart_1(A,B,C,D,E) & k10_mcart_1(A,B,C,D,E) = H & k11_mcart_1(A,B,C,D,E) = I) & k4_mcart_1(F,G,H,I) = E)) & C != k1_xboole_0 & A != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1331 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(A,B,C,D))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1332 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1333 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k7_mcart_1(A,B,C,D),C))) # label(dt_k7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1334 (all A all B all C k1_tarski(k3_mcart_1(A,B,C)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1335 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> k4_zfmisc_1(A,B,C,D) = k1_xboole_0 | A = E & F = B & C = G & H = D)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1336 (all A all B all C all D all E -(r2_hidden(A,k4_zfmisc_1(B,C,D,E)) & (all F all G all H all I -(r2_hidden(F,B) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(H,D) & r2_hidden(G,C))))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1337 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> C = k2_mcart_1(A) & B = k1_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1338 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k16_mcart_1(A) = B <-> (all C (r2_hidden(C,k1_relat_1(A)) -> k2_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1339 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1340 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1341 (all A all B all C (r2_hidden(k2_mcart_1(A),C) & r2_hidden(k1_mcart_1(A),B) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E A != k4_tarski(D,E)))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1342 (all A all B all C (k1_xboole_0 != k3_zfmisc_1(A,B,C) <-> k1_xboole_0 != B & k1_xboole_0 != C & A != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1343 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (B = k1_mcart_1(A) | k1_mcart_1(A) = C) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1344 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k16_mcart_1(A)) & v1_relat_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1345 (all A all B (k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) -> B = A)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1346 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (k2_mcart_1(A) = D | E = k2_mcart_1(A)) & (B = k1_mcart_1(A) | k1_mcart_1(A) = C))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1347 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1348 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1349 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(A,D) & -r1_xboole_0(B,E) & -r1_xboole_0(C,F))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1350 (all A all B all C -(A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0 & (exists D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) & (exists E exists F exists G (-(k5_mcart_1(A,B,C,D) = E & F = k6_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = G) & k3_mcart_1(E,F,G) = D)))))) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1351 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k6_mcart_1(A,B,C,D),B))) # label(dt_k6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1352 (all A all B all C all D all E all F k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F)) = k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1353 (all A -(A != k1_xboole_0 & (all B -((all C all D all E all F all G (r2_hidden(G,B) & r2_hidden(F,G) & r2_hidden(E,F) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1354 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> J = E))))))))) -> k1_xboole_0 = B | k1_xboole_0 = D | E = k11_mcart_1(A,B,C,D,F) | k1_xboole_0 = C | k1_xboole_0 = A))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1355 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> m1_subset_1(k5_mcart_1(A,B,C,D),A))) # label(dt_k5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1356 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k4_tarski(k4_tarski(A,B),C),D)) # label(t31_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1357 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> H = E))))))))) -> k1_xboole_0 = D | E = k9_mcart_1(A,B,C,D,F) | k1_xboole_0 = C | B = k1_xboole_0 | k1_xboole_0 = A))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1358 (all A all B all C -(k1_xboole_0 != A & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> (E = k5_mcart_1(A,B,C,D) <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> E = F))))))) & B != k1_xboole_0)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1359 (all A all B all C all D k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D) = k4_zfmisc_1(A,B,C,D)) # label(t53_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1360 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> ((all F all G all H (k3_mcart_1(F,G,H) = D -> G = E)) <-> k6_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != C & A != k1_xboole_0)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1361 (all A all B all C -(A != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1362 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k2_mcart_1(C) & k1_mcart_1(C) != C)))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1363 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> A = D & C = F & E = B | k3_zfmisc_1(A,B,C) = k1_xboole_0)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1364 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> D = H))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k7_mcart_1(A,B,C,E) = D | k1_xboole_0 = A))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1365 (all A -((all B -(r1_xboole_0(B,A) & r2_hidden(B,A))) & A != k1_xboole_0)) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1366 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != B & C != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) & k10_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(E)) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E))))) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1367 (all A all B all C all D all E all F all G all H (m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(A)) -> k4_zfmisc_1(E,F,G,H) = k14_mcart_1(A,B,C,D,E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1368 (all A all B (k3_zfmisc_1(A,A,A) = k3_zfmisc_1(B,B,B) -> A = B)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1369 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(B,F) & -r1_xboole_0(A,E))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1370 (all A all B all C all D all E all F (k3_mcart_1(D,E,F) = k3_mcart_1(A,B,C) -> E = B & F = C & D = A)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1371 (all A all B all C all D all E all F all G all H (k4_mcart_1(E,F,G,H) = k4_mcart_1(A,B,C,D) -> E = A & G = C & D = H & B = F)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1372 (all A all B all C all D all E all F -(k1_xboole_0 != A & C != k1_xboole_0 & (exists G ((exists H (m1_subset_1(H,k3_zfmisc_1(D,E,F)) & -(k6_mcart_1(A,B,C,G) = k6_mcart_1(D,E,F,H) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H) & k5_mcart_1(D,E,F,H) = k5_mcart_1(A,B,C,G)) & G = H)) & m1_subset_1(G,k3_zfmisc_1(A,B,C)))) & k1_xboole_0 != F & E != k1_xboole_0 & k1_xboole_0 != D & B != k1_xboole_0)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1373 (all A all B all C all D k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k4_tarski(A,C),k4_tarski(A,D),k4_tarski(B,C),k4_tarski(B,D))) # label(t25_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1374 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1375 (all A all B all C all D all E ((all F (r2_hidden(F,A) <-> (exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(I,D) & r2_hidden(J,E) & F = k4_mcart_1(G,H,I,J) & r2_hidden(H,C))))) -> A = k4_zfmisc_1(B,C,D,E))) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1376 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = G))))))) -> D = k6_mcart_1(A,B,C,E) | k1_xboole_0 = C | k1_xboole_0 = B | A = k1_xboole_0))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1377 (all A all B all C all D k4_zfmisc_1(A,B,C,D) = k3_zfmisc_1(k2_zfmisc_1(A,B),C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1378 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k1_mcart_1(A) != A & A != k2_mcart_1(A))) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1379 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D -(B = k4_tarski(C,D) & (r2_hidden(C,A) | r2_hidden(D,A)))))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1380 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1381 (all A -((all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(D,E) & r2_hidden(E,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1382 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1383 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B ((all C all D (A = k4_tarski(C,D) -> B = D)) <-> k2_mcart_1(A) = B)))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1384 (all A all B all C all D -(A != k1_xboole_0 & B != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> ((all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> G = F)) <-> F = k8_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != C)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1385 (all A all B all C -(A != k1_xboole_0 & B != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D != k5_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) != D & D != k6_mcart_1(A,B,C,D))) & C != k1_xboole_0)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1386 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k10_mcart_1(A,B,C,D,I),G) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k8_mcart_1(A,B,C,D,I),E)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1387 (all A all B all C all D all E all F all G all H -(k1_xboole_0 != B & D != k1_xboole_0 & G != k1_xboole_0 & (exists I ((exists J (m1_subset_1(J,k4_zfmisc_1(E,F,G,H)) & -(k8_mcart_1(A,B,C,D,I) = k8_mcart_1(E,F,G,H,J) & k9_mcart_1(A,B,C,D,I) = k9_mcart_1(E,F,G,H,J) & k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k11_mcart_1(E,F,G,H,J) = k11_mcart_1(A,B,C,D,I)) & I = J)) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & H != k1_xboole_0 & F != k1_xboole_0 & E != k1_xboole_0 & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1388 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> F = D))))))) -> A = k1_xboole_0 | k1_xboole_0 = C | D = k5_mcart_1(A,B,C,E) | B = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1389 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1390 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))))) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1391 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> k1_mcart_1(A) = B & (D = k2_mcart_1(A) | C = k2_mcart_1(A)))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1392 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> (all G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) -> (r2_hidden(G,k3_zfmisc_1(D,E,F)) -> r2_hidden(k7_mcart_1(A,B,C,G),F) & r2_hidden(k6_mcart_1(A,B,C,G),E) & r2_hidden(k5_mcart_1(A,B,C,G),D)))))))))) # label(t76_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1393 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (k4_tarski(C,D) = A -> C = B)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.72 1394 (all A all B all C all D all E all F (A = k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) = B & D = k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1395 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1396 (all A all B all C all D all E all F all G all H (r1_tarski(A,B) & r1_tarski(C,D) & r1_tarski(G,H) & r1_tarski(E,F) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1397 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k2_mcart_1(A),C) & r2_hidden(k1_mcart_1(A),B))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1398 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> k2_mcart_1(A) = D & (k1_mcart_1(A) = B | k1_mcart_1(A) = C))) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1399 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> r2_hidden(k2_mcart_1(A),C) & k1_mcart_1(A) = B)) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1400 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1401 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> m1_subset_1(k8_mcart_1(A,B,C,D,E),A))) # label(dt_k8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1402 (all A -(A != k1_xboole_0 & (all B -((all C all D all E -(k3_mcart_1(C,D,E) = B & (r2_hidden(D,A) | r2_hidden(C,A)))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1403 (all A all B all C all D k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k4_mcart_1(A,B,C,D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1404 (all A all B all C all D -((all E all F all G -(r2_hidden(E,B) & r2_hidden(F,C) & r2_hidden(G,D) & A = k3_mcart_1(E,F,G))) & r2_hidden(A,k3_zfmisc_1(B,C,D)))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1405 (all A all B all C all D ((all E (r2_hidden(E,A) <-> (exists F exists G exists H (r2_hidden(G,C) & r2_hidden(H,D) & E = k3_mcart_1(F,G,H) & r2_hidden(F,B))))) -> k3_zfmisc_1(B,C,D) = A)) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1406 (all A all B all C all D all E all F (r2_hidden(k3_mcart_1(A,B,C),k3_zfmisc_1(D,E,F)) <-> r2_hidden(A,D) & r2_hidden(B,E) & r2_hidden(C,F))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1407 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) -> m1_subset_1(k13_mcart_1(A,B,C,D,E,F),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))) # label(dt_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1408 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1409 (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]. 4.65/4.73 1410 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (v2_funct_1(B) & B = k4_funct_2(A,C,B) -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1411 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(C,D) = k1_funct_1(B,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1412 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (exists E (k1_funct_1(C,E) != k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,C))))))))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1413 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,D) = k2_funct_2(A,B,C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1414 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1415 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1416 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (p1_s14_funct_2(A,B) & m1_subset_1(B,f2_s14_funct_2))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1417 (all A all B all C (m2_relset_1(C,A,B) -> C = k7_relset_1(A,A,A,B,k6_partfun1(A),C) & C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)))) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1418 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1419 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1420 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1421 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (r2_hidden(k1_funct_1(E,C),D) & r2_hidden(C,A) -> k1_funct_1(E,C) = k1_funct_1(k9_relset_1(A,B,D,E),C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1422 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (v2_funct_1(C) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & k2_relat_1(C) = B -> k1_xboole_0 = A | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1423 (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]. 4.65/4.73 1424 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (k5_funct_2(A,B,C) = C -> B = k6_partfun1(A)))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1425 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1426 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1427 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1428 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1429 (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]. 4.65/4.73 1430 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1431 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1432 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_1(C) & -v1_xboole_0(A) -> k8_funct_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1433 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1434 (all A -((all B -(p1_s1_funct_2(A,B) & r2_hidden(B,f2_s1_funct_2))) & r2_hidden(A,f1_s1_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & (all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1435 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1436 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1437 (all A all B all C all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> B = k1_funct_1(D,C)))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1438 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> ((all D all E (r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) -> D = E)) <-> v2_funct_1(C))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1439 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -(r2_hidden(E,A) & D = k1_funct_1(C,E))))) -> k2_relat_1(C) = B | B = k1_xboole_0))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1440 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1441 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (k2_relat_1(C) = A & k2_relat_1(B) = A -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1442 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1443 (all A all B all C (m1_relset_1(C,A,B) -> (v1_partfun1(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1444 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1445 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (-(B = k1_xboole_0 & A != k1_xboole_0 & k1_xboole_0 != C) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1446 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1447 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | B = k1_xboole_0))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1448 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1449 (all A all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,B,C) & m2_relset_1(F,B,C) -> -((C = k1_xboole_0 -> k1_xboole_0 = B) & (k1_xboole_0 = B -> A = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D)))))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1450 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_2(D,A,C) & v1_funct_1(D) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1451 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v2_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v3_funct_2(C,A,B) & v1_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1452 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r1_partfun1(C,D) & (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> -(r1_partfun1(D,E) & r1_partfun1(C,E)))) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1453 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1454 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (A = k2_relat_1(B) & B = k4_funct_2(A,B,C) -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1455 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1456 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1457 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1458 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C)))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1459 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (v2_funct_1(D) & r2_hidden(C,A) -> C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) | k1_xboole_0 = B))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1460 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> ((all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))) <-> r1_partfun1(C,D))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1461 (all A all B (m2_relset_1(B,A,A) -> B = k7_relset_1(A,A,A,A,k6_partfun1(A),B) & B = k7_relset_1(A,A,A,A,B,k6_partfun1(A)))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1462 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1463 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(C,f2_s6_funct_2) & r2_hidden(B,f1_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_1(A))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1464 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1465 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> f3_s2_funct_2(B) = k1_funct_1(A,B))) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1466 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1467 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> v2_funct_1(C) & k2_relat_1(D) = A | B = k1_xboole_0))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1468 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1469 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1470 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k4_funct_2(A,B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1471 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1472 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1473 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1474 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1475 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1476 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1477 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1478 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> k1_xboole_0 = B | r2_hidden(k1_funct_1(D,C),k2_relat_1(D))))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1479 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1480 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & -v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1481 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1482 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1483 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1484 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1485 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1486 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k3_funct_2(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1487 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1488 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) -> v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1489 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1490 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1491 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E -((all F (m1_subset_1(F,A) -> -(r2_hidden(F,C) & E = k1_funct_1(D,F)))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1492 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1493 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1494 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1495 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1496 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (B = k2_relat_1(D) & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> k1_xboole_0 = C & k1_xboole_0 != B | v2_funct_1(D) & v2_funct_1(E)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1497 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D) | k1_xboole_0 = B & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1498 (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]. 4.65/4.73 1499 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1500 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> k1_funct_1(A,B) = f3_s9_funct_2(B)))) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1501 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_tarski(B,A) -> k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B & B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B))))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1502 (all A all B -((all C -(r2_hidden(C,f3_s5_funct_2) & p1_s5_funct_2(A,B,C))) & r2_hidden(B,f2_s5_funct_2) & r2_hidden(A,f1_s5_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s5_funct_2) & r2_hidden(C,f2_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1503 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1504 (all A all B all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1505 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(C,A) -> r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) | k1_xboole_0 = B & k1_xboole_0 != A))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1506 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1507 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (k2_relat_1(C) = B <-> v2_funct_2(C,A,B)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1508 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1509 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k6_funct_2(A,B) = k2_funct_1(B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1510 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D)))))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1511 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1512 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v1_partfun1(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1513 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1514 (exists A ((all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1515 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> v1_funct_2(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1516 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1517 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1518 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) -> m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1519 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1520 (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]. 4.65/4.73 1521 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1522 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (B = k2_relat_1(D) & k2_relat_1(E) = C -> C = k2_relat_1(k1_partfun1(A,B,B,C,D,E)) | k1_xboole_0 = C | B = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1523 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1524 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(f4_s11_funct_2 != B & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & B != f3_s11_funct_2))) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2 & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1525 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1526 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1527 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1528 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (exists C (v1_funct_2(C,A,A) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_1(C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1529 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> B = k1_xboole_0 & k1_xboole_0 != A | C = D))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1530 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1531 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1532 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1533 (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]. 4.65/4.73 1534 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1535 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1536 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1537 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (B = k2_relat_1(C) <-> (all D -(r2_hidden(D,B) & k3_funct_2(A,B,C,k1_tarski(D)) = k1_xboole_0))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1538 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> k2_partfun1(A,B,D,C) = D))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1539 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1540 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1541 (all A all B all C (C = k1_funct_2(A,B) <-> (all D ((exists E (v1_funct_1(E) & r1_tarski(k2_relat_1(E),B) & A = k1_relat_1(E) & E = D & v1_relat_1(E))) <-> r2_hidden(D,C))))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1542 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> C = D))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1543 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (k2_relat_1(C) = B & v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1544 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1545 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1546 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (k1_xboole_0 != B -> ((all D (k1_xboole_0 != D -> (all E (v1_funct_2(E,B,D) & m2_relset_1(E,B,D) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,D) & m2_relset_1(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> F = E))))))) <-> k2_relat_1(C) = B)))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1547 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (p1_s3_funct_2(A,B) & m1_subset_1(B,f2_s3_funct_2))))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1548 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E k1_tarski(E) != B) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1549 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1550 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1551 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1552 (all A all B all C (m2_relset_1(C,A,B) -> (k1_xboole_0 = B -> k1_xboole_0 = A | (C = k1_xboole_0 <-> v1_funct_2(C,A,B))) & ((k1_xboole_0 = B -> A = k1_xboole_0) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1553 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1554 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1555 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) & v1_funct_1(B) -> v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1556 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1557 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> E = D))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1558 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1559 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(A) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1560 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> A != k1_xboole_0 & B = k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1561 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),C) -> v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) | B = k1_xboole_0 & A != k1_xboole_0))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1562 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> v1_funct_2(k2_partfun1(A,B,D,C),C,B) & m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) | B = k1_xboole_0 & A != k1_xboole_0))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1563 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) & A = k1_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1564 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1565 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -((all E -(k1_funct_1(D,E) = C & r2_hidden(E,A))) & k2_relat_1(D) = B & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1566 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1567 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1568 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_2(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k2_funct_2(k1_xboole_0,A,C,B))) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1569 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1570 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1571 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (k6_partfun1(B) = k1_partfun1(B,A,A,B,D,C) -> B = k2_relat_1(C)))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1572 (all A all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (r2_hidden(E,B) & r2_hidden(D,A) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1573 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & (all B (m1_subset_1(B,f1_s12_funct_2) -> k8_funct_2(f1_s12_funct_2,f2_s12_funct_2,A,B) = f3_s12_funct_2(B))) & m2_relset_1(A,f1_s12_funct_2,f2_s12_funct_2))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1574 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1575 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1576 (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]. 4.65/4.73 1577 (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]. 4.65/4.73 1578 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C & v2_funct_1(E) -> k2_relat_1(D) = B | C = k1_xboole_0))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1579 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> -(B != k1_xboole_0 & -v2_funct_1(C) & (exists D (v1_funct_1(D) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A)))))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1580 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1581 (all A exists B (m1_relset_1(B,A,A) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_relat_1(B))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1582 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1583 (all A all B all C (v1_funct_1(B) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> k5_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1584 (all A all B exists C (v1_funct_1(C) & v1_funct_2(C,A,B) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1585 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1586 (exists A (m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_1(A))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1587 (exists A (m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) = f4_s10_funct_2 & (all B (m1_subset_1(B,f1_s10_funct_2) -> (B != f3_s10_funct_2 -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1588 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E -((all F -(r2_hidden(F,C) & k1_funct_1(D,F) = E & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1589 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) & A = k2_relat_1(B) -> v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1590 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1591 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1592 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (v2_funct_1(B) -> (all C all D (r2_hidden(C,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(D,A) -> D = C))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1593 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1594 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1595 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C) | k1_xboole_0 = B))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1596 (all A all B all C (v1_funct_1(B) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) -> v1_funct_2(k4_funct_2(A,B,C),A,A) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_1(k4_funct_2(A,B,C)))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1597 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (v2_funct_1(B) <-> (all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> C = D))))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1598 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A) & k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1599 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1600 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.73 1601 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (k2_relat_1(C) = B & (all E all F ((r2_hidden(F,A) & E = k1_funct_1(C,F) -> r2_hidden(E,B) & k1_funct_1(D,E) = F) & (F = k1_funct_1(D,E) & r2_hidden(E,B) -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) -> A = k1_xboole_0 | D = k2_funct_1(C) | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1602 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (k2_relat_1(C) = B & v2_funct_1(C) -> k1_xboole_0 = B | k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C) & k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C))))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1603 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | k1_xboole_0 != A & B = k1_xboole_0 | C = k1_xboole_0 & k1_xboole_0 != B))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1604 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k2_relat_1(B) = k2_funct_2(A,A,B,A))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1605 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1606 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1607 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (p1_s7_funct_2(A,B,C) & m1_subset_1(C,f3_s7_funct_2))))))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1608 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (k5_partfun1(A,B,C) = k5_partfun1(A,B,D) & (all E k1_tarski(E) != B) -> D = C))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1609 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1610 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1611 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1612 (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]. 4.65/4.74 1613 (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]. 4.65/4.74 1614 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> -(k1_xboole_0 != A & -(v2_funct_1(C) <-> (all D all E (v1_funct_1(E) & v1_funct_2(E,D,A) & m2_relset_1(E,D,A) -> (all F (m2_relset_1(F,D,A) & v1_funct_2(F,D,A) & v1_funct_1(F) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> F = E)))))) & B != k1_xboole_0))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1615 (all A all B all C (v1_funct_1(k9_funct_2(A,B,C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1616 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1617 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) -> (all D (m2_relset_1(D,A,A) & v1_funct_2(D,A,A) & v1_funct_1(D) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1618 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1619 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_2(B,k1_relat_1(B),A) & m2_relset_1(B,k1_relat_1(B),A) & v1_funct_1(B)))) # label(t4_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1620 (all A all B all C (v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1621 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,C) & E = k1_funct_1(D,F) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1622 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k3_funct_3(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t25_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1623 (all A all B r1_tarski(k2_relat_1(k4_funct_3(A,B)),k2_tarski(np__0,np__1))) # label(t48_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1624 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(k1_funct_3(A),k1_funct_3(B)) = k1_funct_3(k5_relat_1(A,B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1625 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1626 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D all E (r2_hidden(D,k1_relat_1(A)) & r2_hidden(E,k1_relat_1(B)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)) = k1_funct_1(C,k4_tarski(D,E)))) <-> C = k15_funct_3(A,B)))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1627 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k15_funct_3(A,B)) & v1_relat_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1628 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k10_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)) = k2_zfmisc_1(k10_relat_1(C,A),k10_relat_1(D,B)))))) # label(t94_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1629 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> k5_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)) = k13_funct_3(D,E))))) # label(t99_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1630 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1631 (all A all B all C (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1632 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(k5_relat_1(B,C))) & v2_funct_1(C) -> r1_tarski(k10_relat_1(C,A),k2_relat_1(B))))))) # label(t4_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1633 (all A all B -(r2_hidden(B,f2_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(A,f1_s1_funct_3))) & (all A all B all C all D (r2_hidden(A,f1_s1_funct_3) & r2_hidden(B,f2_s1_funct_3) & p1_s1_funct_3(A,B,C) & p1_s1_funct_3(A,B,D) -> D = C)) -> (exists A (k1_relat_1(A) = k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) & (all B all C (r2_hidden(C,f2_s1_funct_3) & r2_hidden(B,f1_s1_funct_3) -> p1_s1_funct_3(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1634 (all A k12_funct_3(A) = k11_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1635 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1636 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_relat_1(k15_funct_3(A,B)) = k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1637 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1638 (all A all B k6_relat_1(k2_zfmisc_1(A,B)) = k13_funct_3(k9_funct_3(A,B),k10_funct_3(A,B))) # label(t73_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1639 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> k16_funct_3(A,B,C,D,E,F) = k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1640 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1641 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k1_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t15_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1642 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1643 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k13_funct_3(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t71_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1644 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) & v1_funct_2(D,A,C) & v1_funct_1(D) -> r1_tarski(k10_relat_1(k1_funct_3(D),B),k1_zfmisc_1(A)))))) # label(t14_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1645 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k6_funct_3(A,B) = k6_relat_1(B))) # label(redefinition_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1646 (all A all B (v1_funct_1(k9_funct_3(A,B)) & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1647 (all A (v1_funct_1(k11_funct_3(A)) & v1_relat_1(k11_funct_3(A)))) # label(dt_k11_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1648 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1649 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> m2_relset_1(k6_funct_3(A,B),B,A) & v1_funct_2(k6_funct_3(A,B),B,A) & v1_funct_1(k6_funct_3(A,B)))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1650 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(k15_funct_3(B,D),k15_funct_3(A,C)) = k15_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t92_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1651 (all A r1_tarski(k2_relat_1(k11_funct_3(A)),k2_zfmisc_1(A,A))) # label(t66_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1652 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (A = k1_relat_1(B) & k1_relat_1(C) = A -> k1_relat_1(k13_funct_3(B,C)) = A))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1653 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k15_funct_3(A,B) = k13_funct_3(k5_relat_1(k9_funct_3(k1_relat_1(A),k1_relat_1(B)),A),k5_relat_1(k10_funct_3(k1_relat_1(A),k1_relat_1(B)),B)))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1654 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) -> r1_tarski(k9_relat_1(k1_funct_3(A),B),k10_relat_1(k3_funct_3(A),B)))))) # label(t36_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1655 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1656 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k2_zfmisc_1(k9_relat_1(C,A),k9_relat_1(D,B)) = k9_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)))))) # label(t93_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1657 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1658 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & k1_relat_1(B) = A -> k5_relat_1(k12_funct_3(A),k15_funct_3(B,C)) = k13_funct_3(B,C)))))) # label(t89_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1659 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k1_funct_1(k3_funct_3(B),A) = k10_relat_1(B,A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1660 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1661 (all A all B (v1_funct_1(k5_funct_3(A,B)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & m2_relset_1(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1662 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k7_funct_3(A,B) <-> (all D all E (r2_hidden(E,B) & r2_hidden(D,A) -> D = k1_funct_1(C,k4_tarski(D,E)))) & k2_zfmisc_1(A,B) = k1_relat_1(C)))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1663 (all A all B k9_funct_3(A,B) = k7_funct_3(A,B)) # label(redefinition_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1664 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (B = k1_relat_1(D) & r2_hidden(A,B) & B = k1_relat_1(C) -> k4_tarski(k1_funct_1(C,A),k1_funct_1(D,A)) = k1_funct_1(k13_funct_3(C,D),A)))))) # label(t69_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1665 (all A all B (k1_xboole_0 != A -> k2_relat_1(k7_funct_3(B,A)) = B)) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1666 (all A all B r1_tarski(k2_relat_1(k8_funct_3(A,B)),B)) # label(t61_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1667 (all A all B (v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1668 (all A all B k5_funct_3(A,B) = k4_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1669 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -(-(D = k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) & k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) = E) & (k1_xboole_0 = C -> k1_xboole_0 = A) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1670 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k1_funct_3(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t10_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1671 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r1_tarski(C,k2_relat_1(A)) -> k1_funct_1(B,C) = k10_relat_1(A,C))) & k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) <-> k3_funct_3(A) = B))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1672 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1673 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k1_funct_3(A) <-> k1_zfmisc_1(k1_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k9_relat_1(A,C)))))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1674 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k3_xboole_0(k1_relat_1(B),k1_relat_1(C))) -> k4_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k1_funct_1(k13_funct_3(B,C),A)))))) # label(t68_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1675 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_3(A)) & v1_funct_1(k3_funct_3(A)))) # label(dt_k3_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1676 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,C) & v1_funct_2(F,A,C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,A,C) & v1_funct_2(G,A,C) -> (k14_funct_3(A,B,C,D,F) = k14_funct_3(A,B,C,E,G) -> F = G & D = E))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1677 (all A all B (A != k1_xboole_0 -> k2_relat_1(k8_funct_3(A,B)) = B)) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1678 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k2_zfmisc_1(A,B) & (all E all F (r2_hidden(E,A) & r2_hidden(F,B) -> k1_funct_1(D,k4_tarski(E,F)) = k1_funct_1(C,k4_tarski(E,F)))) & k1_relat_1(C) = k2_zfmisc_1(A,B) -> C = D))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1679 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k4_funct_3(A,B) <-> B = k1_relat_1(C) & (all D (r2_hidden(D,B) -> (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D)) & (r2_hidden(D,A) -> k1_funct_1(C,D) = np__1)))))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1680 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k5_relat_1(k3_funct_3(B),k3_funct_3(A)) = k3_funct_3(k5_relat_1(A,B))))))) # label(t38_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1681 (all A all B all C all D all E all F (m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) -> k16_funct_3(A,B,C,D,E,F) = k15_funct_3(E,F))) # label(redefinition_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1682 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k1_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t18_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1683 (all A all B k10_funct_3(A,B) = k8_funct_3(A,B)) # label(redefinition_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1684 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1685 (all A all B (v1_funct_1(k8_funct_3(A,B)) & v1_relat_1(k8_funct_3(A,B)))) # label(dt_k8_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1686 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1687 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1688 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1689 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_1(k1_funct_3(A),k1_xboole_0) = k1_xboole_0)) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1690 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & k13_funct_3(A,B) = k13_funct_3(D,C) & k1_relat_1(B) = k1_relat_1(A) -> D = A & B = C))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1691 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1692 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) -> r1_tarski(k10_relat_1(k3_funct_3(A),B),k9_relat_1(k1_funct_3(A),B)))))) # label(t35_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1693 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k3_funct_3(B),A))))) # label(t30_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1694 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = A & (all C (r2_hidden(C,A) -> k4_tarski(C,C) = k1_funct_1(B,C))) <-> B = k11_funct_3(A)))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1695 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & m1_relset_1(D,A,B) & -v1_xboole_0(C) -> k13_funct_3(D,E) = k14_funct_3(A,B,C,D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1696 (all A all B all C (k1_funct_1(k4_funct_3(B,C),A) = np__1 -> r2_hidden(A,B))) # label(t42_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1697 (all A all B (v1_relat_1(k7_funct_3(A,B)) & v1_funct_1(k7_funct_3(A,B)))) # label(dt_k7_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1698 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) <-> k13_funct_3(A,B) = C))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1699 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k1_funct_3(B),A))))) # label(t16_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1700 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_funct_2(k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A)),k1_relat_1(A),k9_funct_3(k1_relat_1(A),k2_relat_1(A)),A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1701 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> D = k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)) & E = k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)))))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1702 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1703 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k3_funct_3(A)) & m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1704 (all A all B all C all D all E all F (v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & m1_relset_1(E,A,C) -> v1_funct_1(k16_funct_3(A,B,C,D,E,F)) & m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1705 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funct_3(A)) & v1_relat_1(k1_funct_3(A)))) # label(dt_k1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1706 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & -(m2_relset_1(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k13_funct_3(D,E))) & (C = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1707 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k10_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t28_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1708 (all A all B (m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_1(k10_funct_3(A,B)))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1709 (all A all B all C (r1_tarski(A,B) & r1_tarski(C,B) & k4_funct_3(C,B) = k4_funct_3(A,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1710 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k10_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t13_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1711 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,A,C) & m2_relset_1(F,A,C) & v1_funct_1(F) -> (all G (v1_funct_2(G,A,C) & m2_relset_1(G,A,C) & v1_funct_1(G) -> (k13_funct_3(D,F) = k13_funct_3(E,G) -> B = k1_xboole_0 & k1_xboole_0 != A | A != k1_xboole_0 & C = k1_xboole_0 | F = G & E = D))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1712 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1713 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) -> (r1_tarski(B,k1_zfmisc_1(A)) -> k3_tarski(k9_relat_1(k1_funct_3(D),B)) = k2_funct_2(A,C,D,k3_tarski(B))))))) # label(t17_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1714 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k1_funct_3(B))) -> k1_funct_1(k1_funct_3(B),A) = k9_relat_1(B,A)))) # label(t8_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1715 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1716 (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) & (all B all C (r2_hidden(B,f1_s2_funct_3) & r2_hidden(C,f2_s2_funct_3) -> k1_funct_1(A,k4_tarski(B,C)) = f3_s2_funct_3(B,C))))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1717 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & m1_relset_1(D,A,B) & -v1_xboole_0(C) -> v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k14_funct_3(A,B,C,D,E)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1718 (all A all B all C (r2_hidden(A,k4_xboole_0(B,C)) -> np__0 = k1_funct_1(k4_funct_3(C,B),A))) # label(t43_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1719 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k8_funct_3(A,B) = C <-> k2_zfmisc_1(A,B) = k1_relat_1(C) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> k1_funct_1(C,k4_tarski(D,E)) = E))))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1720 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> k4_tarski(k8_funct_2(A,B,D,F),k8_funct_2(A,C,E,F)) = k8_funct_2(A,k2_zfmisc_1(B,C),k14_funct_3(A,B,C,D,E),F))))))))))))) # label(t79_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1721 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> m2_relset_1(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & v1_funct_1(k15_funct_3(E,F)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1722 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(k4_tarski(C,D),k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))) -> k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1723 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1724 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k13_funct_3(A,B)) & v1_relat_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1725 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(D) = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A) & r1_tarski(k2_relat_1(D),B) -> k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B)) = D & k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) = C))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1726 (all A (v1_funct_1(k12_funct_3(A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1727 (all A all B all C all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> -((D = k1_xboole_0 -> k1_xboole_0 = C) & k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F)) != k16_funct_3(A,C,B,D,E,F) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1728 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(C,k13_funct_3(A,B)) = k13_funct_3(k5_relat_1(C,A),k5_relat_1(C,B)))))))) # label(t75_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1729 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k3_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t29_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1730 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k10_relat_1(k1_funct_3(B),A)))) # label(t33_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1731 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1732 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) & v2_funct_1(A) -> k10_relat_1(k3_funct_3(A),B) = k9_relat_1(k1_funct_3(A),B))))) # label(t37_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1733 (all A all B k15_funct_3(k6_relat_1(A),k6_relat_1(B)) = k6_relat_1(k2_zfmisc_1(A,B))) # label(t90_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1734 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> v1_funct_1(k1_funct_3(C)) & v1_funct_2(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1735 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> v1_funct_1(k2_funct_3(A,B,C)) & m2_relset_1(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_2(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1736 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,C) -> r2_hidden(k1_funct_1(k6_funct_3(B,C),A),B)))) # label(t56_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1737 (all A all B (v1_funct_2(B,A,k2_tarski(np__0,np__1)) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) & v1_funct_1(B) -> B = k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A))) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1738 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k3_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t31_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1739 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k1_funct_3(B),A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1740 (all A all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1741 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k9_relat_1(k13_funct_3(B,C),A),k2_zfmisc_1(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t76_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1742 (all A all B r1_tarski(k2_relat_1(k7_funct_3(A,B)),A)) # label(t59_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1743 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> r1_tarski(k2_relat_1(k13_funct_3(D,E)),k2_zfmisc_1(B,C)))))) # label(t80_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1744 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k3_funct_3(B),A) = k10_relat_1(k1_funct_3(B),A)))) # label(t34_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1745 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k3_funct_3(B),A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1746 (all A all B (r1_tarski(A,B) -> k7_relat_1(k6_relat_1(B),A) = k6_relat_1(A))) # label(t1_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1747 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1748 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1749 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1750 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k7_relat_1(k6_relat_1(A),B) = k6_funct_3(A,B))) # label(t53_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1751 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t27_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1752 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)) = k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1753 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1754 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,C) -> k1_funct_1(k16_funct_3(A,C,B,D,E,F),k4_tarski(G,H)) = k4_tarski(k8_funct_2(A,B,E,G),k8_funct_2(C,D,F,H)))))))))))))))))) # label(t96_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1755 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1756 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k9_relat_1(B,A),k1_relat_1(C)) & r1_tarski(A,k1_relat_1(B)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1757 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_7_domain_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1758 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & -$T & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_domain_1(B))))) # label(fraenkel_a_1_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1759 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(E,k1_zfmisc_1(C)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists F exists G (m1_subset_1(F,B) & A = k1_domain_1(B,C,F,G) & r2_hidden(G,E) & r2_hidden(F,D) & m1_subset_1(G,C))) <-> r2_hidden(A,a_4_1_domain_1(B,C,D,E))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1760 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> m1_subset_1(a_4_2_domain_1(A,B,C,D),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))))))))) # label(s4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1761 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1762 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = a_3_3_domain_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1763 (all A all B all C all D all E all F all G (-v1_xboole_0(B) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) & -v1_xboole_0(D) & -v1_xboole_0(C) -> ((exists H exists I exists J (m1_subset_1(J,D) & A = k4_domain_1(B,C,D,H,I,J) & r2_hidden(H,E) & r2_hidden(I,F) & r2_hidden(J,G) & m1_subset_1(I,C) & m1_subset_1(H,B))) <-> r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1764 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1765 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k7_mcart_1(A,B,C,E) = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,E) = k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1766 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k16_domain_1(A,B,C,D),B))) # label(dt_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1767 (all A all B all C all D all E (m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k2_enumset1(B,C,D,E) = k9_domain_1(A,B,C,D,E))) # label(redefinition_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1768 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_7_domain_1(B,C,D)) <-> (exists E (A = E & -(r2_hidden(E,C) <-> r2_hidden(E,D)) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1769 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) -> m1_subset_1(k10_domain_1(A,B,C,D,E,F),k1_zfmisc_1(A)))) # label(dt_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1770 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_3_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & -r2_hidden(E,D) & r2_hidden(E,C)))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1771 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F ((exists G (m1_subset_1(G,B) & (exists H (m1_subset_1(H,C) & (exists I (m1_subset_1(I,D) & (exists J (k4_mcart_1(G,H,I,J) = F & m1_subset_1(J,E))))))))) <-> r2_hidden(F,A))) <-> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1772 (all A all B all C all D all E all F all G all H (-v1_xboole_0(D) & m1_subset_1(E,A) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(F,B) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_mcart_1(E,F,G,H) = k5_domain_1(A,B,C,D,E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1773 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_1_domain_1(A,B,C) = k5_subset_1(A,B,C))))))) # label(t58_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.74 1774 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1775 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k7_subset_1(A,B,C) = a_3_4_domain_1(A,B,C))))))) # label(t61_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1776 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> a_2_2_domain_1(A,B) = k3_subset_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1777 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1778 (all A (r2_hidden(A,a_0_2_domain_1) <-> (exists B exists C (f4_s9_domain_1(B,C) = A & p1_s9_domain_1(B,C) & m1_subset_1(C,f2_s9_domain_1) & m1_subset_1(B,f1_s9_domain_1))))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1779 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1780 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (r2_hidden(A,k4_zfmisc_1(B,C,D,E)) <-> (exists F (m1_subset_1(F,B) & (exists G ((exists H ((exists I (k4_mcart_1(F,G,H,I) = A & m1_subset_1(I,E))) & m1_subset_1(H,D))) & m1_subset_1(G,C)))))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1781 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,B) & A = E & (r2_hidden(E,D) <-> -r2_hidden(E,C)))) <-> r2_hidden(A,a_3_5_domain_1(B,C,D))))) # label(fraenkel_a_3_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1782 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(A) -> m1_subset_1(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1783 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1784 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1785 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1786 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1787 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G (m1_subset_1(G,B) & (exists H ((exists I (m1_subset_1(I,D) & (exists J (k4_mcart_1(G,H,I,J) = F & m1_subset_1(J,E))))) & m1_subset_1(H,C))))))) -> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1788 (all A (-v1_xboole_0(A) -> m1_subset_1(a_1_2_domain_1(A),k1_zfmisc_1(A)))) # label(s1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1789 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k1_enumset1(B,C,D) = k8_domain_1(A,B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1790 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_2_domain_1(A,B,C) = k4_subset_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1791 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1792 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((exists E ((exists F ((exists G (A = k3_mcart_1(E,F,G) & m1_subset_1(G,D))) & m1_subset_1(F,C))) & m1_subset_1(E,B))) <-> r2_hidden(A,k3_zfmisc_1(B,C,D))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1793 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1794 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(A) -> k2_mcart_1(C) = k3_domain_1(A,B,C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1795 (all A (r2_hidden(A,a_0_1_domain_1) <-> (exists B (m1_subset_1(B,f1_s8_domain_1) & p1_s8_domain_1(B) & f3_s8_domain_1(B) = A)))) # label(fraenkel_a_0_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1796 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1797 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1798 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (k3_zfmisc_1(B,C,D) = A <-> (all E ((exists F ((exists G ((exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))) & m1_subset_1(G,C))) & m1_subset_1(F,B))) <-> r2_hidden(E,A)))))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1799 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_5_domain_1(B)) <-> (exists C (p1_s6_domain_1(C) & A = C & m1_subset_1(C,B)))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1800 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1801 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1802 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k1_tarski(B) = k6_domain_1(A,B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1803 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1804 (all A all B all C (m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k2_domain_1(A,B,C),A))) # label(dt_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1805 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k11_domain_1(A,B,C,D,E,F,G) = k4_enumset1(B,C,D,E,F,G))) # label(redefinition_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1806 (all A all B all C (-v1_xboole_0(B) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_3_domain_1(B,C)) <-> (exists D exists E (A = k1_domain_1(B,C,D,E) & p1_s2_domain_1(D,E) & m1_subset_1(E,C) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1807 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (p1_s1_domain_1(C) & A = C & m1_subset_1(C,B)))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1808 (all A (r2_hidden(A,a_0_3_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & p2_s10_domain_1(B) & A = B)))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1809 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists E (E = A & r2_hidden(E,C) & r2_hidden(E,D) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_1_domain_1(B,C,D))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1810 (all A all B all C all D all E all F all G all H all I (m1_subset_1(E,A) & m1_subset_1(I,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k13_domain_1(A,B,C,D,E,F,G,H,I) = k6_enumset1(B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1811 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k7_domain_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1812 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> ((exists D (-r2_hidden(D,C) & D = A & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_2_domain_1(B,C))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1813 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_subset_1(D,A) & m1_subset_1(F,C) & m1_subset_1(E,B) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k3_mcart_1(D,E,F) = k4_domain_1(A,B,C,D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1814 (all A (-v1_xboole_0(A) -> a_1_1_domain_1(A) = k1_subset_1(A))) # label(t56_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1815 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (k4_domain_1(B,C,D,F,G,H) = E -> A = F))))))) <-> A = k5_mcart_1(B,C,D,E)))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1816 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> H = A))))))))) <-> k9_mcart_1(B,C,D,E,F) = A))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1817 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1818 (all A all B all C all D (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k8_domain_1(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1819 (all A all B all C all D (-v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1820 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k11_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> A = J)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1821 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1822 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F (m1_subset_1(F,B) & (exists G ((exists H (E = k3_mcart_1(F,G,H) & m1_subset_1(H,D))) & m1_subset_1(G,C))))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D)))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1823 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_1_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & r2_hidden(D,C) & A = D))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1824 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1825 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -((all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> k4_tarski(D,E) != A)))) & r2_hidden(A,k2_zfmisc_1(B,C))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1826 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(A) -> m1_subset_1(k14_domain_1(A,B,C,D),A))) # label(dt_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1827 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> (all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> (k1_mcart_1(C) = k1_mcart_1(D) & k2_mcart_1(D) = k2_mcart_1(C) -> D = C))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1828 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> m1_subset_1(a_2_3_domain_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))))))) # label(s2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1829 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k12_domain_1(A,B,C,D,E,F,G,H) = k5_enumset1(B,C,D,E,F,G,H))) # label(redefinition_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1830 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) = k2_domain_1(A,B,C))) # label(redefinition_k2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1831 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_2_domain_1(B,C,D)) <-> (exists E ((r2_hidden(E,D) | r2_hidden(E,C)) & A = E & m1_subset_1(E,B)))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1832 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1833 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1834 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1835 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists D exists E (m1_subset_1(D,B) & m1_subset_1(E,C) & A = k1_domain_1(B,C,D,E))) <-> r2_hidden(A,a_2_0_domain_1(B,C))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1836 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> a_3_0_domain_1(A,B,C) = k3_zfmisc_1(A,B,C))))))) # label(t50_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1837 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_domain_1(B)) <-> (exists C (C = A & p1_s5_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1838 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & -v1_xboole_0(E) & -v1_xboole_0(D) -> (r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I)) <-> (exists J exists K exists L exists M (m1_subset_1(J,B) & k5_domain_1(B,C,D,E,J,K,L,M) = A & r2_hidden(M,I) & r2_hidden(L,H) & r2_hidden(K,G) & r2_hidden(J,F) & m1_subset_1(M,E) & m1_subset_1(L,D) & m1_subset_1(K,C)))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1839 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1840 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_6_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & (r2_hidden(E,C) <-> -r2_hidden(E,D)) & A = E))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1841 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1842 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B))))) # label(t49_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1843 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_5_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t62_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1844 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k7_domain_1(A,B,C) = k2_tarski(B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1845 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) -> k15_domain_1(A,B,C,D) = k18_mcart_1(D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1846 (all A all B all C all D (m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1847 (all A all B all C all D all E all F (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k3_enumset1(B,C,D,E,F) = k10_domain_1(A,B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1848 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> ((all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> A = H))))))) <-> k7_mcart_1(B,C,D,E) = A))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1849 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1850 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,B) & m1_subset_1(C,A) -> k1_domain_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1851 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(E) & -v1_xboole_0(D) -> ((exists F exists G exists H exists I (m1_subset_1(G,C) & m1_subset_1(H,D) & A = k5_domain_1(B,C,D,E,F,G,H,I) & p1_s4_domain_1(F,G,H,I) & m1_subset_1(I,E) & m1_subset_1(F,B))) <-> r2_hidden(A,a_4_2_domain_1(B,C,D,E))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1852 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(F,B) & m1_subset_1(E,A) & -v1_xboole_0(D) & -v1_xboole_0(B) -> m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)))) # label(dt_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1853 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p2_s5_domain_1(C) & C = A)) <-> r2_hidden(A,a_1_4_domain_1(B))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1854 (all A (r2_hidden(A,a_0_4_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & A = B & p1_s10_domain_1(B))))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1855 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1856 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> (k8_mcart_1(A,B,C,D,E) = k8_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,F) = k10_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k9_mcart_1(A,B,C,D,E) = k9_mcart_1(A,B,C,D,F) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1857 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> a_4_1_domain_1(A,B,C,D) = k12_mcart_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1858 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1859 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1860 (all A all B all C all D all E all F all G all H (m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k12_domain_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(A)))) # label(dt_k12_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1861 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B) & B = A)))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1862 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> k4_zfmisc_1(A,B,C,D) = a_4_0_domain_1(A,B,C,D))))))))) # label(t51_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1863 (all A all B all C all D all E (m1_subset_1(B,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k9_domain_1(A,B,C,D,E),k1_zfmisc_1(A)))) # label(dt_k9_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1864 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1865 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k7_domain_1(A,B,C) = k7_domain_1(A,C,B))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1866 (all A all B all C all D all E (-v1_xboole_0(C) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_0_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(I,E) & k5_domain_1(B,C,D,E,F,G,H,I) = A & m1_subset_1(H,D)))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1867 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1868 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & C = A)) <-> r2_hidden(A,a_1_0_domain_1(B))))) # label(fraenkel_a_1_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1869 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p2_s6_domain_1(B) <-> p1_s6_domain_1(B)))) -> a_1_6_domain_1(A) = a_1_5_domain_1(A)))) # label(s6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1870 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1871 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1872 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> (k8_mcart_1(B,C,D,E,F) = A <-> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (F = k5_domain_1(B,C,D,E,G,H,I,J) -> G = A)))))))))))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1873 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k3_zfmisc_1(B,C,D)) -> (k6_mcart_1(B,C,D,E) = A <-> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,C) -> (all H (m1_subset_1(H,D) -> (E = k4_domain_1(B,C,D,F,G,H) -> G = A)))))))))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1874 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1875 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) -> ((all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (all I (m1_subset_1(I,D) -> (all J (m1_subset_1(J,E) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> I = A))))))))) <-> k10_mcart_1(B,C,D,E,F) = A))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1876 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(I,A) & m1_subset_1(H,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> m1_subset_1(k13_domain_1(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(A)))) # label(dt_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1877 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> a_6_0_domain_1(A,B,C,D,E,F) = k13_mcart_1(A,B,C,D,E,F))))))))))))) # label(t54_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1878 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> ((exists E exists F exists G (m1_subset_1(F,C) & m1_subset_1(G,D) & p1_s3_domain_1(E,F,G) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1879 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_6_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t63_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1880 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1881 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> m1_subset_1(a_3_8_domain_1(A,B,C),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))))))) # label(s3_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1882 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D) & k4_domain_1(B,C,D,E,F,G) = A))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1883 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> a_8_0_domain_1(A,B,C,D,E,F,G,H) = k14_mcart_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1884 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = a_2_1_domain_1(A,B))))) # label(t52_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1885 (all A all B all C all D all E all F (-v1_xboole_0(C) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k4_domain_1(A,B,C,D,E,F),k3_zfmisc_1(A,B,C)))) # label(dt_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1886 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1887 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_4_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & (r2_hidden(E,D) & -r2_hidden(E,C) | -r2_hidden(E,D) & r2_hidden(E,C))))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1888 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) -> k17_mcart_1(D) = k14_domain_1(A,B,C,D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1889 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1890 (all A all B all C all D all E all F all G (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(G,A) & m1_subset_1(F,A) & m1_subset_1(D,A) -> m1_subset_1(k11_domain_1(A,B,C,D,E,F,G),k1_zfmisc_1(A)))) # label(dt_k11_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1891 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & p2_s6_domain_1(C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_6_domain_1(B))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1892 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (p1_s7_domain_1(B) & B = A & m1_subset_1(B,f1_s7_domain_1))))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1893 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1894 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1895 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)) = B)))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1896 (all A all B all C all D (v1_relat_1(k4_funct_4(A,B,C,D)) & v1_funct_1(k4_funct_4(A,B,C,D)))) # label(fc1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1897 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C))) -> k1_funct_1(C,k4_tarski(B,A)) = k1_funct_1(k2_funct_4(C),k4_tarski(A,B))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1898 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> r1_tarski(A,C))) # label(t6_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1899 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1900 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k1_funct_4(A,k7_relat_1(A,B)) = A))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1901 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1902 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1903 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> k2_zfmisc_1(B,A) = k1_relat_1(k2_funct_4(C))))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1904 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1905 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_relat_1(B) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1906 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(B),D) & r1_xboole_0(C,D) & r1_tarski(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),D) = B & A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1907 (all A all B (r1_tarski(k6_partfun1(A),k6_partfun1(B)) <-> r1_tarski(A,B))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1908 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F))) -> k4_tarski(k1_funct_1(E,k4_tarski(A,C)),k1_funct_1(F,k4_tarski(B,D))) = k1_funct_1(k3_funct_4(E,F),k4_tarski(k4_tarski(A,B),k4_tarski(C,D)))))))) # label(t58_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1909 (all A all B all C k2_funcop_1(k2_tarski(A,B),C) = k4_funct_4(A,B,C,C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1910 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1911 (all A (v1_relat_1(A) & v1_funct_1(A) -> (exists B exists C r1_tarski(k1_relat_1(k2_funct_4(A)),k2_zfmisc_1(B,C))))) # label(t45_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1912 (all A all B all C all D (k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B) & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)))) # label(t65_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1913 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1914 (all A -((all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) & (all B all C -r1_tarski(A,k2_zfmisc_1(B,C))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1915 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> B = k1_funct_4(A,B)))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1916 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1917 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> k4_funct_4(B,C,D,E) = k5_funct_4(A,B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1918 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(k2_funct_4(C)),k2_zfmisc_1(B,A))))) # label(t46_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1919 (all A all B all C all D (C != A -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1920 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_funct_4(k2_funct_4(C)) = C))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1921 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1922 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1923 (all A all B all C all D (A != B -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1924 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1925 (all A all B all C all D all E all F (k4_funct_4(A,B,E,F) = k4_funct_4(A,B,C,D) -> F = D & E = C | B = A)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1926 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,k1_funct_4(B,C)))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1927 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (m2_relset_1(G,k2_zfmisc_1(A,B),E) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & v1_funct_1(G) -> (all H (m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_1(k3_funct_4(G,H)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1928 (all A all B all C all D all E all F all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_2(G,k2_zfmisc_1(A,B),C) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_2(H,k2_zfmisc_1(D,E),F) -> -(F != k1_xboole_0 & -(m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H))) & k1_xboole_0 != C))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1929 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1930 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k1_funct_4(A,B) <-> k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,D)) & (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1931 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(D,C)))) & (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & C = k4_tarski(E,D))))) <-> B = k2_funct_4(A)))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1932 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1933 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(B),C) & r1_tarski(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = A)))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1934 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1935 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1936 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k1_funct_4(C,D) = D))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1937 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) = k7_relat_1(k1_funct_4(A,B),C)))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1938 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = k7_relat_1(A,k2_xboole_0(B,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1939 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> A = k1_funct_4(A,A))) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1940 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1941 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D all E all F all G (r2_hidden(k4_tarski(F,G),k1_relat_1(B)) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)) -> k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G))) = k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))))) & (all D ((exists E exists F exists G exists H (r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)) & D = k4_tarski(k4_tarski(E,G),k4_tarski(F,H)))) <-> r2_hidden(D,k1_relat_1(C)))) <-> k3_funct_4(A,B) = C))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1942 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.75 1943 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_partfun1(A,B) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) -> k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B)) = k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1944 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) <-> r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C)))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1945 (all A all B k1_tarski(k4_tarski(A,B)) = k2_funcop_1(k1_tarski(A),B)) # label(t70_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1946 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_funct_1(E,A) = C & D = k1_funct_1(E,B) & k2_tarski(A,B) = k1_relat_1(E) -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1947 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1948 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,A) = k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1949 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1950 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> v1_funct_1(k2_funct_4(D)) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1951 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (k1_relat_1(F) = k2_zfmisc_1(C,D) & k1_relat_1(E) = k2_zfmisc_1(A,B) -> k1_relat_1(k3_funct_4(E,F)) = k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D))))))) # label(t61_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1952 (all A all B all C all D all E all F all G (m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H)))))) # label(t62_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1953 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1954 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k1_funct_4(k1_xboole_0,A))) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1955 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(A,k1_xboole_0) = A)) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1956 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(A,B) & k1_funct_4(B,A) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1957 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (C != k1_xboole_0 -> v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D))))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1958 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k2_xboole_0(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1959 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1960 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1961 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1962 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k3_funct_4(A,B)) & v1_funct_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1963 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> k1_xboole_0 = A | D = B)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1964 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_1(k5_funct_4(A,B,C,D,E)))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1965 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_4(A)) & v1_relat_1(k2_funct_4(A)))) # label(dt_k2_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1966 (all A all B all C all D (A != B -> D = k1_funct_1(k4_funct_4(A,B,C,D),B) & k1_funct_1(k4_funct_4(A,B,C,D),A) = C)) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1967 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k2_xboole_0(A,B) = k1_funct_4(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1968 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1969 (all A all B all C all D k4_funct_4(A,B,C,D) = k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D))) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1970 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1971 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_funct_4(A,B)) <-> r1_partfun1(A,B)))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1972 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> v1_funct_1(k1_funct_4(C,D)) & m2_relset_1(k1_funct_4(C,D),A,B))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1973 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1974 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1975 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(C) = k2_relat_1(k2_funct_4(C))))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1976 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(B,C) = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1977 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_funcop_1(A,C),k2_funcop_1(B,C)))) # label(t5_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1978 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_partfun1(B,C) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1979 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1980 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> C = k1_funct_4(B,C))))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1981 (all A all B k6_partfun1(k2_xboole_0(A,B)) = k1_funct_4(k6_partfun1(A),k6_partfun1(B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1982 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (C != k1_xboole_0 -> k2_funct_4(k2_funct_4(D)) = D))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1983 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (r2_hidden(k4_tarski(B,D),k1_relat_1(F)) & r2_hidden(k4_tarski(A,C),k1_relat_1(E)) <-> r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F)))))))) # label(t57_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1984 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) | r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k1_funct_4(B,C)))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1985 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1986 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1987 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1988 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1989 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k14_ordinal2(A,k4_ordinal2))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1990 (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]. 4.65/4.76 1991 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f1_s14_ordinal2(A) <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s14_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(A) & v1_relat_1(C)))))))) -> f2_s14_ordinal2 = f1_s14_ordinal2(k1_xboole_0) # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1992 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (v3_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k1_funct_1(A,B) = C & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | k1_xboole_0 = B)))))))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1993 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(A,B) <-> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B))))))) # label(t1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.76 1994 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 1995 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k1_ordinal1(k14_ordinal2(A,B)) = k14_ordinal2(A,k1_ordinal1(B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 1996 (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]. 4.65/4.78 1997 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 1998 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) -> D = k1_xboole_0 | f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & v1_ordinal2(C) & v1_relat_1(C))) & (exists C (v1_ordinal2(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> f4_s13_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) & A != B))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 1999 (exists A (v3_ordinal1(A) & (exists B (v1_funct_1(B) & v5_ordinal1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) -> k1_xboole_0 = C | k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & A = k1_ordinal2(B) & v1_ordinal2(B) & v1_relat_1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2000 (all A all B (k3_ordinal2(A) = B <-> (all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (v4_ordinal1(D) & D = C & v3_ordinal1(D))))))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2001 (all A all B (B = k2_ordinal2(A) <-> (all C (r2_hidden(C,B) <-> v3_ordinal1(C) & r2_hidden(C,A))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2002 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2003 (all A all B (v1_funct_1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_relat_1(A) -> v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)) & v1_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2004 (all A (v3_ordinal1(A) -> (all B (B = f4_s9_ordinal2(A) <-> (exists C (k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s9_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s9_ordinal2(D,k1_funct_1(C,D))))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))))))) -> (all A (v3_ordinal1(A) -> f2_s9_ordinal2(A,f4_s9_ordinal2(A)) = f4_s9_ordinal2(k1_ordinal1(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2005 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & f2_s8_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s8_ordinal2(D,k1_funct_1(C,D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B)) <-> f1_s8_ordinal2(A) = B)))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2006 (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]. 4.65/4.78 2007 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2008 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2009 (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]. 4.65/4.78 2010 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k16_ordinal2(A,B) = C <-> (exists D (v1_relat_1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k15_ordinal2(A,k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E) | E = k1_xboole_0))) & k1_funct_1(D,k1_xboole_0) = k4_ordinal2 & k1_relat_1(D) = k1_ordinal1(B) & C = k1_ordinal2(D) & v1_ordinal2(D) & v5_ordinal1(D) & v1_funct_1(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2011 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2012 (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]. 4.65/4.78 2013 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2014 (all A (k5_ordinal2 = A <-> r2_hidden(k1_xboole_0,A) & v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v4_ordinal1(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2015 (all A (v3_ordinal1(A) -> (all B all C (r2_hidden(A,B) & r1_tarski(B,C) -> r1_ordinal1(k6_ordinal2(C),k6_ordinal2(B)))))) # label(t24_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2016 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2017 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B)))) | A = k1_xboole_0))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2018 (exists A (v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_relat_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2019 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2020 (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = f1_s5_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s5_ordinal2(B,k1_funct_1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> f4_s5_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B) | B = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> f2_s5_ordinal2 = k1_funct_1(A,k1_xboole_0)) & v5_ordinal1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.65/4.78 2021 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A) & k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2022 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & k1_relat_1(C) = k1_relat_1(A) & k8_ordinal2(C) = B)) <-> k11_ordinal2(A) = B))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2023 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & k1_relat_1(C) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k9_ordinal2(C) = B & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C))) <-> B = k10_ordinal2(A)))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2024 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2025 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2026 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2027 (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]. 4.72/4.84 2028 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2029 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2030 (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]. 4.72/4.84 2031 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2032 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_ordinal2(A) <-> (exists B (v3_ordinal1(B) & r1_tarski(k2_relat_1(A),B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2033 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2034 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2035 (all A all B (v3_ordinal1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2036 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2037 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & k1_relat_1(A) = f1_s2_ordinal2 & v5_ordinal1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2038 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2039 (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]. 4.72/4.84 2040 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.72/4.84 2041 (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]. 4.72/4.84 2042 f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> f4_s12_ordinal2 = k1_funct_1(f1_s12_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f3_s12_ordinal2) & v4_ordinal1(A) -> A = k1_xboole_0 | k1_funct_1(f1_s12_ordinal2,A) = f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f6_s12_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_ordinal1(A) = k1_relat_1(C) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> f2_s12_ordinal2(A) = B))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> k1_funct_1(f1_s12_ordinal2,A) = f2_s12_ordinal2(A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2043 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2044 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2045 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k14_ordinal2(B,D)))) & k1_relat_1(C) = A -> k14_ordinal2(B,A) = k8_ordinal2(C)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2046 (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]. 4.82/4.88 2047 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2048 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2049 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2050 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2051 (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]. 4.82/4.88 2052 f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> k1_funct_1(f1_s10_ordinal2,A) = f3_s10_ordinal2(A)))) & f2_s10_ordinal2 = k1_relat_1(f1_s10_ordinal2) & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B (B = f3_s10_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & f4_s10_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s10_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2053 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,A) | A = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f6_s4_ordinal2,k1_xboole_0)) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f5_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2054 (all A (v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A) -> (v2_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C)))))))))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2055 (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]. 4.82/4.88 2056 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) -> (k1_xboole_0 != A -> (r1_ordinal2(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(A,D) & (all E (v3_ordinal1(E) -> -(r2_hidden(E,k1_relat_1(B)) & (all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(C,k1_funct_1(B,F)) & r2_hidden(k1_funct_1(B,F),D))))))) & r2_hidden(C,A)))))))) & (A = k1_xboole_0 -> ((exists C (r2_hidden(C,k1_relat_1(B)) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(B)) & r1_ordinal1(C,D) -> k1_xboole_0 = k1_funct_1(B,D)))) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2057 (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]. 4.82/4.88 2058 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2059 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & A = k14_ordinal2(B,C) & v4_ordinal2(C))) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2060 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2061 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_ordinal2(D) & C = k1_ordinal2(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_ordinal1(k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k8_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & A = k1_funct_1(D,k1_xboole_0) & k1_relat_1(D) = k1_ordinal1(B) & v5_ordinal1(D) & v1_funct_1(D) & v1_relat_1(D))) <-> k14_ordinal2(A,B) = C))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2062 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2063 (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]. 4.82/4.88 2064 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> k1_xboole_0 = A | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2065 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2066 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.82/4.88 2067 (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]. 4.82/4.88 2068 (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]. 4.88/5.00 2069 (exists A (v1_funct_1(A) & v5_ordinal1(A) & f1_s11_ordinal2 = k1_relat_1(A) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s11_ordinal2) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> B = k1_xboole_0 | f4_s11_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s11_ordinal2(B,k1_funct_1(A,B))))) & v1_ordinal2(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2070 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> p1_s1_ordinal2(A) | A = k1_xboole_0))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2071 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & k1_ordinal2(B) = A & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & k1_relat_1(B) = k1_ordinal1(f1_s7_ordinal2))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2072 (all A all B -((exists C (v1_funct_1(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> D = k1_xboole_0 | k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_ordinal2(C) = A & v5_ordinal1(C) & v1_relat_1(C))) & B != A & (exists C (v5_ordinal1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2073 (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]. 4.88/5.00 2074 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) -> k12_ordinal2(k2_ordinal1(B,A)) = k13_ordinal2(A,B))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2075 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2076 (all A (v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> ((exists B (v3_ordinal1(B) & r1_ordinal2(B,A))) -> (all B (v3_ordinal1(B) -> (k12_ordinal2(A) = B <-> r1_ordinal2(B,A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2077 (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s6_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & k1_funct_1(C,k1_xboole_0) = f4_s6_ordinal2 & v5_ordinal1(C) & v1_relat_1(C))))))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> f4_s6_ordinal2 = k1_funct_1(f1_s6_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A))))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2078 (exists A (v1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & k1_relat_1(A) = f1_s3_ordinal2 & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2079 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2080 (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]. 4.88/5.00 2081 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s15_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f3_s15_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s15_ordinal2 & k1_ordinal1(A) = k1_relat_1(C) & v1_ordinal2(C))) <-> f4_s15_ordinal2(A) = B))))) -> (all A (v3_ordinal1(A) -> f4_s15_ordinal2(k1_ordinal1(A)) = f2_s15_ordinal2(A,f4_s15_ordinal2(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2082 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> r1_ordinal1(A,k6_ordinal2(B)) | k1_xboole_0 = k2_ordinal2(B))))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2083 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k16_ordinal2(B,D) = k1_funct_1(C,D)))) -> k16_ordinal2(B,A) = k12_ordinal2(C)))) | A = k1_xboole_0))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2084 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2085 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k15_ordinal2(A,B) = C <-> (exists D (v1_relat_1(D) & v1_funct_1(D) & k1_funct_1(D,k1_xboole_0) = k1_xboole_0 & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k14_ordinal2(k1_funct_1(D,E),B) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_xboole_0 = E | k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E)))))) & k1_relat_1(D) = k1_ordinal1(A) & k1_ordinal2(D) = C & v1_ordinal2(D) & v5_ordinal1(D)))))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2086 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2087 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(A,k1_xboole_0))) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2088 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2089 (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]. 4.88/5.00 2090 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2091 (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]. 4.88/5.00 2092 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2093 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2094 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2095 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2096 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2097 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2098 (all A (v3_ordinal1(A) -> k15_ordinal2(k4_ordinal2,A) = A & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2099 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2100 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2101 (all A (v3_ordinal1(A) -> (exists B (r2_hidden(A,B) & v4_ordinal1(B) & v3_ordinal1(B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2102 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2103 (all A (v3_ordinal1(A) -> A = k7_ordinal2(A))) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2104 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2105 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2106 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f6_s16_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s16_ordinal2(D,k1_funct_1(C,D))))) & k1_relat_1(C) = k1_ordinal1(A) & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_funct_1(C))) <-> B = f3_s16_ordinal2(A)))))) & f2_s16_ordinal2 != k1_xboole_0 & v4_ordinal1(f2_s16_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> f3_s16_ordinal2(A) = k1_funct_1(f1_s16_ordinal2,A)))) & f2_s16_ordinal2 = k1_relat_1(f1_s16_ordinal2) -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2107 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2108 (all A (v3_ordinal1(A) -> k16_ordinal2(k4_ordinal2,A) = k4_ordinal2 & A = k16_ordinal2(A,k4_ordinal2))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2109 (all A all B (v3_ordinal1(B) -> (r1_tarski(k2_ordinal2(A),B) & (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) <-> B = k7_ordinal2(A)))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2110 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2111 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2112 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2113 (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]. 4.88/5.00 2114 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(t14_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2115 (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]. 4.88/5.00 2116 (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]. 4.88/5.00 2117 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2118 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2119 (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]. 4.88/5.00 2120 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2121 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(k1_relat_1(A)) <-> v1_finset_1(A)))) # label(t29_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2122 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2123 (all A all B all C (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2124 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2125 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2126 (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]. 4.88/5.00 2127 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(B,C))))) & v6_ordinal1(A) & A != k1_xboole_0 & v1_finset_1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2128 (exists A (v1_finset_1(A) & -v1_xboole_0(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2129 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2130 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2131 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & -v1_xboole_0(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2132 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2133 (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]. 4.88/5.00 2134 (exists A (v1_funct_1(A) & f1_s1_finset_1 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B)) & (-p1_s1_finset_1(B) -> f3_s1_finset_1(B) = k1_funct_1(A,B))))) & v1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2135 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2136 (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]. 4.88/5.00 2137 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2138 (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]. 4.88/5.00 2139 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2140 (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]. 4.88/5.00 2141 (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]. 4.88/5.00 2142 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> v1_finset_1(B) | k1_xboole_0 = A)) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2143 (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]. 4.88/5.00 2144 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2145 (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]. 4.88/5.00 2146 v1_finset_1(f1_s2_finset_1) & p1_s2_finset_1(k1_xboole_0) & (all A all B (r1_tarski(B,f1_s2_finset_1) & p1_s2_finset_1(B) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2147 (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]. 4.88/5.00 2148 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2149 (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]. 4.88/5.00 2150 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2151 (all A -(v6_ordinal1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & k1_xboole_0 != A & v1_finset_1(A))) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2152 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2153 (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]. 4.88/5.00 2154 (all A all B all C all D (v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2155 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2156 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2157 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2158 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> k1_xboole_0 = A | v1_finset_1(B))) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2159 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2160 (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]. 4.88/5.00 2161 (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]. 4.88/5.00 2162 (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]. 4.88/5.00 2163 (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]. 4.88/5.00 2164 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & v1_funct_1(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2165 (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]. 4.88/5.00 2166 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2167 (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]. 4.88/5.00 2168 (all A ((exists B (A = k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) & p1_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & m1_subset_1(B,f1_s9_fraenkel))) <-> r2_hidden(A,a_0_16_fraenkel))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2169 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & A = f3_s2_fraenkel(B,C) & p1_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2170 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]. 4.88/5.00 2171 (all A ((exists B (m1_subset_1(B,f1_s15_fraenkel) & p2_s15_fraenkel(B) & A = B)) <-> r2_hidden(A,a_0_28_fraenkel))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2172 (all A ((exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & p2_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel))) <-> r2_hidden(A,a_0_7_fraenkel))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2173 (all A (r2_hidden(A,a_0_35_fraenkel) <-> (exists B (m1_subset_1(B,f1_s19_fraenkel) & p1_s19_fraenkel(B,f4_s19_fraenkel) & f3_s19_fraenkel(B,f4_s19_fraenkel) = A)))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2174 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(B,A) = f3_s8_fraenkel(A,B))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p2_s8_fraenkel(A,B) <-> p1_s8_fraenkel(A,B)))))) -> a_0_15_fraenkel = a_0_14_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2175 (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]. 4.88/5.00 2176 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2177 (all A ((all B (r2_hidden(B,A) -> v1_relat_1(B) & v1_funct_1(B))) <-> v1_fraenkel(A))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2178 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2179 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -(r2_hidden(A,f3_s26_fraenkel) & (all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B)))))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & (all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2180 (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]. 4.88/5.00 2181 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2182 (all A ((exists B (m1_subset_1(B,f1_s9_fraenkel) & p2_s9_fraenkel(B) & r2_hidden(B,f3_s9_fraenkel) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B) = A)) <-> r2_hidden(A,a_0_17_fraenkel))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2183 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (m2_fraenkel(F,B,A,k1_fraenkel(B,A)) & E = k7_relat_1(F,C))))) | k1_funct_2(C,D) = k1_xboole_0)))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2184 (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p1_s9_fraenkel(A) <-> p2_s9_fraenkel(A))))) & k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) -> a_0_16_fraenkel = a_0_17_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2185 (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]. 4.88/5.00 2186 (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]. 4.88/5.00 2187 (all A (r2_hidden(A,a_0_15_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & A = f3_s8_fraenkel(C,B) & p2_s8_fraenkel(B,C) & m1_subset_1(C,f2_s8_fraenkel))))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2188 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2189 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p2_s19_fraenkel(A,B) <-> B = f4_s19_fraenkel & p1_s19_fraenkel(A,B)))))) -> a_0_34_fraenkel = a_0_35_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2190 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (f2_s14_fraenkel(B) = A & p1_s14_fraenkel(B) & r2_hidden(B,a_0_25_fraenkel) & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2191 (all A ((exists B exists C (m1_subset_1(B,f1_s16_fraenkel) & f3_s16_fraenkel(B,C) = A & p1_s16_fraenkel(B,C) & m1_subset_1(C,f2_s16_fraenkel))) <-> r2_hidden(A,a_0_30_fraenkel))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2192 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2193 (all A ((exists B exists C (p1_s20_fraenkel(B,C) & f4_s20_fraenkel = C & f3_s20_fraenkel(B,C) = A & m1_subset_1(C,f2_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))) <-> r2_hidden(A,a_0_36_fraenkel))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2194 (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]. 4.88/5.00 2195 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & f2_s6_fraenkel(B) = A & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_10_fraenkel))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2196 (all A (r2_hidden(A,a_0_19_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s11_fraenkel) & f3_s11_fraenkel(B,C) = A & p1_s11_fraenkel(B,C) & m1_subset_1(B,f1_s11_fraenkel))))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2197 (all A ((exists B (m1_subset_1(B,f1_s1_fraenkel) & f2_s1_fraenkel(B) = A & p2_s1_fraenkel(B))) <-> r2_hidden(A,a_0_1_fraenkel))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.00 2198 (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]. 4.88/5.00 2199 (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]. 4.88/5.00 2200 (all A (r2_hidden(A,a_0_29_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & f3_s15_fraenkel(B,C) = A & p1_s15_fraenkel(B,C) & p2_s15_fraenkel(B) & m1_subset_1(C,f2_s15_fraenkel))))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2201 (all A ((exists B exists C (m1_subset_1(B,f1_s16_fraenkel) & m1_subset_1(C,f2_s16_fraenkel) & p2_s16_fraenkel(B,C) & A = f3_s16_fraenkel(B,C))) <-> r2_hidden(A,a_0_31_fraenkel))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2202 (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]. 4.88/5.01 2203 (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]. 4.88/5.01 2204 (all A ((exists B (m1_subset_1(B,f1_s18_fraenkel) & f3_s18_fraenkel(B) = A & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel) & p1_s18_fraenkel(B))) <-> r2_hidden(A,a_0_33_fraenkel))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2205 v1_finset_1(f3_s25_fraenkel) & v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(A,f3_s25_fraenkel) = k7_relat_1(B,f3_s25_fraenkel) -> f5_s25_fraenkel(B) = f5_s25_fraenkel(A)))))) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2206 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(C,B) & r1_tarski(D,A) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))) | k1_xboole_0 = k1_funct_2(C,D))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2207 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2208 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -(p1_s16_fraenkel(A,B) & (all C (m1_subset_1(C,f1_s16_fraenkel) -> -(f3_s16_fraenkel(A,B) = f3_s16_fraenkel(C,B) & p2_s16_fraenkel(C,B))))))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2209 (all A (r2_hidden(A,a_0_3_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s2_fraenkel) & A = f3_s2_fraenkel(B,C) & p2_s2_fraenkel(B,C) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2210 (all A ((exists B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) & f5_s25_fraenkel(B) = A & r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2211 (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]. 4.88/5.01 2212 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2213 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,D,F) = k8_funct_2(A,B,C,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2214 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2215 (all A ((exists B (A = B & p2_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_25_fraenkel))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2216 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2217 (all A ((exists B exists C (m1_subset_1(B,f1_s22_fraenkel) & m1_subset_1(C,f2_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel) & r2_hidden(C,f4_s22_fraenkel) & f5_s22_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_39_fraenkel))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2218 (exists A ((all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (r2_hidden(C,f3_s24_fraenkel) & p1_s24_fraenkel(B,C) & f4_s24_fraenkel(C) = B & m1_subset_1(C,f2_s24_fraenkel))) <-> r2_hidden(B,A)))) & m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2219 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f2_s5_fraenkel(A) = f3_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2220 (all A ((exists B (p1_s5_fraenkel(B) & A = f2_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))) <-> r2_hidden(A,a_0_8_fraenkel))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2221 (all A (-v1_xboole_0(A) -> (all B all C all D (m2_fraenkel(D,B,A,k1_fraenkel(B,A)) -> k7_relat_1(D,k3_xboole_0(B,C)) = k7_relat_1(D,C))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2222 (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]. 4.88/5.01 2223 (all A (m1_subset_1(A,f1_s27_fraenkel) -> -(r2_hidden(A,f3_s27_fraenkel) & (all B (m1_subset_1(B,f2_s27_fraenkel) -> -p1_s27_fraenkel(A,B)))))) -> (exists A ((all B (m1_subset_1(B,f1_s27_fraenkel) -> (r2_hidden(B,f3_s27_fraenkel) -> p1_s27_fraenkel(B,k8_funct_2(f1_s27_fraenkel,f2_s27_fraenkel,A,B))))) & m2_fraenkel(A,f1_s27_fraenkel,f2_s27_fraenkel,k1_fraenkel(f1_s27_fraenkel,f2_s27_fraenkel)))) # label(s27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2224 (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]. 4.88/5.01 2225 (all A ((exists B (A = f2_s14_fraenkel(B) & p2_s14_fraenkel(B) & p1_s14_fraenkel(B) & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_26_fraenkel))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2226 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2227 (all A ((exists B exists C (m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & f4_s13_fraenkel(B,C) = A & m1_subset_1(B,f1_s13_fraenkel))) <-> r2_hidden(A,a_0_22_fraenkel))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2228 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (p1_s1_fraenkel(B) & A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2229 (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]. 4.88/5.01 2230 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s8_fraenkel) & m1_subset_1(C,f2_s8_fraenkel) & A = f3_s8_fraenkel(B,C) & p1_s8_fraenkel(B,C))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2231 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2232 (all A (r2_hidden(A,a_0_18_fraenkel) <-> (exists B (A = B & p1_s10_fraenkel(B) & m1_subset_1(B,f1_s10_fraenkel))))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2233 (all A (r2_hidden(A,a_0_5_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p2_s3_fraenkel(B))))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2234 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f2_s6_fraenkel(A) = f3_s6_fraenkel(A)))) -> a_0_10_fraenkel = a_0_11_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2235 (all A ((exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & p1_s7_fraenkel(B,C) & f3_s7_fraenkel(B,C) = A & m1_subset_1(C,f2_s7_fraenkel))) <-> r2_hidden(A,a_0_12_fraenkel))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2236 (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]. 4.88/5.01 2237 (all A ((exists B (m1_subset_1(B,f1_s6_fraenkel) & f3_s6_fraenkel(B) = A & p1_s6_fraenkel(B))) <-> r2_hidden(A,a_0_11_fraenkel))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2238 (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]. 4.88/5.01 2239 (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(B,C) & p1_s23_fraenkel(A,B) -> p1_s23_fraenkel(A,C)))))))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -(r2_hidden(A,f2_s23_fraenkel) & (all B (m1_subset_1(B,f1_s23_fraenkel) -> -(r2_hidden(B,f2_s23_fraenkel) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(C,B) & r2_hidden(C,f2_s23_fraenkel) -> p1_s23_fraenkel(B,C)))) & p1_s23_fraenkel(B,A))))))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2240 (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]. 4.88/5.01 2241 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2242 (all A ((exists B (A = f3_s21_fraenkel(B) & r2_hidden(B,f2_s21_fraenkel) & m1_subset_1(B,f1_s21_fraenkel))) <-> r2_hidden(A,a_0_38_fraenkel))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2243 (all A ((exists B exists C (m1_subset_1(C,f2_s15_fraenkel) & f3_s15_fraenkel(B,C) = A & p1_s15_fraenkel(B,C) & r2_hidden(B,a_0_28_fraenkel) & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_27_fraenkel))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2244 (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]. 4.88/5.01 2245 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2246 (all A (r2_hidden(A,a_0_37_fraenkel) <-> (exists B (m1_subset_1(B,f1_s20_fraenkel) & A = f3_s20_fraenkel(B,f4_s20_fraenkel) & p1_s20_fraenkel(B,f4_s20_fraenkel))))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2247 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2248 (all A (r2_hidden(A,a_0_6_fraenkel) <-> (exists B exists C (p1_s4_fraenkel(B,C) & A = f3_s4_fraenkel(B,C) & m1_subset_1(C,f2_s4_fraenkel) & m1_subset_1(B,f1_s4_fraenkel))))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2249 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p1_s3_fraenkel(A) <-> p2_s3_fraenkel(A)))) -> a_0_5_fraenkel = a_0_4_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2250 (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]. 4.88/5.01 2251 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2252 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2253 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2254 (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]. 4.88/5.01 2255 (all A (r2_hidden(A,a_0_20_fraenkel) <-> (exists B exists C (A = f3_s12_fraenkel(B,C) & p1_s12_fraenkel(B,C) & m1_subset_1(C,f2_s12_fraenkel) & m1_subset_1(B,f1_s12_fraenkel))))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2256 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (f2_s3_fraenkel(B) = A & p1_s3_fraenkel(B) & m1_subset_1(B,f1_s3_fraenkel))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2257 (all A (r2_hidden(A,a_0_13_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s7_fraenkel) & m1_subset_1(C,f2_s7_fraenkel) & p1_s7_fraenkel(B,C) & f4_s7_fraenkel(B,C) = A)))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2258 (all A (r2_hidden(A,a_0_34_fraenkel) <-> (exists B exists C (A = f3_s19_fraenkel(B,C) & p2_s19_fraenkel(B,C) & m1_subset_1(C,f2_s19_fraenkel) & m1_subset_1(B,f1_s19_fraenkel))))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2259 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2260 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2261 (all A ((exists B (np__0 = k1_funct_1(B,k13_arytm_3) & B = A & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))) <-> r2_hidden(A,a_0_0_numbers))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2262 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2263 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2264 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2265 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) & v2_funct_1(B) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2266 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2267 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2268 (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]. 4.88/5.01 2269 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2270 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) <-> k4_card_1(A) = B))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2271 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2272 (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]. 4.88/5.01 2273 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2274 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(A,k2_relat_1(C)) & k1_relat_1(C) = B)) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2275 (all A all B (r2_wellord2(A,B) <-> k1_card_1(A) = k1_card_1(B))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2276 (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]. 4.88/5.01 2277 (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]. 4.88/5.01 2278 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2279 (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]. 4.88/5.01 2280 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2281 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2282 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B != A & r1_tarski(A,B) <-> r2_hidden(A,B)))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2283 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2284 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k3_card_1(A),k3_card_1(B)) <-> r1_ordinal1(A,B)))))) # label(t43_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2285 (all A (v3_ordinal1(A) -> (all B (k3_card_1(A) = B <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D))) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_card_1(k5_numbers) = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v1_funct_1(C))))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2286 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2287 (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]. 4.88/5.01 2288 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2289 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2290 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2291 (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]. 4.88/5.01 2292 (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]. 4.88/5.01 2293 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2294 (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]. 4.88/5.01 2295 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2296 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2297 (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]. 4.88/5.01 2298 (all A ((exists B (v3_ordinal1(B) & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))) & A = B)) <-> v1_card_1(A))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2299 (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]. 4.88/5.01 2300 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2301 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2302 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k3_card_1(C) = k1_funct_1(B,C)))) & A = k1_relat_1(B) -> k1_card_1(k8_ordinal2(B)) = k3_card_1(A))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2303 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & A = k1_relat_1(C) & r1_tarski(k2_relat_1(C),B) & v2_funct_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2304 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2305 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2306 (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]. 4.88/5.01 2307 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2308 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2309 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_nat_1(A,np__1) = k1_ordinal1(A))) # label(t52_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2310 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2311 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k1_card_1(A)) & v1_finset_1(A))) # label(t69_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2312 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2313 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2314 p1_s1_card_1(k1_xboole_0) & (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & (all A (v1_card_1(A) -> (v2_card_1(A) & (all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) -> p1_s1_card_1(A) | A = k1_xboole_0))) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2315 (all A (v1_card_1(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2316 (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]. 4.88/5.01 2317 (all A (v1_card_1(A) -> (v2_card_1(A) <-> (all B (v1_card_1(B) -> A != k2_card_1(B)))))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2318 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2319 (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]. 4.88/5.01 2320 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2321 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2322 (all A all B all C (r2_hidden(C,B) & r2_hidden(A,B) -> r2_wellord2(k4_xboole_0(B,k1_tarski(A)),k4_xboole_0(B,k1_tarski(C))))) # label(t59_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2323 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2324 (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]. 4.88/5.01 2325 (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]. 4.88/5.01 2326 (all A all B (k1_card_1(k1_tarski(B)) = k1_card_1(A) <-> (exists C k1_tarski(C) = A))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2327 (all A all B (k1_card_1(B) = k1_card_1(A) -> k2_card_1(B) = k2_card_1(A))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2328 (all A all B (r2_wellord2(A,k1_tarski(B)) <-> (exists C A = k1_tarski(C)))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2329 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2330 (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]. 4.88/5.01 2331 (all A all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) & (all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2332 (all A (v1_finset_1(A) -> v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2333 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2334 (all A (m1_subset_1(A,k5_numbers) -> v4_ordinal2(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v1_xcmplx_0(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2335 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2336 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (B = A <-> r2_wellord2(A,B)))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2337 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2338 (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]. 4.88/5.01 2339 (all A (k1_xboole_0 = A <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2340 (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]. 4.88/5.01 2341 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2342 (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]. 4.88/5.01 2343 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2344 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2345 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2346 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2347 (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]. 4.88/5.01 2348 (all A -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,B))) & v1_finset_1(A))) # label(t74_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2349 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2350 (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]. 4.88/5.01 2351 (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]. 4.88/5.01 2352 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2353 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2354 (exists A (v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2355 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_wellord2(A,B) -> k4_card_1(A) = k4_card_1(B)))))) # label(t81_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2356 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2357 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2358 (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]. 4.88/5.01 2359 (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]. 4.88/5.01 2360 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2361 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) <-> r1_tarski(k1_card_1(A),k1_card_1(B))))))) # label(t72_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2362 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2363 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2364 (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]. 4.88/5.01 2365 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2366 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2367 (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]. 4.88/5.01 2368 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2369 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2370 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & v2_funct_1(A) & k2_relat_1(A) = k2_relat_1(B) -> k3_finseq_1(A) = k3_finseq_1(B)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2371 (all A all B (v1_finseq_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & v1_relat_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2372 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) & r1_xreal_0(np__1,A) <-> r2_hidden(A,k2_finseq_1(B))))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2373 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2374 (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]. 4.88/5.01 2375 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2376 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(B)) & k4_tarski(C,k1_funct_1(B,C)) = A))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2377 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(B)) & r1_xreal_0(np__1,C) -> k1_funct_1(B,C) = k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C))))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2378 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & k3_finseq_1(A) = f1_s2_finseq_1 & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> f2_s2_finseq_1(B) = k1_funct_1(A,B)))))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2379 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (A = k1_xboole_0 <-> k1_xboole_0 = k4_finseq_1(A)))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2380 (all A k1_tarski(k4_tarski(np__1,A)) = k5_finseq_1(A)) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2381 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A))))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2382 (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]. 4.88/5.01 2383 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> k7_finseq_1(A,k7_finseq_1(B,C)) = k7_finseq_1(k7_finseq_1(A,B),C))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2384 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2385 (all A all B (v1_relat_1(A) & v1_finset_1(A) & v1_funct_1(A) -> v1_finset_1(k10_relat_1(A,B)))) # label(fc18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2386 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B)))))))))) # label(t41_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2387 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2388 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & -r2_hidden(C,k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(D,k4_finseq_1(B)) & C = k1_nat_1(k3_finseq_1(A),D))))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2389 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(A,C) & m2_finseq_1(B,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2390 (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]. 4.88/5.01 2391 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_relat_1(B,k2_finseq_1(A)) = C & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C) & k2_finseq_1(A) = k4_finseq_1(C)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2392 (all A all B (v4_ordinal2(B) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & A = C & r1_xreal_0(C,B) & r1_xreal_0(np__1,C))) <-> r2_hidden(A,a_1_0_finseq_1(B))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2393 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> A = k7_finseq_1(k1_xboole_0,A) & k7_finseq_1(A,k1_xboole_0) = A)) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2394 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2395 (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]. 4.88/5.01 2396 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k4_finseq_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2397 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k4_card_1(k1_card_1(A)) & A = k4_card_1(A))) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2398 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2399 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2400 (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]. 4.88/5.01 2401 (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]. 4.88/5.01 2402 (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]. 4.88/5.01 2403 (all A all B ((all C (r2_hidden(C,B) <-> m2_finseq_1(C,A))) <-> k13_finseq_1(A) = B)) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2404 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(B) -> B = A))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2405 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2406 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k12_finseq_1(A,B) = k5_finseq_1(B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2407 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2408 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2409 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2410 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2411 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2412 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2413 (all A all B (m1_finseq_1(B,A) -> v1_funct_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)) & v1_xboole_0(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2414 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k2_relat_1(k14_finseq_1(k1_relat_1(A))) = k1_relat_1(A))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2415 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> k7_finseq_1(B,C) = k8_finseq_1(A,B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2416 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2417 (all A (v1_relat_1(A) & v1_funct_1(A) -> -((all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -r1_tarski(A,B))) & (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B))))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2418 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2419 (all A all B (v1_finseq_1(A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & -v1_xboole_0(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2420 (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]. 4.88/5.01 2421 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2422 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f2_s5_finseq_1)) & (all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B)))))) -> (exists A (m2_finseq_1(A,f1_s5_finseq_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & k2_finseq_1(f2_s5_finseq_1) = k4_finseq_1(A))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2423 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) & r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) -> k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2424 (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]. 4.88/5.01 2425 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2426 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(k2_finseq_1(A),k2_finseq_1(B)) -> A = B))))) # label(t74_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2427 (all A (v1_fraenkel(k13_finseq_1(A)) & -v1_xboole_0(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2428 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k7_finseq_1(B,A) = k7_finseq_1(B,C) | k7_finseq_1(A,B) = k7_finseq_1(C,B) -> C = A))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2429 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)) = A)))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2430 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C) | r1_xreal_0(C,k3_finseq_1(A))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2431 (all A all B all C (k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C) & k11_finseq_1(A,B,C) = k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2432 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2433 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = a_1_0_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2434 (all A -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,k2_finseq_1(B)))) & v1_finset_1(A))) # label(t77_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2435 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2436 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.01 2437 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k3_finseq_1(B) = k3_finseq_1(A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2438 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (k1_xboole_0 = k14_finseq_1(A) <-> A = k1_xboole_0))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2439 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2440 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1) = A)) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2441 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (B = k1_funct_1(C,np__2) & A = k1_funct_1(C,np__1) & np__2 = k3_finseq_1(C) <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2442 (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]. 4.88/5.02 2443 (exists A (v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_funct_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2444 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2445 (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]. 4.88/5.02 2446 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k17_finseq_1(A) <-> (all C all D (r2_hidden(C,k3_relat_1(A)) & (exists E (r1_xreal_0(np__1,k3_finseq_1(E)) & C = k1_funct_1(E,np__1) & D = k1_funct_1(E,k3_finseq_1(E)) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,F) -> r1_xreal_0(k3_finseq_1(E),F) | r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),A)))) & v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E))) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(C,D),B)))))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2447 (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]. 4.88/5.02 2448 (all A all B all C all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (D = k11_finseq_1(A,B,C) <-> C = k1_funct_1(D,np__3) & B = k1_funct_1(D,np__2) & k1_funct_1(D,np__1) = A & np__3 = k3_finseq_1(D)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2449 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2450 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k2_relat_1(B) & k3_finseq_1(B) = np__1 <-> k9_finseq_1(A) = B))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2451 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> v2_finseq_1(k7_relat_1(B,A)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2452 (all A (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2453 (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]. 4.88/5.02 2454 (exists A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2455 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (B = k14_finseq_1(A) <-> k2_relat_1(B) = A & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(r1_xreal_0(np__1,C) & k1_funct_1(B,D) = F & r1_xreal_0(F,E) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & -r1_xreal_0(D,C))))))))))))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2456 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2457 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(A) = k1_card_1(k2_finseq_1(A)))) # label(t76_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2458 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2459 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) <-> r1_xreal_0(A,B)))))) # label(t7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2460 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (np__0 = k3_finseq_1(A) <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2461 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2462 (all A (v4_ordinal2(A) -> r2_hidden(A,k2_finseq_1(A)) | A = np__0)) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2463 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k9_finseq_1(A) = B <-> k1_funct_1(B,np__1) = A & k3_finseq_1(B) = np__1))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2464 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2465 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2466 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2467 (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]. 4.88/5.02 2468 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2469 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k2_finseq_1(B) = k1_relat_1(A) <-> k3_finseq_1(A) = B))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2470 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D)))) & k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) <-> k7_finseq_1(A,B) = C))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2471 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k6_finseq_1(B) = A <-> k3_finseq_1(A) = np__0)))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2472 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2473 (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]. 4.88/5.02 2474 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2475 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k9_finseq_1(A) <-> k2_finseq_1(np__1) = k1_relat_1(B) & k1_funct_1(B,np__1) = A))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2476 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_funct_1(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2477 (all A all B (m2_finseq_1(B,A) -> v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) & v1_funct_1(B))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2478 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2479 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)) = A)) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2480 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2481 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,C) & p1_s1_finseq_1(A,B) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & (all B -p1_s1_finseq_1(A,B))))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2482 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2483 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2484 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2485 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(A),k2_finseq_1(B)) -> r1_xreal_0(A,B)))))) # label(t10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2486 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2487 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2488 (all A all B all C k11_finseq_1(A,B,C) = k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C))) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2489 (all A all B (v1_funct_1(A) & -v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & -v1_xboole_0(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2490 (all A (v1_relat_1(A) -> (v1_finseq_1(A) <-> (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k1_relat_1(A) = k2_finseq_1(B)))))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2491 (exists A (-v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2492 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2493 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) = k3_finseq_1(k7_finseq_1(A,B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2494 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2495 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]. 4.88/5.02 2496 (all A (v1_relat_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2497 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(D = A & r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B)))))) & r2_hidden(A,k4_finseq_1(B))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2498 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k9_finseq_1(A) = B <-> k2_relat_1(B) = k1_tarski(A) & k4_finseq_1(B) = k2_finseq_1(np__1)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2499 (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]. 4.88/5.02 2500 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k7_finseq_1(A,B) = k1_xboole_0 -> k1_xboole_0 = A & k1_xboole_0 = B))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2501 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2502 (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]. 4.88/5.02 2503 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2504 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (m1_finseq_1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2505 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_finseq_1(A) <-> (exists B (r1_tarski(k1_relat_1(A),k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers)))))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2506 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2507 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2508 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (A = k3_finseq_1(C) & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2509 (all A all B k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)) = k10_finseq_1(A,B)) # label(d9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2510 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2511 (exists A (-v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2512 (all A k5_finseq_1(A) = k9_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2513 (all A exists B (m1_finseq_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_funct_1(B) & v1_xboole_0(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2514 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k3_finseq_1(A) = k1_card_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2515 (all A all B (m2_finseq_1(B,A) <-> m1_finseq_1(B,A))) # label(redefinition_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2516 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (A = k1_xboole_0 <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2517 (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]. 4.88/5.02 2518 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> v1_funct_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))) & v1_relat_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2519 (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & B = C & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2520 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> A = B))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2521 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> -(k1_xboole_0 != A & (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2522 (all A all B all C (m1_finseq_1(B,A) & v4_ordinal2(C) -> m2_finseq_1(k16_finseq_1(A,B,C),A))) # label(dt_k16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2523 (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]. 4.88/5.02 2524 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> -(k7_finseq_1(A,B) = k7_finseq_1(C,D) & (all E (v1_relat_1(E) & v1_finseq_1(E) & v1_funct_1(E) -> C != k7_finseq_1(A,E))) & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C))))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2525 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2526 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2527 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & A = k2_relat_1(B) & v1_finseq_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2528 (all A (m2_finseq_1(k6_finseq_1(A),A) & v1_xboole_0(k6_finseq_1(A)))) # label(dt_k6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2529 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (v1_relat_1(E) & v1_funct_1(E) & (exists F (r2_hidden(F,k1_relat_1(E)) & k1_funct_1(A,D) = E & r2_hidden(D,k1_relat_1(A)) & C = k4_tarski(D,F))))))) & (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(C,k1_relat_1(B)) & k1_funct_1(A,k1_mcart_1(C)) = D -> k1_funct_1(D,k2_mcart_1(C)) = k1_funct_1(B,C)))) <-> B = k4_funct_5(A)))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2530 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k3_funct_5(C) = k3_funct_5(D) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> D = C))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2531 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(r2_hidden(B,k1_relat_1(A)) & v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) -> k4_funct_5(A) = k1_xboole_0 & k1_xboole_0 = k6_funct_5(A)))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2532 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_funct_1(k1_funct_1(k5_funct_5(B),A)) & v1_relat_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2533 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = k6_funct_5(k5_funct_5(C)) & C = k4_funct_5(k3_funct_5(C))))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2534 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2535 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(D) = k2_zfmisc_1(A,B) & k5_funct_5(D) = k5_funct_5(C) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = D))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2536 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_funct_5(A),k2_funct_5(B)) & r1_tarski(k1_funct_5(A),k1_funct_5(B)))) # label(t5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2537 (all A (k1_funct_5(A) = k1_xboole_0 | k2_funct_5(A) = k1_xboole_0 -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2538 (all A all B (r1_tarski(k2_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k2_funct_5(A),k2_funct_5(B))) & r1_tarski(k1_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k1_funct_5(A),k1_funct_5(B))))) # label(t7_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2539 (all A all B all C (r1_xboole_0(A,B) -> k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) = k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)) & r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2540 (all A all B all C all D (k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(B,D) & k2_tarski(A,C) = k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))))) # label(t16_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2541 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k4_funct_5(C) = k4_funct_5(D) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> C = D | A = k1_xboole_0))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2542 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A))) & r1_tarski(k2_relat_1(k5_funct_5(A)),k4_partfun1(k1_funct_5(k1_relat_1(A)),k2_relat_1(A))))) # label(t43_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2543 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k2_zfmisc_1(A,B) = k1_xboole_0 | k1_relat_1(k3_funct_5(C)) = A & B = k1_relat_1(k5_funct_5(C))))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2544 (all A all B (r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2545 (all A k1_tarski(k1_xboole_0) = k1_funct_2(k1_xboole_0,A)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2546 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2547 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | k5_funct_5(k6_funct_5(C)) = C & k3_funct_5(k4_funct_5(C)) = C))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2548 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_5(k1_relat_1(A)) = k1_relat_1(k5_funct_5(A)))) # label(t30_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2549 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_funct_5(A) = k1_xboole_0 & k2_funct_5(A) = k1_xboole_0)) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2550 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> v1_funct_1(k1_funct_1(k5_funct_5(C),B)) & v1_relat_1(k1_funct_1(k5_funct_5(C),B)) & r2_hidden(B,k1_relat_1(k5_funct_5(C)))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2551 (all A all B all C (r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C))) & k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)) = k1_card_1(k1_funct_2(A,k1_funct_2(B,C))))) # label(t70_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2552 (all A all B all C (r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) & k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) = k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))))) # label(t71_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2553 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_funct_1(k3_funct_5(B),A) = C & r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> k1_relat_1(C) = k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B))))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(A,D),k1_relat_1(B)) & k1_funct_1(B,k4_tarski(A,D)) = k1_funct_1(C,D))) & r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B)))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2554 (all A (v1_relat_1(A) -> k1_funct_5(A) = k1_relat_1(A) & k2_relat_1(A) = k2_funct_5(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2555 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k3_funct_5(C) = k3_funct_5(D) & k2_zfmisc_1(A,B) = k1_relat_1(D) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = D))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2556 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C))) & r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2557 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k2_relat_1(k4_funct_5(C)),B) & r1_tarski(k2_relat_1(k6_funct_5(C)),B)))) # label(t47_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2558 (all A all B (r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B) & r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A))) # label(t12_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2559 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2560 (all A all B (r2_wellord2(A,k1_funct_2(k1_tarski(B),A)) & k1_card_1(k1_funct_2(k1_tarski(B),A)) = k1_card_1(A))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2561 (all A all B all C all D (k1_card_1(A) = k1_card_1(B) & k1_card_1(D) = k1_card_1(C) -> k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2562 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(r2_hidden(C,B) & (all E (v1_relat_1(E) & v1_funct_1(E) -> -(r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,A) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)))) & A = k1_relat_1(E) & k1_funct_1(k5_funct_5(D),C) = E))) & k2_zfmisc_1(A,B) = k1_relat_1(D) & k2_zfmisc_1(A,B) != k1_xboole_0))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2563 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) -> r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k4_funct_5(C),k4_tarski(A,B)) & r2_hidden(k4_tarski(A,B),k1_relat_1(k4_funct_5(C)))))))) # label(t45_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2564 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(k3_funct_5(C)),A) & r1_tarski(k1_relat_1(k5_funct_5(C)),B)))) # label(t32_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2565 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_funct_5(A),C) & r1_tarski(k1_funct_5(A),B))) # label(t13_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2566 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A)) & r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C)))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2567 (all A all B (-(k1_xboole_0 = k2_zfmisc_1(A,B) & k2_zfmisc_1(B,A) = k1_xboole_0 & A = k1_xboole_0) -> k1_funct_5(k2_zfmisc_1(B,A)) = B & B = k2_funct_5(k2_zfmisc_1(A,B)))) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2568 (all A all B all C (A != B -> k1_card_1(k1_zfmisc_1(C)) = k1_card_1(k1_funct_2(C,k2_tarski(A,B))) & r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C)))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2569 (all A all B (k2_xboole_0(k1_funct_5(A),k1_funct_5(B)) = k1_funct_5(k2_xboole_0(A,B)) & k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) = k2_funct_5(k2_xboole_0(A,B)))) # label(t6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2570 (all A all B all C all D (r2_wellord2(C,D) & r2_wellord2(A,B) -> k1_card_1(k1_funct_2(B,D)) = k1_card_1(k1_funct_2(A,C)) & r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2571 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2572 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k6_funct_5(A)) & v1_relat_1(k6_funct_5(A)))) # label(dt_k6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2573 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k1_funct_5(C)) & r2_hidden(B,k2_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2574 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) & k5_funct_5(C) = k5_funct_5(D) & r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> C = D))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2575 (all A all B (k1_tarski(A) = k1_funct_5(k1_tarski(k4_tarski(A,B))) & k2_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(B))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2576 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) & C = k1_funct_1(k5_funct_5(B),A) -> k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A)))) = k1_relat_1(C) & (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(D,A),k1_relat_1(B)) & k1_funct_1(B,k4_tarski(D,A)) = k1_funct_1(C,D))) & r1_tarski(k2_relat_1(C),k2_relat_1(B)) & r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B)))))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2577 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k2_zfmisc_1(k1_relat_1(C),A) = k1_relat_1(k4_funct_5(C)) & k2_zfmisc_1(A,k1_relat_1(C)) = k1_relat_1(k6_funct_5(C))))) # label(t33_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2578 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_5(k2_funct_4(A)) = k5_funct_5(A))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2579 (all A all B k1_tarski(k2_funcop_1(A,B)) = k1_funct_2(A,k1_tarski(B))) # label(t66_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.02 2580 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(B,f1_s1_funct_5) -> f2_s1_funct_5(B) = k1_funct_1(A,B)))) & f1_s1_funct_5 = k1_relat_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2581 (all A all B all C (B != A -> r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C)) & k1_card_1(k1_funct_2(k2_tarski(A,B),C)) = k1_card_1(k2_zfmisc_1(C,C)))) # label(t73_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2582 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t48_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2583 (all A all B (k2_funct_5(A) = B <-> (all C ((exists D r2_hidden(k4_tarski(D,C),A)) <-> r2_hidden(C,B))))) # label(d2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2584 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(D) = k6_funct_5(C) -> A = k1_xboole_0 | D = C))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2585 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> v1_funct_1(k1_funct_1(k3_funct_5(B),A)) & v1_relat_1(k1_funct_1(k3_funct_5(B),A))))) # label(t37_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2586 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k1_xboole_0 = k5_funct_5(A) & k1_xboole_0 = k3_funct_5(A)))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2587 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k3_funct_5(A) = B <-> k1_funct_5(k1_relat_1(A)) = k1_relat_1(B) & (all C -(r2_hidden(C,k1_funct_5(k1_relat_1(A))) & (all D (v1_funct_1(D) & v1_relat_1(D) -> -(k1_relat_1(D) = k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E)))) & k1_funct_1(B,C) = D)))))))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2588 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) -> r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C)))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2589 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k5_funct_5(A)) & v1_relat_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2590 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> v1_funct_1(k1_funct_1(k3_funct_5(C),A)) & v1_relat_1(k1_funct_1(k3_funct_5(C),A)) & r2_hidden(A,k1_relat_1(k3_funct_5(C)))))) # label(t26_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2591 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2592 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k3_funct_5(A)) & v1_funct_1(k3_funct_5(A)))) # label(dt_k3_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2593 (all A all B (B = k1_funct_5(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2594 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> D = C | r2_hidden(k1_xboole_0,k2_relat_1(D)) | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2595 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_5(k1_relat_1(A)) = k2_funct_5(k1_relat_1(k2_funct_4(A))) & k2_funct_5(k1_relat_1(A)) = k1_funct_5(k1_relat_1(k2_funct_4(A))))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2596 (all A (k2_funct_5(A) = k1_xboole_0 <-> k1_funct_5(A) = k1_xboole_0)) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2597 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> -(k1_relat_1(D) = k2_zfmisc_1(A,B) & r2_hidden(C,A) & (all E (v1_relat_1(E) & v1_funct_1(E) -> -(B = k1_relat_1(E) & (all F (r2_hidden(F,B) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(C,F)))) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & E = k1_funct_1(k3_funct_5(D),C)))) & k1_xboole_0 != k2_zfmisc_1(A,B)))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2598 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_xboole_0 = A | k3_funct_5(k4_funct_5(C)) = C & k5_funct_5(k6_funct_5(C)) = C))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2599 (all A (v1_relat_1(A) & v1_funct_1(A) -> k6_funct_5(A) = k2_funct_4(k4_funct_5(A)))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2600 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k4_funct_5(k3_funct_5(C)) = C & k6_funct_5(k5_funct_5(C)) = C))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2601 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2602 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) & D = k1_funct_1(k3_funct_5(C),A) -> k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,B) & r2_hidden(B,k1_relat_1(D))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2603 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k4_funct_5(C) = k4_funct_5(D) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | D = C | r2_hidden(k1_xboole_0,k2_relat_1(D))))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2604 (all A all B (r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))) & r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B))))) # label(t8_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2605 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2606 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2607 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k4_funct_5(A)) & v1_funct_1(k4_funct_5(A)))) # label(dt_k4_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2608 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) & D = k1_funct_1(k5_funct_5(C),B) -> r2_hidden(A,k1_relat_1(D)) & k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,A)))))) # label(t29_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2609 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)))) # label(t63_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2610 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2611 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k12_qc_lang1(A),k8_qc_lang1))) # label(dt_k12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2612 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2613 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1)))))))) # label(d19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2614 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2615 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__3 -> v5_qc_lang1(A)) & ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) -> v2_qc_lang1(A)) & (np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v4_qc_lang1(A)) & (np__1 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v3_qc_lang1(A)) & (np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> A = k11_qc_lang1))) # label(t36_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2616 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2617 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_xboole_0 = k24_qc_lang1(A) <-> v6_qc_lang1(A)))) # label(d30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2618 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2619 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2620 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) <-> (exists B ((exists C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) & (exists D (m1_qc_lang1(D,B) & k9_qc_lang1(C,D) = A)))) & m2_subset_1(B,k1_numbers,k5_numbers)))))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2621 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2622 (all A (m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k23_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2623 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2624 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2625 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> a_1_0_qc_lang1(A) = k7_qc_lang1(A))) # label(d7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2626 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2627 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2628 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k17_qc_lang1(A) = B <-> k12_qc_lang1(B) = A)))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2629 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2630 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2631 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (C = A & B = k6_qc_lang1(C) & m1_subset_1(C,k5_qc_lang1))) <-> r2_hidden(A,a_1_0_qc_lang1(B))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2632 (all A (m1_subset_1(A,k8_qc_lang1) -> r1_xreal_0(np__1,k3_finseq_1(k10_qc_lang1(A))))) # label(t34_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2633 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (k13_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))) <-> k18_qc_lang1(A) = B)))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2634 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.88/5.03 2635 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> A = k6_qc_lang1(B))))) # label(t35_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2636 (all A (m2_finseq_1(A,k1_qc_lang1) -> a_1_1_qc_lang1(A) = k22_qc_lang1(A))) # label(d28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2637 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),k10_qc_lang1(A)),k10_qc_lang1(B)) = k13_qc_lang1(A,B))))) # label(d15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2638 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_finseq_1(k16_qc_lang1(A),k1_qc_lang1))) # label(dt_k16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2639 (all A (m1_subset_1(A,k8_qc_lang1) -> k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),k10_qc_lang1(A)) = k12_qc_lang1(A))) # label(d14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2640 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2641 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k19_qc_lang1(A),k8_qc_lang1))) # label(dt_k19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2642 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2643 (all A ((exists B exists C (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(np__7,B) & A = k4_tarski(B,C))) <-> r2_hidden(A,a_0_0_qc_lang1))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2644 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2645 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2646 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2647 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) & k14_qc_lang1(C,B) = A)) <-> k21_qc_lang1(A) = B)))))) # label(d27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2648 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D ((exists E (B = E & k9_qc_lang1(E,D) = A & m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)))) & m1_qc_lang1(D,C))))) <-> B = k15_qc_lang1(A))))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2649 (all A (m1_subset_1(A,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k17_qc_lang1(A)))) & v3_qc_lang1(A)))) # label(t45_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2650 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_subset_1(k20_qc_lang1(A),k1_qc_lang1,k2_qc_lang1))) # label(dt_k20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2651 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2652 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2653 (exists A (v1_funct_1(A) & v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) = f2_s3_qc_lang1 & (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> f3_s3_qc_lang1(B) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v5_qc_lang1(B) -> f6_s3_qc_lang1(B,k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k21_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v4_qc_lang1(B) -> f5_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k18_qc_lang1(B)),k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k19_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v3_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f4_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k17_qc_lang1(B)))))) & m2_relset_1(A,k8_qc_lang1,f1_s3_qc_lang1))) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2654 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2655 (all A (m1_subset_1(A,k5_numbers) -> -v1_xboole_0(k7_qc_lang1(A)))) # label(fc6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2656 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2657 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2658 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k7_finseq_1(k12_finseq_1(k7_qc_lang1(A),B),C) = k9_qc_lang1(B,C))))))) # label(t23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2659 (all A (-v1_xboole_0(A) -> ((all B (-v1_xboole_0(B) -> (v1_qc_lang1(B) -> r1_tarski(A,B)))) & v1_qc_lang1(A) <-> A = k8_qc_lang1))) # label(d10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2660 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2661 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(C,k3_finseq_1(B)) & r2_hidden(k1_funct_1(B,C),k2_qc_lang1) & r1_xreal_0(np__1,C) & k1_funct_1(B,C) = A)) <-> r2_hidden(A,a_1_1_qc_lang1(B))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2662 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> p1_s1_qc_lang1(k9_qc_lang1(B,C)))))))) & p1_s1_qc_lang1(k11_qc_lang1) & (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(B) & p1_s1_qc_lang1(A) -> p1_s1_qc_lang1(k13_qc_lang1(A,B))))))) & (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k14_qc_lang1(A,B))))))) & (all A (m1_subset_1(A,k8_qc_lang1) -> (p1_s1_qc_lang1(A) -> p1_s1_qc_lang1(k12_qc_lang1(A))))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s1_qc_lang1(A))) # label(s1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2663 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> k1_mcart_1(B) != np__2 & np__3 != k1_mcart_1(B) & k1_mcart_1(B) != np__1 & k1_mcart_1(B) != np__0)))) # label(t48_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2664 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2665 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_finseq_1(k10_qc_lang1(A),k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) # label(dt_k10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2666 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2667 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (m1_subset_1(C,k8_qc_lang1) & A = k13_qc_lang1(C,B))) <-> k19_qc_lang1(A) = B)))))) # label(d25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2668 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k14_qc_lang1(A,B) = k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,A)),k10_qc_lang1(B)))))) # label(d16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2669 (all A (m1_subset_1(A,k8_qc_lang1) -> -(-v2_qc_lang1(A) & -v3_qc_lang1(A) & -v4_qc_lang1(A) & -v5_qc_lang1(A) & A != k11_qc_lang1))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2670 (all A (m1_subset_1(A,k8_qc_lang1) -> -((all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) & v2_qc_lang1(A)) & (v4_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__2) & (v5_qc_lang1(A) -> np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & (v3_qc_lang1(A) -> k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1) & np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(k11_qc_lang1),np__1)))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2671 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C ((exists D (m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C)) & (exists E (A = k9_qc_lang1(D,E) & B = E & m1_qc_lang1(E,C))))) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> B = k16_qc_lang1(A))))))) # label(d22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2672 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2673 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (k12_qc_lang1(B) = A & m1_subset_1(B,k8_qc_lang1))) <-> v3_qc_lang1(A)))) # label(d18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2674 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2675 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k15_qc_lang1(A),k5_qc_lang1))) # label(dt_k15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2676 (all A all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,a_1_2_qc_lang1(B)) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & r1_xreal_0(np__1,C) & A = k1_funct_1(k16_qc_lang1(B),C)))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2677 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k24_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.03 2678 (all A (m1_subset_1(A,k2_qc_lang1) -> k23_qc_lang1(A) = k1_tarski(A))) # label(redefinition_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2679 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k7_finseq_1(k10_qc_lang1(B),C) = k10_qc_lang1(A) -> k10_qc_lang1(A) = k10_qc_lang1(B)))))))) # label(t37_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2680 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2681 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k18_qc_lang1(A),k8_qc_lang1))) # label(dt_k18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2682 (all A (m1_subset_1(A,k5_numbers) -> m1_subset_1(k7_qc_lang1(A),k1_zfmisc_1(k5_qc_lang1)))) # label(dt_k7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2683 (all A (m1_subset_1(A,k5_numbers) -> (exists B m1_qc_lang1(B,A)))) # label(existence_m1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2684 (all A (m1_subset_1(A,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> m2_finseq_1(B,k1_qc_lang1))))) # label(dt_m1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2685 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> r1_tarski(k2_zfmisc_1(k1_tarski(C),B),k2_zfmisc_1(A,B)))))) # label(t1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2686 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v5_qc_lang1(A) & v4_qc_lang1(A)) & -(v3_qc_lang1(A) & v5_qc_lang1(A)) & -(v4_qc_lang1(A) & v3_qc_lang1(A)) & -(v5_qc_lang1(A) & v2_qc_lang1(A)) & -(v4_qc_lang1(A) & v2_qc_lang1(A)) & -(v2_qc_lang1(A) & v3_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2687 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2688 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2689 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2690 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> np__1 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__3 & np__2 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__0))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2691 (all A (m1_subset_1(A,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k21_qc_lang1(A)))) & v5_qc_lang1(A)))) # label(t47_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2692 (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(k11_qc_lang1) & (v3_qc_lang1(A) & p1_s2_qc_lang1(k17_qc_lang1(A)) -> p1_s2_qc_lang1(A)) & (p1_s2_qc_lang1(k19_qc_lang1(A)) & p1_s2_qc_lang1(k18_qc_lang1(A)) & v4_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (p1_s2_qc_lang1(k21_qc_lang1(A)) & v5_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (v2_qc_lang1(A) -> p1_s2_qc_lang1(A)))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(A))) # label(s2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2693 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2694 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> ((exists C (k14_qc_lang1(B,C) = A & m1_subset_1(C,k8_qc_lang1))) <-> k20_qc_lang1(A) = B)))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2695 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2696 (all A (m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> r2_hidden(k7_finseq_1(k12_finseq_1(k7_qc_lang1(B),C),D),A))))))) & (all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),B),A)))) & (all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),B),C),A)))))) & (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,B)),C),A)))))) & r2_hidden(k9_finseq_1(k4_tarski(np__0,np__0)),A) <-> v1_qc_lang1(A))) # label(d9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2697 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2698 (all A (m1_finseq_1(A,k1_qc_lang1) -> m1_subset_1(k22_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2699 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2700 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k17_qc_lang1(A),k8_qc_lang1))) # label(dt_k17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2701 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_nat_1(np__7,B) = k1_mcart_1(A) <-> B = k6_qc_lang1(A)))))) # label(d6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2702 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2703 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2704 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k3_finseq_1(B) = A <-> m1_qc_lang1(B,A)))))) # label(d8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2705 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & k14_qc_lang1(B,C) = A)) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1))) <-> v5_qc_lang1(A)))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2706 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> ((exists C (k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,A) = B & (all D (m1_subset_1(D,k8_qc_lang1) -> (v2_qc_lang1(D) -> a_1_2_qc_lang1(D) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k17_qc_lang1(D)) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = k6_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k21_qc_lang1(D)),k23_qc_lang1(k20_qc_lang1(D)))) & (v4_qc_lang1(D) -> k4_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k18_qc_lang1(D)),k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k19_qc_lang1(D))) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k11_qc_lang1) = k1_xboole_0)) & m2_relset_1(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & v1_funct_2(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & v1_funct_1(C))) <-> B = k24_qc_lang1(A)))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2707 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> r1_tarski(k2_zfmisc_1(k1_enumset1(C,D,E),B),k2_zfmisc_1(A,B)))))))))) # label(t2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2708 (all A all B (m1_finseq_1(B,k1_qc_lang1) & m1_subset_1(A,k5_qc_lang1) -> m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2709 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k21_qc_lang1(A),k8_qc_lang1))) # label(dt_k21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2710 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k19_qc_lang1(A)))) & -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k18_qc_lang1(A))))))) # label(t46_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2711 (all A (m1_subset_1(A,k5_qc_lang1) -> m2_subset_1(k6_qc_lang1(A),k1_numbers,k5_numbers))) # label(dt_k6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2712 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k3_finseq_1(B) = k6_qc_lang1(A) -> k7_finseq_1(k12_finseq_1(k5_qc_lang1,A),B) = k9_qc_lang1(A,B)))))) # label(d11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2713 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) & r3_qc_lang2(A,B)))))) # label(t74_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2714 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2715 (all A all B all C (m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2716 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,k15_qc_lang2(B)) -> r2_qc_lang2(A,B)))))) # label(t103_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2717 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & A = k3_qc_lang2(B,C)))))))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2718 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(A,k3_qc_lang2(A,B)) & r3_qc_lang2(B,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B)))))) # label(t94_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2719 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k4_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))))))) # label(t115_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2720 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k12_qc_lang2(A),k8_qc_lang1))) # label(dt_k12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2721 (all A (m1_subset_1(A,k8_qc_lang1) -> -r1_qc_lang2(A,k11_qc_lang1))) # label(t58_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2722 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (A = k2_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1))))) <-> v2_qc_lang2(A)))) # label(d11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2723 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2724 (all A (m1_subset_1(A,k8_qc_lang1) -> (k15_qc_lang2(A) = k1_tarski(A) <-> v2_qc_lang1(A) | A = k11_qc_lang1))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2725 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(A,k14_qc_lang1(B,C)) = k6_qc_lang2(A,B,C))))))) # label(d6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2726 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang2(k18_qc_lang1(A)) = k13_qc_lang2(A))) # label(d18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.04 2727 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k15_qc_lang2(k9_qc_lang1(B,C)) = k1_tarski(k9_qc_lang1(B,C)))))))) # label(t108_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2728 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k4_qc_lang2(C,D) = k4_qc_lang2(A,B) -> B = D & C = A))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2729 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k14_qc_lang1(C,E) = k6_qc_lang2(A,B,D) -> C = A & k14_qc_lang1(B,D) = E))))))))))) # label(t22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2730 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2731 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2732 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2733 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k14_qc_lang1(A,k6_qc_lang2(B,C,D)) = k8_qc_lang2(A,B,C,D))))))))) # label(d8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2734 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> r3_qc_lang2(k19_qc_lang1(A),A) & r3_qc_lang2(k18_qc_lang1(A),A)))) # label(t97_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2735 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2736 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(A,B,C,D) = k14_qc_lang1(F,E) -> E = k6_qc_lang2(B,C,D) & F = A))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2737 (all A (m1_subset_1(A,k8_qc_lang1) -> k14_qc_lang2(A) = k11_qc_lang2(k18_qc_lang1(A)))) # label(d19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2738 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) <-> (exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (B = k1_funct_1(D,C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(r1_xreal_0(np__1,E) & -r1_xreal_0(C,E) & (all F (m1_subset_1(F,k8_qc_lang1) -> (all G (m1_subset_1(G,k8_qc_lang1) -> -(k1_funct_1(D,E) = F & r1_qc_lang2(F,G) & G = k1_funct_1(D,k1_nat_1(E,np__1)))))))))) & A = k1_funct_1(D,np__1) & k3_finseq_1(D) = C & r1_xreal_0(np__1,C) & v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D)))))))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2739 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k12_qc_lang2(k2_qc_lang2(A,B)) & k13_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k2_qc_lang2(A,B)) & k11_qc_lang2(k2_qc_lang2(A,B)) = B)))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2740 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> v2_qc_lang2(k19_qc_lang1(A)) & v2_qc_lang2(k18_qc_lang1(A)) & v4_qc_lang1(A)))) # label(t51_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2741 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & (all C (m1_subset_1(C,k8_qc_lang1) -> -r1_qc_lang2(C,B)))))))) # label(t75_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2742 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k2_enumset1(k12_qc_lang1(B),k12_qc_lang1(A),k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))) = k15_qc_lang2(k3_qc_lang2(A,B)))))) # label(t114_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2743 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(A,B) & r3_qc_lang2(B,C) -> r3_qc_lang2(A,C)))))))) # label(t76_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2744 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(A,B,C,D) = k5_qc_lang2(F,E) -> A = F & E = k7_qc_lang2(B,C,D)))))))))))))) # label(t31_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2745 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> r3_qc_lang2(k21_qc_lang1(A),A)))) # label(t98_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2746 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> -r1_qc_lang2(A,k9_qc_lang1(C,D)))))))))) # label(t59_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2747 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k2_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2748 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> B = k18_qc_lang1(A) | k19_qc_lang1(A) = B)))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2749 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (A = B | A = C <-> r1_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2750 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(A)))) # label(t50_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2751 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2752 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_tarski(k13_qc_lang1(A,B))) = k15_qc_lang2(k13_qc_lang1(A,B)))))) # label(t111_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2753 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> k15_qc_lang2(k14_qc_lang1(B,A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k14_qc_lang1(B,A))))))) # label(t112_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2754 (all A (m1_subset_1(A,k8_qc_lang1) -> k17_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) = k10_qc_lang2(A))) # label(d14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2755 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)))))))) # label(d7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2756 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2757 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(B,A) & v2_qc_lang1(A)))))) # label(t95_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2758 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k18_qc_lang1(k13_qc_lang1(A,B)) & k19_qc_lang1(k13_qc_lang1(A,B)) = B)))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2759 (all A (m1_subset_1(A,k8_qc_lang1) -> (r3_qc_lang2(A,k1_qc_lang2) <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t88_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2760 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D)) & k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)))))))))) # label(t26_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2761 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k5_qc_lang2(C,E) = k7_qc_lang2(A,B,D) -> k5_qc_lang2(B,D) = E & C = A))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2762 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(k13_qc_lang1(A,B),C) -> r3_qc_lang2(A,C) & r3_qc_lang2(B,C)))))))) # label(t90_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2763 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(D,F,H,B) = k9_qc_lang2(C,E,G,A) -> C = D & A = B & H = G & E = F))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2764 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) -> r2_qc_lang2(A,B)))))) # label(t72_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2765 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k13_qc_lang1(A,B) = k13_qc_lang1(C,D) -> A = C & B = D))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2766 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(A,k13_qc_lang1(B,C)) <-> r2_qc_lang2(A,C) | r2_qc_lang2(A,B)))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2767 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k6_qc_lang2(C,E,A) = k6_qc_lang2(D,F,B) -> D = C & A = B & E = F))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2768 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t117_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2769 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(A) -> (B = k17_qc_lang1(A) <-> r1_qc_lang2(B,A))))))) # label(t65_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2770 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (-(-(r3_qc_lang2(B,C) & r2_qc_lang2(A,B)) & -(r2_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r1_qc_lang2(A,B) & r2_qc_lang2(B,C)) & -(r3_qc_lang2(B,C) & r1_qc_lang2(A,B)) & -(r1_qc_lang2(B,C) & r3_qc_lang2(A,B)) & -(r3_qc_lang2(A,B) & r2_qc_lang2(B,C))) -> r3_qc_lang2(A,C)))))))) # label(t83_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2771 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2772 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2773 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(k12_qc_lang1(A),B) -> r3_qc_lang2(A,B)))))) # label(t87_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2774 (all A (m1_subset_1(A,k8_qc_lang1) -> k15_qc_lang2(k12_qc_lang1(A)) = k2_xboole_0(k15_qc_lang2(A),k1_tarski(k12_qc_lang1(A))))) # label(t110_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2775 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B ((all C ((exists D (m1_subset_1(D,k8_qc_lang1) & C = D & r2_qc_lang2(D,A))) <-> r2_hidden(C,B))) <-> B = k15_qc_lang2(A))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2776 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(A,B) & r2_qc_lang2(B,C) -> r2_qc_lang2(A,C)))))))) # label(t77_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2777 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> A = k2_qc_lang2(k12_qc_lang2(A),k11_qc_lang2(A))))) # label(t54_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2778 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_qc_lang2(A,B) = k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)))))) # label(d4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2779 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_hidden(B,k15_qc_lang2(C)) -> r2_hidden(A,k15_qc_lang2(C)) | -r3_qc_lang2(A,B) & -r2_qc_lang2(A,B) & -r1_qc_lang2(A,B)))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2780 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2781 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> B = k14_qc_lang2(k4_qc_lang2(A,B)) & k2_qc_lang2(B,A) = k19_qc_lang1(k4_qc_lang2(A,B)) & k2_qc_lang2(A,B) = k18_qc_lang1(k4_qc_lang2(A,B)) & k13_qc_lang2(k4_qc_lang2(A,B)) = A)))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2782 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(k14_qc_lang1(C,A),B) -> r3_qc_lang2(A,B)))))))) # label(t92_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2783 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k13_qc_lang2(A),k8_qc_lang1))) # label(dt_k13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2784 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k3_qc_lang2(A,B) = k3_qc_lang2(C,D) -> C = A & B = D))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2785 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) & r2_qc_lang2(B,A) -> A = B))))) # label(t78_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2786 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k10_qc_lang2(k3_qc_lang2(A,B)) = A & k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) & B = k11_qc_lang2(k3_qc_lang2(A,B)))))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2787 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(A,B) & r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A)))))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2788 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t91_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2789 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B ((exists C (k4_qc_lang2(B,C) = A & m1_subset_1(C,k8_qc_lang1))) & m1_subset_1(B,k8_qc_lang1))) <-> v3_qc_lang2(A)))) # label(d12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2790 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k14_qc_lang1(k20_qc_lang1(A),k21_qc_lang1(A)) = A))) # label(t7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2791 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t82_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2792 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2793 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k14_qc_lang1(A,k12_qc_lang1(B))) = k5_qc_lang2(A,B))))) # label(d5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2794 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(C,E,G,A) = k8_qc_lang2(D,F,H,B) -> G = H & B = A & E = F & C = D))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2795 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2796 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k10_qc_lang2(A),k8_qc_lang1))) # label(dt_k10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2797 (all A (m1_subset_1(A,k8_qc_lang1) -> (k11_qc_lang1 = A | k1_qc_lang2 = A <-> r2_qc_lang2(A,k1_qc_lang2)))) # label(t101_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2798 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2799 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> k5_qc_lang2(k20_qc_lang1(k17_qc_lang1(A)),k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A)))) = A))) # label(t56_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2800 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> r2_qc_lang2(A,A))) # label(reflexivity_r2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2801 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k7_qc_lang2(C,E,A) = k7_qc_lang2(D,F,B) -> A = B & E = F & D = C))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2802 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2803 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B = A <-> r1_qc_lang2(A,k12_qc_lang1(B))))))) # label(t60_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2804 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang2(A) = k18_qc_lang1(k17_qc_lang1(A)))) # label(d16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2805 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k6_qc_lang2(F,G,E) = k8_qc_lang2(A,B,C,D) -> E = k14_qc_lang1(C,D) & B = G & A = F))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2806 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k3_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2807 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k2_qc_lang2(A,B) = k2_qc_lang2(C,D) -> A = C & D = B))))))))) # label(t17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2808 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k11_qc_lang2(A),k8_qc_lang1))) # label(dt_k11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2809 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) -> r3_qc_lang2(A,B)))))) # label(t73_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2810 (all A (m1_subset_1(A,k8_qc_lang1) -> k17_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) = k11_qc_lang2(A))) # label(d15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2811 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B)) & r3_qc_lang2(A,k2_qc_lang2(A,B)) & r3_qc_lang2(B,k2_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k2_qc_lang2(A,B)))))) # label(t93_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2812 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) -> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B))))))) # label(t104_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2813 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k4_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2814 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))) = k2_qc_lang2(A,B))))) # label(d2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2815 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2816 (all A all B all C (m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k7_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2817 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A != B & r2_qc_lang2(A,B) <-> r3_qc_lang2(A,B)))))) # label(d22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2818 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(A,B,C,D) = k7_qc_lang2(F,G,E) -> F = A & E = k5_qc_lang2(C,D) & B = G))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2819 (all A all B all C all D (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(C,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k9_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2820 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r2_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t79_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2821 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2822 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(v2_qc_lang1(A) & r1_qc_lang2(B,A)))))) # label(t64_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2823 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A)) = A))) # label(t55_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2824 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r2_qc_lang2(A,B) & r1_qc_lang2(B,A)))))) # label(t81_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2825 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (k21_qc_lang1(A) = B <-> r1_qc_lang2(B,A))))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2826 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k14_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k5_qc_lang2(A,B)))))) # label(t48_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2827 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) & v5_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A)))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2828 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (B = A <-> r1_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t63_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2829 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2830 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k17_qc_lang1(k12_qc_lang1(A)))) # label(t2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2831 (all A (m1_subset_1(A,k8_qc_lang1) -> (r1_qc_lang2(A,k1_qc_lang2) <-> A = k11_qc_lang1))) # label(t61_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2832 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> -r3_qc_lang2(A,A))) # label(irreflexivity_r3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2833 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2834 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> -r3_qc_lang2(A,k9_qc_lang1(C,D)))))))))) # label(t85_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2835 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> v4_qc_lang2(k7_qc_lang2(A,B,D)) & v4_qc_lang2(k9_qc_lang2(A,B,C,D)))))))))) # label(t38_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2836 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k5_qc_lang2(A,k5_qc_lang2(B,C)) = k7_qc_lang2(A,B,C) & k14_qc_lang1(A,k14_qc_lang1(B,C)) = k6_qc_lang2(A,B,C))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2837 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> k3_qc_lang2(k10_qc_lang2(A),k11_qc_lang2(A)) = A))) # label(t53_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2838 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k2_xboole_0(k15_qc_lang2(k21_qc_lang1(A)),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t119_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2839 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k14_qc_lang2(A),k8_qc_lang1))) # label(dt_k14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2840 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2841 (all A (m1_subset_1(A,k8_qc_lang1) -> (A = k11_qc_lang1 <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t99_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2842 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2843 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k6_qc_lang2(B,C,D) = k21_qc_lang1(k8_qc_lang2(A,B,C,D)) & A = k20_qc_lang1(k8_qc_lang2(A,B,C,D)) & v5_qc_lang1(k8_qc_lang2(A,B,C,D)))))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2844 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2845 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B))) = k15_qc_lang2(k2_qc_lang2(A,B)))))) # label(t113_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2846 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> (k9_qc_lang1(C,D) = A <-> r2_qc_lang2(A,k9_qc_lang1(C,D))))))))))) # label(t100_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2847 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)))))))))) # label(d9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2848 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B))) = k3_qc_lang2(A,B))))) # label(d3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2849 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k14_qc_lang1(B,D) = k14_qc_lang1(A,C) -> B = A & D = C))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2850 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> r3_qc_lang2(k17_qc_lang1(A),A)))) # label(t96_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2851 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r3_qc_lang2(A,k12_qc_lang1(B)) <-> r2_qc_lang2(A,B)))))) # label(t86_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2852 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,k15_qc_lang2(B)) -> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B))))))) # label(t105_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2853 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) <-> -(k12_qc_lang1(A) != B & (all C (m1_subset_1(C,k8_qc_lang1) -> B != k13_qc_lang1(A,C) & k13_qc_lang1(C,A) != B)) & (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> k14_qc_lang1(C,A) != B)))))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2854 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> A = k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A))))) # label(t4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2855 (all A all B all C all D (m1_subset_1(C,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2856 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(B,C) = k21_qc_lang1(k6_qc_lang2(A,B,C)) & k20_qc_lang1(k6_qc_lang2(A,B,C)) = A & v5_qc_lang1(k6_qc_lang2(A,B,C)))))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2857 (all A (m1_subset_1(A,k8_qc_lang1) -> -r3_qc_lang2(A,k11_qc_lang1))) # label(t84_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2858 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k5_qc_lang2(A,C) = k5_qc_lang2(B,D) -> A = B & C = D))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2859 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A))))) # label(t118_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2860 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k12_qc_lang1(B) = k12_qc_lang1(A) -> B = A))))) # label(t1_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2861 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2862 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k3_qc_lang2(A,B) = k2_qc_lang2(k12_qc_lang1(A),B))))) # label(t14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2863 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t80_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2864 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k20_qc_lang1(k14_qc_lang1(A,B)) & k21_qc_lang1(k14_qc_lang1(A,B)) = B)))) # label(t8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2865 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v2_qc_lang2(A) & v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(A)))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2866 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2867 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) <-> (exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & k5_qc_lang2(B,C) = A))))))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2868 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> k3_cqc_lang(A,B) = k6_cqc_lang(A,B))) # label(redefinition_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2869 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> ((exists D (v1_funct_2(D,k8_qc_lang1,k8_qc_lang1) & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1) & C = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A) & (all E (m1_subset_1(E,k8_qc_lang1) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang) = k9_cqc_lang & (v3_qc_lang1(E) -> k12_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k17_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v4_qc_lang1(E) -> k13_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k18_qc_lang1(E)),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k19_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v5_qc_lang1(E) -> k2_cqc_lang(k8_qc_lang1,k20_qc_lang1(E),B,E,k14_qc_lang1(k20_qc_lang1(E),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k21_qc_lang1(E)))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v2_qc_lang1(E) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k9_qc_lang1(k15_qc_lang1(E),k4_cqc_lang(k16_qc_lang1(E),k6_cqc_lang(k3_qc_lang3(np__0),B)))))) & v1_funct_1(D))) <-> k17_cqc_lang(A,B) = C))))))) # label(d6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2870 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2871 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2872 (all A all B all C (m1_qc_lang1(C,A) & v1_cqc_lang(C,A) & m1_subset_1(B,k7_qc_lang1(A)) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k8_cqc_lang(A,B,C),k8_qc_lang1,k7_cqc_lang))) # label(dt_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2873 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1) & v1_funct_1(k3_cqc_lang(B,A)))))) # label(t10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2874 (all A all B all C k3_cqc_lang(k4_tarski(A,B),C) = k9_funct_2(A,B,C)) # label(t42_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2875 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A)) -> (all D (m1_qc_lang1(D,A) -> k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))) = k17_cqc_lang(k9_qc_lang1(C,D),B))))))))) # label(t30_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2876 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k2_cqc_lang(A,B,C,D,E),A))) # label(dt_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2877 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2878 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2879 (all A all B (v1_funct_1(k3_cqc_lang(A,B)) & v1_relat_1(k3_cqc_lang(A,B)))) # label(fc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2880 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k2_qc_lang2(A,B) = k12_cqc_lang(A,B))) # label(redefinition_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2881 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2882 (all A all B all C (m1_qc_lang1(C,B) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_2_1_cqc_lang(B,C)) <-> (exists D (r1_xreal_0(np__1,D) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)) & k1_funct_1(C,D) = A & m2_subset_1(D,k1_numbers,k5_numbers)))))) # label(fraenkel_a_2_1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2883 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(B) -> k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A)) = k17_cqc_lang(B,A)))))) # label(t31_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2884 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k4_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t22_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2885 (all A all B B = k1_funct_1(k3_cqc_lang(A,B),A)) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2886 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> (m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang) <-> a_2_1_cqc_lang(A,C) = k1_xboole_0 & k1_xboole_0 = a_2_0_cqc_lang(A,C)))))))) # label(t17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2887 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> (r2_hidden(A,a_2_0_cqc_lang(B,C)) <-> (exists D (m2_subset_1(D,k1_numbers,k5_numbers) & k1_funct_1(C,D) = A & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)) & r1_xreal_0(np__1,D)))))) # label(fraenkel_a_2_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2888 (exists A (m1_subset_1(A,f1_s4_cqc_lang) & (exists B (v1_funct_1(B) & (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (m1_qc_lang1(G,F) & v1_cqc_lang(G,F) -> (all H (m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F)) -> f4_s4_cqc_lang(F,H,G) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,C)) = f7_s4_cqc_lang(E,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k11_cqc_lang(C,D)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,D)) & f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k10_cqc_lang(C)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_cqc_lang) = f3_s4_cqc_lang & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang) = A & m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang))))) # label(s4_cqc_lang_AndLHS) # label(axiom) # label(non_clause). [assumption]. 4.99/5.05 2889 (all A (m1_subset_1(A,f1_s4_cqc_lang) -> (all B (m1_subset_1(B,f1_s4_cqc_lang) -> -(B != A & (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) & f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)))))))))))))) & B = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang))) & (exists C (m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) = f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)))))))))))))) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = A & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(C)))))))) # label(s4_cqc_lang_AndRHS) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2890 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(B) -> k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A)) = k17_cqc_lang(B,A) | k20_qc_lang1(B) = A))))) # label(t36_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2891 (all A all B all C all D ((A = B -> k1_cqc_lang(A,B,C,D) = C) & (A != B -> D = k1_cqc_lang(A,B,C,D)))) # label(d1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2892 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s5_cqc_lang) -> ((exists C (v1_funct_1(C) & m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A) = B & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s5_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k10_cqc_lang(D)) = f5_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E)))))))))))))) & f3_s5_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang))) <-> f2_s5_cqc_lang(A) = B))))) -> f3_s5_cqc_lang = f2_s5_cqc_lang(k9_cqc_lang) # label(s5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2893 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k13_qc_lang1(A,B) = k11_cqc_lang(A,B))) # label(redefinition_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2894 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(B) -> k13_qc_lang1(k17_cqc_lang(k18_qc_lang1(B),A),k17_cqc_lang(k19_qc_lang1(B),A)) = k17_cqc_lang(B,A)))))) # label(t33_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2895 (all A all B k2_funcop_1(k1_tarski(A),B) = k3_cqc_lang(A,B)) # label(d2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2896 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2897 (all A all B (k1_tarski(A) = k1_relat_1(k3_cqc_lang(A,B)) & k2_relat_1(k3_cqc_lang(A,B)) = k1_tarski(B))) # label(t5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2898 (all A (m1_subset_1(A,k8_qc_lang1) -> (m2_subset_1(k12_qc_lang1(A),k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)))) # label(t18_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2899 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k15_cqc_lang(A,B) = k14_qc_lang1(A,B))) # label(redefinition_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2900 (all A all B all C C = k1_binop_1(k9_funct_2(A,B,C),A,B)) # label(t43_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2901 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s6_cqc_lang) -> (B = f3_s6_cqc_lang(A) <-> (exists C (B = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s6_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) & f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) = f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) & f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)))))))))))))) & f2_s6_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang) & v1_funct_1(C)))))))) -> f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) = f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) # label(s6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2902 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2903 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (r1_tarski(k2_relat_1(B),k2_qc_lang1) <-> v1_cqc_lang(B,A)))))) # label(d5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2904 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2905 (all A (m1_subset_1(A,k7_cqc_lang) -> k10_cqc_lang(A) = k12_qc_lang1(A))) # label(redefinition_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2906 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (k1_xboole_0 = a_2_1_cqc_lang(A,B) & k1_xboole_0 = a_2_0_cqc_lang(A,B) <-> m1_qc_lang1(B,A) & v1_cqc_lang(B,A)))))) # label(t15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2907 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> B = k17_cqc_lang(B,A))))) # label(t40_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2908 (all A all B all C (m1_subset_1(B,k7_qc_lang1(A)) & v1_cqc_lang(C,A) & m1_qc_lang1(C,A) & m1_subset_1(A,k5_numbers) -> k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C))) # label(redefinition_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2909 (all A (m1_subset_1(A,k5_numbers) -> (exists B (m1_qc_lang1(B,A) & v1_cqc_lang(B,A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))))) # label(rc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2910 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1))) # label(dt_k17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2911 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k14_cqc_lang(A,B) = k4_qc_lang2(A,B))) # label(redefinition_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2912 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k1_xboole_0 = k5_qc_lang3(B) -> k17_cqc_lang(B,A) = B))))) # label(t39_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2913 (all A all B (m1_finseq_1(A,k1_qc_lang1) & v1_funct_1(B) & m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) -> m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1))) # label(dt_k4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2914 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k3_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t21_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2915 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k17_cqc_lang(B,A)) = k17_cqc_lang(k12_qc_lang1(B),A))))) # label(t32_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2916 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2917 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2918 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2919 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2920 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> p1_s1_cqc_lang(k9_cqc_lang) & (p1_s1_cqc_lang(B) & p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k11_cqc_lang(A,B))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k15_cqc_lang(C,A))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k10_cqc_lang(A))) & p1_s1_cqc_lang(k8_cqc_lang(D,F,E)))))))))))))) -> (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> p1_s1_cqc_lang(A))) # label(s1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2921 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1) & v1_funct_1(k6_cqc_lang(A,B)))) # label(dt_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2922 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k14_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2923 (exists A (v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang) & m2_relset_1(A,k7_cqc_lang,f1_s2_cqc_lang) & (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_cqc_lang(F,E) & m1_qc_lang1(F,E) -> (all G (m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) -> k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)) = f3_s2_cqc_lang(E,G,F) & f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) & f5_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B),k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,C)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) = f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)))))))))))))) & f2_s2_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k9_cqc_lang) & v1_funct_1(A))) # label(s2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2924 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k5_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t24_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2925 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) & m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)))))) # label(t19_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2926 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (A != B -> k17_cqc_lang(k14_qc_lang1(A,C),B) = k14_qc_lang1(A,k17_cqc_lang(C,B))))))))) # label(t38_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2927 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> k17_cqc_lang(k9_cqc_lang,A) = k9_cqc_lang)) # label(t28_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2928 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s7_cqc_lang) -> (f2_s7_cqc_lang(A) = B <-> (exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) = f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) = f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) & f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)))))))))))))) & f3_s7_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) & B = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A) & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang)))))))) -> f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) = f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) # label(s7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2929 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k4_qc_lang1) -> (all D (m2_finseq_1(D,k1_qc_lang1) -> (all E (m2_finseq_1(E,k1_qc_lang1) -> (all F (v1_funct_1(F) & m2_relset_1(F,k4_qc_lang1,k1_qc_lang1) -> (k6_cqc_lang(C,B) = F & k4_cqc_lang(E,F) = D & r1_xreal_0(np__1,A) & r1_xreal_0(A,k3_finseq_1(E)) -> (C = k1_funct_1(E,A) -> B = k1_funct_1(D,A)) & (C != k1_funct_1(E,A) -> k1_funct_1(D,A) = k1_funct_1(E,A))))))))))))))) # label(t11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2930 (all A (m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang))) # label(dt_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2931 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)) = k17_cqc_lang(k13_qc_lang1(B,C),A))))))) # label(t34_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2932 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2933 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k3_qc_lang2(A,B) = k13_cqc_lang(A,B))) # label(redefinition_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2934 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k14_qc_lang1(A,B) = k17_cqc_lang(k14_qc_lang1(A,B),A))))) # label(t37_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2935 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & m1_qc_lang1(B,A) & m1_subset_1(A,k5_numbers) -> k5_cqc_lang(A,B,C) = k4_cqc_lang(B,C))) # label(redefinition_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2936 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> k17_cqc_lang(B,A) = k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A)))))))) # label(t29_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2937 (all A all B (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k7_cqc_lang) -> k5_qc_lang2(A,B) = k16_cqc_lang(A,B))) # label(redefinition_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2938 (all A all B all C all D all E (m1_subset_1(D,A) & m1_subset_1(E,A) & -v1_xboole_0(A) -> k1_cqc_lang(B,C,D,E) = k2_cqc_lang(A,B,C,D,E))) # label(redefinition_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2939 (all A (m2_finseq_1(A,k1_qc_lang1) -> (all B (m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(B) -> (all C (m2_finseq_1(C,k1_qc_lang1) -> (k3_finseq_1(C) = k3_finseq_1(A) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) & r1_xreal_0(D,k3_finseq_1(A)) -> (-r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D)) & (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))))) <-> k4_cqc_lang(A,B) = C))))))) # label(d3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2940 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k12_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2941 (all A (m1_subset_1(A,k8_qc_lang1) -> (k5_qc_lang3(A) = k1_xboole_0 & k6_qc_lang3(A) = k1_xboole_0 <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang)))) # label(t13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2942 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2943 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k8_cqc_lang(D,F,E)) = f5_s3_cqc_lang(D,F,E) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) & f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)) & f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k15_cqc_lang(C,A)))))))))))))) & (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_qc_lang1(E,D) & v1_cqc_lang(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> f5_s3_cqc_lang(D,F,E) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k8_cqc_lang(D,F,E)) & f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,B)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k11_cqc_lang(A,B)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang & f4_s3_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_cqc_lang) -> f3_s3_cqc_lang = f2_s3_cqc_lang # label(s3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2944 (all A (r2_hidden(A,k1_qc_lang1) <-> -(-r2_hidden(A,k3_qc_lang1) & -r2_hidden(A,k4_qc_lang1) & -r2_hidden(A,k2_qc_lang1)))) # label(t7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2945 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s8_cqc_lang) -> ((exists C (m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A) = B & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) = f3_s8_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f4_s8_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)) & f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)) & f6_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) & f5_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k10_cqc_lang(D)))))))))))))) & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang) & v1_funct_1(C))) <-> B = f2_s8_cqc_lang(A)))))) -> f6_s8_cqc_lang(f2_s8_cqc_lang(f7_s8_cqc_lang),f2_s8_cqc_lang(f8_s8_cqc_lang)) = f2_s8_cqc_lang(k11_cqc_lang(f7_s8_cqc_lang,f8_s8_cqc_lang)) # label(s8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2946 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(k14_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)))))) # label(t23_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2947 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2948 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k2_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t20_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2949 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = k20_qc_lang1(B) & v5_qc_lang1(B) -> k17_cqc_lang(B,A) = B))))) # label(t35_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2950 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s9_cqc_lang) -> ((exists C (v1_funct_1(C) & f3_s9_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s9_cqc_lang(G,I,H) & f5_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k10_cqc_lang(D)) & f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)))))))))))))) & B = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A) & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang))) <-> f2_s9_cqc_lang(A) = B))))) -> f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) = f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) # label(s9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2951 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2952 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(C) & m1_qc_lang1(B,A) -> m1_qc_lang1(k5_cqc_lang(A,B,C),A))) # label(dt_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2953 (all A ((exists B (k1_xboole_0 = k5_qc_lang3(B) & k6_qc_lang3(B) = k1_xboole_0 & A = B & m1_subset_1(B,k8_qc_lang1))) <-> r2_hidden(A,a_0_0_cqc_lang))) # label(fraenkel_a_0_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2954 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2955 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(k17_cqc_lang(B,A)) = k6_qc_lang3(B))))) # label(t41_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2956 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,B) = k3_cat_1(A,D) & k4_cat_1(A,C,B) = k4_cat_1(A,D,B) & k3_cat_1(A,C) = k2_cat_1(A,B) & k2_cat_1(A,D) = k2_cat_1(A,C) -> D = C))))) <-> v3_cat_1(B,A)))))) # label(d10_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2957 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2958 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C) & k2_cat_1(A,B) = k2_cat_1(A,k4_cat_1(A,B,C))))))))) # label(t42_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2959 (all A (l1_cat_1(A) -> v1_funct_1(u3_cat_1(A)) & m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2960 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k5_cat_1(A,B) = k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))))) # label(d5_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2961 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2962 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))))) # label(t103_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2963 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2964 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,E),k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F)) = k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k14_cat_1(A,B,C,D,E)),F))))))))))))) # label(t112_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2965 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> m1_cat_1(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t125_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2966 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k3_cat_1(A,B))))) # label(d3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2967 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (r2_hidden(F,k6_cat_1(A,D,E)) -> r2_hidden(k1_funct_1(C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t123_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2968 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) & v2_cat_1(B) -> m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)))) # label(dt_k13_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2969 (all A (l1_cat_1(A) & v2_cat_1(A) -> v8_cat_1(k15_cat_1(A),A,A))) # label(t122_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2970 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> k5_cat_1(A,B) = k10_cat_1(A,B))) # label(redefinition_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2971 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (m2_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(k4_tarski(E,D),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(B),k4_tarski(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k1_funct_1(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D)))))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u4_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u3_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) & (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) & m1_subset_1(E,u1_cat_1(B))))))))))))) # label(d18_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2972 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,E,B) -> (all G (m1_cat_1(G,A,E,B) -> (k9_cat_1(A,E,B,C,F,D) = k9_cat_1(A,E,B,C,G,D) -> F = G | k1_xboole_0 = k6_cat_1(A,E,B)))))))) <-> v3_cat_1(D,A))))))))))) # label(t60_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2973 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v4_cat_1(B,A) <-> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) & k3_cat_1(A,B) = k2_cat_1(A,D) & k3_cat_1(A,D) = k3_cat_1(A,C) & k4_cat_1(A,B,D) = k4_cat_1(A,B,C) -> D = C)))))))))) # label(d11_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2974 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,C) = k2_cat_1(A,B) <-> r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A)))))))))) # label(t40_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2975 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) & v2_cat_1(C) & v2_cat_1(B) -> k5_relat_1(D,E) = k14_cat_1(A,B,C,D,E))) # label(redefinition_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2976 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k6_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2977 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k5_cat_1(A,B) = k5_cat_1(A,C) -> B = C))))))) # label(t45_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2978 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2979 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t110_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2980 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)))) # label(dt_k2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2981 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,C,B) & (exists D (m1_cat_1(D,A,C,B) & (all E (m1_cat_1(E,A,C,B) -> E = D))))))))))) # label(d15_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2982 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> -((exists E (m1_cat_1(E,A,C,B) & (exists F (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & k9_cat_1(A,B,C,B,D,F) = k10_cat_1(A,B) & E != F & m1_cat_1(F,A,C,B))))) & k6_cat_1(A,C,B) != k1_xboole_0 & k6_cat_1(A,B,C) != k1_xboole_0))))))))) # label(t71_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2983 (all A all B all C (k1_relat_1(k1_cat_1(A,B,C)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) & k1_relat_1(k1_cat_1(A,B,C)) = k1_tarski(k4_tarski(A,B)))) # label(t7_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2984 (exists A (v2_cat_1(A) & v1_cat_1(A) & l1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2985 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,E)))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k3_cat_1(A,E) = k2_cat_1(A,F) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F))))))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k3_cat_1(A,E)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)))) -> m2_cat_1(C,A,B)))))))))) # label(t100_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2986 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,C,E) -> (all G (m1_cat_1(G,A,C,E) -> (k9_cat_1(A,B,C,E,D,G) = k9_cat_1(A,B,C,E,D,F) -> k6_cat_1(A,C,E) = k1_xboole_0 | F = G))))))) <-> v4_cat_1(D,A))))))))))) # label(t65_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2987 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2988 (all A all B all C all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,D) & v1_funct_2(E,A,D) -> (r1_tarski(k2_funct_2(A,D,E,B),C) & r1_tarski(B,A) -> v1_funct_2(k2_partfun1(A,D,E,B),B,C) & m2_relset_1(k2_partfun1(A,D,E,B),B,C) & v1_funct_1(k2_partfun1(A,D,E,B))))))) # label(t4_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2989 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)))) # label(dt_k3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2990 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) = k1_tarski(D) -> (all E (m1_cat_1(E,A,B,C) -> E = D))))))))))) # label(t25_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2991 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v3_cat_1(k10_cat_1(A,B),A))))) # label(t64_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2992 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2993 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D))))))))))) # label(t43_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2994 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v2_funct_1(C) & u2_cat_1(B) = k2_relat_1(C) & u1_cat_1(B) = k2_relat_1(k12_cat_1(A,B,C)) <-> v8_cat_1(C,A,B)))))))) # label(d22_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2995 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> k13_cat_1(A,B,C,D) = E))))))))))) # label(t107_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2996 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k16_cat_1(A,B,C,D,E) = k2_partfun1(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)))))))))))) # label(d25_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2997 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(E,A) & v4_cat_1(F,A) -> v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k1_xboole_0 = k6_cat_1(A,C,D) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))) # label(t66_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2998 (all A all B all C C = k1_funct_1(k1_cat_1(A,B,C),k4_tarski(A,B))) # label(t8_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 2999 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v10_cat_1(D,A,B) & v10_cat_1(E,B,C) -> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t128_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3000 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3001 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(F,A) & v3_cat_1(E,A) -> k1_xboole_0 = k6_cat_1(A,C,D) | v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t61_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3002 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> (exists C m2_cat_1(C,A,B)))) # label(existence_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3003 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u2_cat_1(k8_cat_1(A,B))) -> r2_hidden(E,k6_cat_1(k8_cat_1(A,B),C,D)))))))) # label(t36_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3004 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,D) = B & C = k3_cat_1(A,D) <-> r2_hidden(D,k6_cat_1(A,B,C))))))))))) # label(t18_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3005 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3006 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,B,C) & k6_cat_1(A,B,C) = k1_tarski(D))))) <-> v7_cat_1(B,A)))))) # label(t82_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3007 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> v4_cat_1(D,A) & v3_cat_1(D,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t73_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3008 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3009 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) & m1_subset_1(E,u1_cat_1(B)))))) -> (all D (v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(D) -> (D = k12_cat_1(A,B,C) <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),E)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),F) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E) = F))))))))))))))) # label(d19_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.06 3010 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))))))))) # label(t105_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3011 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3012 (all A all B all C (m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k1_cat_1(A,B,C)))) # label(dt_k1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3013 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u2_cat_1(k8_cat_1(A,B))) -> m1_cat_1(E,k8_cat_1(A,B),C,D))))))) # label(t37_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3014 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k6_cat_1(A,B,C) != k1_xboole_0 & k6_cat_1(A,C,D) != k1_xboole_0 & -r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D))))))))))))))) # label(t51_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3015 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k10_cat_1(A,B) = k9_cat_1(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)))))) # label(t59_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3016 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & m1_cat_1(E,A,B,C) & m1_cat_1(F,A,C,D) -> m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D))) # label(dt_k9_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3017 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> k6_cat_1(k8_cat_1(A,B),C,D) != k1_xboole_0)))) # label(t38_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3018 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,C,D) | v3_cat_1(E,A)))))))))))))) # label(t62_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3019 (exists A (v2_cat_1(A) & l1_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3020 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v6_cat_1(B,A) & r1_cat_1(A,C,B) -> v6_cat_1(C,A)))))))) # label(t89_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3021 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3022 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k13_cat_1(B,C,E,k13_cat_1(A,B,D,F)) = k13_cat_1(A,C,k14_cat_1(A,B,C,D,E),F))))))))))))) # label(t113_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3023 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k13_cat_1(A,B,C,D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D))))))))) # label(d20_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3024 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) & k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E))))))) -> m2_cat_1(C,A,B)))))))) # label(t96_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3025 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3026 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k6_cat_1(A,B,C) != k1_xboole_0 & (exists D ((exists E (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) & m1_cat_1(E,A,C,B))) & m1_cat_1(D,A,B,C))) & k6_cat_1(A,C,B) != k1_xboole_0 <-> r1_cat_1(A,B,C)))))))) # label(t81_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3027 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v9_cat_1(D,A,B) & v9_cat_1(E,B,C) -> v9_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t127_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3028 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v9_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) = k2_relat_1(k16_cat_1(A,B,C,D,E))))))))))))) # label(t132_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3029 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,D,E) -> (F = G -> k1_xboole_0 = k6_cat_1(A,B,C) | B = D & C = E | k1_xboole_0 = k6_cat_1(A,D,E)))))))))))))))) # label(t24_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3030 (all A all B all C all D (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_cat_1(D,A,B,C) & m1_subset_1(C,u1_cat_1(A)) & v2_cat_1(A) -> m1_cat_1(k11_cat_1(A,B,C,D),A,C,B))) # label(dt_k11_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3031 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(A),k4_tarski(C,B)) = k4_cat_1(A,B,C)))))))) # label(d4_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3032 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3033 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3034 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) -> k1_xboole_0 = k6_cat_1(A,C,B) | v4_cat_1(D,A) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))) # label(t68_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3035 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k3_cat_1(A,k5_cat_1(A,B)) & k2_cat_1(A,k5_cat_1(A,B)) = B)))) # label(t44_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3036 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v6_cat_1(C,A) & v6_cat_1(B,A) -> r1_cat_1(A,B,C)))))))) # label(t88_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3037 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> -(r2_tarski(k6_cat_1(A,B,C),k6_cat_1(A,D,E)) & (all G (m1_cat_1(G,A,D,E) -> k1_tarski(G) != k6_cat_1(A,D,E))) & k6_cat_1(A,B,C) = k1_tarski(F)))))))))))))) # label(t27_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3038 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) -> r1_cat_1(A,C,B)))))))) # label(t92_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3039 (all A all B m1_subset_1(A,u2_cat_1(k8_cat_1(B,A)))) # label(t33_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3040 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (r1_cat_1(A,C,D) & r1_cat_1(A,B,C) -> r1_cat_1(A,B,D)))))))))) # label(t93_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3041 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3042 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> D = k9_cat_1(A,B,C,C,D,k10_cat_1(A,C))))))))))) # label(t57_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3043 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> -(k6_cat_1(A,C,D) != k1_xboole_0 & k1_xboole_0 = k6_cat_1(A,B,D) & k6_cat_1(A,B,C) != k1_xboole_0))))))))) # label(t52_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3044 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)))))) # label(t19_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3045 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3046 (all A all B m1_subset_1(A,u1_cat_1(k8_cat_1(A,B)))) # label(t32_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3047 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> (all C (m2_cat_1(C,A,B) -> m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C))))) # label(dt_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3048 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> B = k2_cat_1(A,D) & C = k3_cat_1(A,D)))))))))) # label(t23_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3049 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3050 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> -(k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) = k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,D,E)))))))))))) # label(t126_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3051 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u1_cat_1(k8_cat_1(A,B))) -> (all F (m1_subset_1(F,u1_cat_1(k8_cat_1(A,B))) -> (all G (m1_cat_1(G,k8_cat_1(A,B),C,D) -> (all H (m1_cat_1(H,k8_cat_1(A,B),E,F) -> G = H)))))))))))) # label(t39_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3052 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B))))) # label(d2_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3053 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k6_cat_1(A,B,B) != k1_xboole_0)))) # label(t56_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3054 (all A all B g1_cat_1(k1_tarski(A),k1_tarski(B),k7_cat_1(B,A),k7_cat_1(B,A),k1_cat_1(B,B,B),k7_cat_1(A,B)) = k8_cat_1(A,B)) # label(d9_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3055 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3056 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v5_cat_1(k10_cat_1(A,B),A))))) # label(t74_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3057 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k13_cat_1(A,B,C,D)))))))))) # label(t108_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3058 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> C = k10_cat_1(A,B)))))))) # label(t83_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3059 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3060 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3061 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)))))) # label(t55_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3062 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) & v2_cat_1(C) & l1_cat_1(B) -> m2_cat_1(k14_cat_1(A,B,C,D,E),A,C))) # label(dt_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3063 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) -> v3_cat_1(E,A) | k1_xboole_0 = k6_cat_1(A,C,B) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))) # label(t63_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3064 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3065 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(F,A) & v5_cat_1(E,A) -> k6_cat_1(A,C,D) = k1_xboole_0 | v5_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t75_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3066 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3067 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> C = k10_cat_1(A,B)))))))) # label(t87_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3068 (all A (l1_cat_1(A) -> (v1_cat_1(A) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = A))) # label(abstractness_v1_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3069 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k9_cat_1(A,B,C,D,E,F) != k4_cat_1(A,E,F) & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))) # label(d13_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3070 (all A all B all C (m1_subset_1(C,u2_cat_1(k8_cat_1(A,B))) -> C = B)) # label(t35_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3071 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> r2_hidden(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))))))))))))))) # label(t124_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3072 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) != k1_xboole_0 -> (all F (m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> k1_xboole_0 != k6_cat_1(A,D,E) & (exists G (m1_cat_1(G,A,D,E) & F = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G)))))))))) <-> v9_cat_1(C,A,B)))))))) # label(d23_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3073 (all A (l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k6_partfun1(u2_cat_1(A)),A,A))) # label(t111_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3074 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) != k1_xboole_0 & (exists D (m1_cat_1(D,A,B,C) & (all E (m1_cat_1(E,A,B,C) -> E = D))))))))))) # label(d16_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3075 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3076 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> m1_cat_1(B,A,k2_cat_1(A,B),k3_cat_1(A,B)))))) # label(t22_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3077 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> r1_tarski(k2_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))) # label(t129_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3078 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) <-> k11_cat_1(A,B,C,D) = E))) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(d14_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3079 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v5_cat_1(B,A) <-> (exists C (m1_subset_1(C,u2_cat_1(A)) & k4_cat_1(A,B,C) = k5_cat_1(A,k2_cat_1(A,B)) & k4_cat_1(A,C,B) = k5_cat_1(A,k3_cat_1(A,B)) & k3_cat_1(A,C) = k2_cat_1(A,B) & k3_cat_1(A,B) = k2_cat_1(A,C)))))))) # label(d12_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3080 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B) = B)))) # label(t115_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3081 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> k9_cat_1(A,B,B,C,k10_cat_1(A,B),D) = D))))))))) # label(t58_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3082 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(B,A) & v7_cat_1(C,A) -> r1_cat_1(A,B,C)))))))) # label(t84_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3083 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E))))) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D))))))))))))) # label(t102_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3084 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,E) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) & k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E))))))))))))) # label(t99_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3085 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3086 (all A all B (v1_funct_1(k7_cat_1(A,B)) & v1_funct_2(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) & m2_relset_1(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)))) # label(dt_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3087 (all A (l1_cat_1(A) -> v1_funct_1(u6_cat_1(A)) & m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)))) # label(dt_u6_cat_1) # label(axiom) # label(non_clause). [assumption]. 4.99/5.07 3088 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v6_cat_1(B,A) -> k6_cat_1(A,B,C) = k1_xboole_0 | v3_cat_1(D,A)))))))))) # label(t90_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3089 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3090 (all A (l1_cat_1(A) -> (v2_cat_1(A) <-> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) -> k1_funct_1(u4_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & k1_funct_1(u3_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B)))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D) -> k1_funct_1(u5_cat_1(A),k4_tarski(k1_funct_1(u5_cat_1(A),k4_tarski(D,C)),B)) = k1_funct_1(u5_cat_1(A),k4_tarski(D,k1_funct_1(u5_cat_1(A),k4_tarski(C,B))))))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B & (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = B -> k1_funct_1(u5_cat_1(A),k4_tarski(k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),C)) = C))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = B -> k1_funct_1(u5_cat_1(A),k4_tarski(C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))) = C))) & B = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) <-> r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))))))))))) # label(d8_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3091 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3092 (all A all B all C (l1_cat_1(A) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)))) # label(dt_k4_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3093 (all A all B all C all D (m1_subset_1(C,u1_cat_1(B)) & m1_subset_1(D,u1_cat_1(B)) & l1_cat_1(B) -> (r2_hidden(A,a_3_0_cat_1(B,C,D)) <-> (exists E (A = E & C = k2_cat_1(B,E) & k3_cat_1(B,E) = D & m1_subset_1(E,u2_cat_1(B))))))) # label(fraenkel_a_3_0_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3094 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E))))))))))) # label(t97_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3095 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(B,A) & r1_cat_1(A,B,C) -> v7_cat_1(C,A)))))))) # label(t85_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3096 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v4_cat_1(k10_cat_1(A,B),A))))) # label(t69_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3097 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3098 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r1_cat_1(A,B,B))))) # label(t91_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.19/5.30 3099 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v10_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> (all G (m1_cat_1(G,A,D,E) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) -> G = F))))))))))))))))) # label(d24_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3100 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> m1_cat_1(k10_cat_1(A,B),A,B,B))) # label(dt_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3101 (all A (v2_cat_1(A) & l1_cat_1(A) -> m2_cat_1(k15_cat_1(A),A,A))) # label(dt_k15_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3102 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_1(F) & v1_funct_2(F,A,B) & m1_relset_1(F,A,B) & v1_funct_1(E) & m1_relset_1(D,B,A) & m1_relset_1(C,B,A) & v1_funct_2(C,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> l1_cat_1(g1_cat_1(A,B,C,D,E,F)) & v1_cat_1(g1_cat_1(A,B,C,D,E,F)))) # label(dt_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3103 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k13_cat_1(A,A,k15_cat_1(A),B))))) # label(t118_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3104 (all A (l1_cat_1(A) -> m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)) & v1_funct_1(u5_cat_1(A)))) # label(dt_u5_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3105 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3106 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3107 (all A (l1_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) <-> r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A)))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k3_cat_1(A,C) = k3_cat_1(A,k4_cat_1(A,B,C)) & k2_cat_1(A,B) = k2_cat_1(A,k4_cat_1(A,B,C))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,B,k4_cat_1(A,C,D)) = k4_cat_1(A,k4_cat_1(A,B,C),D)))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k2_cat_1(A,k5_cat_1(A,B)) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k3_cat_1(A,C) -> k4_cat_1(A,C,k5_cat_1(A,B)) = C))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = B -> C = k4_cat_1(A,k5_cat_1(A,B),C)))) & B = k3_cat_1(A,k5_cat_1(A,B)))) -> v2_cat_1(A)))) # label(t29_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3108 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3109 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> C = A)) # label(t34_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3110 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,C) = B -> k4_cat_1(A,C,k5_cat_1(A,B)) = C))))))) # label(t46_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3111 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3112 (all A all B all C all D (m1_subset_1(D,k1_tarski(A)) -> (all E (m1_subset_1(E,k1_tarski(B)) -> C = k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)))))) # label(t9_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3113 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,B) = k3_cat_1(A,C) -> k1_funct_1(u5_cat_1(A),k4_tarski(B,C)) = k4_cat_1(A,C,B)))))))) # label(t41_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3114 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_cat_1(A,B,C) = a_3_0_cat_1(A,B,C))))))) # label(d6_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3115 (all A (l1_cat_1(A) & v2_cat_1(A) -> k15_cat_1(A) = k6_partfun1(u2_cat_1(A)))) # label(d21_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3116 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)))))))))) # label(t104_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3117 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) & k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))))))))))) # label(t98_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3118 (all A all B (v1_cat_1(k8_cat_1(A,B)) & l1_cat_1(k8_cat_1(A,B)) & v2_cat_1(k8_cat_1(A,B)))) # label(dt_k8_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3119 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (m1_cat_1(D,A,B,C) <-> r2_hidden(D,k6_cat_1(A,B,C)))))))))))) # label(d7_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3120 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,C,B) & k6_cat_1(A,C,B) = k1_tarski(D)))))))))) # label(t86_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3121 (all A (l1_cat_1(A) & v2_cat_1(A) -> k6_partfun1(u1_cat_1(A)) = k12_cat_1(A,A,k15_cat_1(A)))) # label(t117_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3122 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (r2_hidden(D,k6_cat_1(A,B,C)) -> m1_cat_1(D,A,B,C))))))))) # label(t21_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3123 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)))) # label(dt_k5_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3124 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3125 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> ((exists E (m1_cat_1(E,A,C,B) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D))) & k6_cat_1(A,C,B) != k1_xboole_0 <-> v5_cat_1(D,A))))))))))) # label(t70_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3126 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(A),k12_cat_1(A,A,k15_cat_1(A)),B) = B)))) # label(t116_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3127 (all A all B all C (m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> (all D (m1_cat_1(D,A,B,C) -> m1_subset_1(D,u2_cat_1(A)))))) # label(dt_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3128 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k1_funct_1(k16_cat_1(A,B,C,D,E),F)))))))))))))) # label(t131_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3129 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & l1_cat_1(B) -> m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(k12_cat_1(A,B,C)))) # label(dt_k12_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3130 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> v2_funct_1(k16_cat_1(A,B,C,D,E)))))) <-> v10_cat_1(C,A,B)))))))) # label(t133_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3131 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3132 (exists A (v1_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3133 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3134 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) <-> (exists D (m1_cat_1(D,A,B,C) & v5_cat_1(D,A))) & k1_xboole_0 != k6_cat_1(A,B,C)))))))) # label(d17_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3135 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,C,D) -> (all H (m1_cat_1(H,A,D,E) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k1_xboole_0 != k6_cat_1(A,C,D) & k6_cat_1(A,D,E) != k1_xboole_0 & k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) != k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H))))))))))))))))))) # label(t54_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3136 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> ((all E (m1_cat_1(E,A,B,C) -> D = E)) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_tarski(D) = k6_cat_1(A,B,C)))))))))) # label(t26_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3137 (all A all B all C k3_cqc_lang(k4_tarski(A,B),C) = k1_cat_1(A,B,C)) # label(d1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3138 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3139 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & m1_subset_1(E,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & l1_cat_1(B) -> v1_funct_1(k16_cat_1(A,B,C,D,E)) & v1_funct_2(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) & m2_relset_1(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))) # label(dt_k16_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3140 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3141 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3142 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,C,D) | v4_cat_1(F,A)))))))))))))) # label(t67_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3143 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(E,A) & v5_cat_1(F,A) -> k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E)) = k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) | k1_xboole_0 = k6_cat_1(A,C,D) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t77_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3144 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) -> (exists D m1_cat_1(D,A,B,C)))) # label(existence_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3145 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_2(C,B,A) & m1_relset_1(D,B,A) & v1_funct_1(F) & v1_funct_2(F,A,B) & m1_relset_1(F,A,B) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & v1_funct_2(D,B,A) & v1_funct_1(D) & m1_relset_1(C,B,A) & v1_funct_1(C) & -v1_xboole_0(A) -> (all G all H all I all J all K all L (g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L) -> B = H & D = J & L = F & K = E & C = I & G = A)))) # label(free_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3146 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = B -> k4_cat_1(A,k5_cat_1(A,B),C) = C))))))) # label(t47_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.37 3147 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> v5_cat_1(k11_cat_1(A,B,C,D),A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t76_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3148 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3149 (all A (l1_cat_1(A) -> v1_funct_1(u4_cat_1(A)) & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u4_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3150 (all A all B k3_cqc_lang(A,B) = k7_cat_1(A,B)) # label(redefinition_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3151 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k2_cat_1(A,D)) & k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k3_cat_1(A,D)))))))))) # label(t109_cat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3152 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(A,C,k1_cat_2(B,A,C,k1_fraenkel(A,C),k3_cat_2(A,B,C,F),E),D))))))))))))) # label(t4_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3153 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (r1_cat_2(B,A) <-> v9_cat_1(k8_cat_2(A,B),B,A)))))) # label(t27_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3154 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) -> ((exists F ((all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(B)) -> k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,H) = k14_cat_2(B,A,C,F,H) & k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,G) = k15_cat_2(B,A,C,F,G))))) & m2_cat_1(F,k11_cat_2(B,A),C))) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)) = k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G))))))))))))))))) # label(t53_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3155 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> v10_cat_1(k8_cat_2(A,B),B,A))))) # label(t24_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3156 $T # label(t9_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3157 $T # label(t56_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3158 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (-v1_xboole_0(C) -> (m1_cat_2(C,A,B) <-> (all D (m1_subset_1(D,C) -> m2_cat_1(D,A,B)))))))))) # label(d3_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3159 $T # label(t49_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3160 (all A all B all C all D all E all F (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(E) & m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & v1_funct_2(E,A,C) & -v1_xboole_0(A) -> k15_funct_3(E,F) = k9_cat_2(A,B,C,D,E,F))) # label(redefinition_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3161 $T # label(t26_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3162 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(B) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(D,u2_cat_1(B)) & v2_cat_1(B) & l1_cat_1(A) -> m1_subset_1(k13_cat_2(A,B,C,D),u2_cat_1(k11_cat_2(A,B))))) # label(dt_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3163 (all A all B all C all D all E (v2_cat_1(A) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> k13_funct_3(D,E) = k18_cat_2(A,B,C,D,E))) # label(redefinition_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3164 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(C),k14_cat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,k10_cat_1(A,E),F)))))))))))))) # label(t47_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3165 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m1_subset_1(E,u1_cat_1(B)) & m2_cat_1(D,k11_cat_2(A,B),C) & v2_cat_1(B) -> m2_cat_1(k15_cat_2(A,B,C,D,E),A,C))) # label(dt_k15_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3166 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> m1_subset_1(k3_tarski(a_2_0_cat_2(A,B)),k1_zfmisc_1(u2_cat_1(A))) & -v1_xboole_0(k3_tarski(a_2_0_cat_2(A,B))))))) # label(t28_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3167 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)) = k15_cat_2(A,B,C,D,E))))))))))) # label(d9_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3168 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(D) & m2_cat_1(E,A,C) & m2_cat_1(F,B,D) & v2_cat_1(D) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) -> m2_cat_1(k19_cat_2(A,B,C,D,E,F),k11_cat_2(A,B),k11_cat_2(C,D)))) # label(dt_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3169 $T # label(t46_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3170 $T # label(t8_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3171 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(E) & v1_funct_2(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) & m1_relset_1(E,A,C) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> m2_relset_1(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_1(k9_cat_2(A,B,C,D,E,F)))) # label(dt_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3172 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)) = k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k15_cat_2(A,B,C,D,F)),E))))))))))))) # label(t51_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3173 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(k11_cat_2(A,B))) -> (exists D ((exists E (m1_subset_1(E,u1_cat_1(B)) & k12_cat_2(A,B,D,E) = C)) & m1_subset_1(D,u1_cat_1(A)))))))))) # label(t35_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3174 $T # label(t10_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3175 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> D = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(B),k12_cat_1(k11_cat_2(A,B),B,k17_cat_2(A,B)),k12_cat_2(A,B,C,D)))))))))) # label(t61_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3176 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> m1_subset_1(k1_domain_1(u2_cat_1(A),u2_cat_1(B),C,D),u2_cat_1(k11_cat_2(A,B))))))))))) # label(t36_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3177 $T # label(dt_k5_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3178 $T # label(t32_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3179 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> m2_cat_1(k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)),A,C))))))))))) # label(t45_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3180 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k10_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),B))))) # label(t55_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3181 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> m1_subset_1(k1_domain_1(u1_cat_1(A),u1_cat_1(B),C,D),u1_cat_1(k11_cat_2(A,B))))))))))) # label(t34_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3182 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> D = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(B),k17_cat_2(A,B),k13_cat_2(A,B,C,D)))))))))) # label(t60_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3183 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> m2_cat_1(k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F),k11_cat_2(A,C),k11_cat_2(B,D)))))))))))))) # label(t65_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3184 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (m3_cat_2(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (C = E & D = F -> r1_tarski(k6_cat_1(B,C,D),k6_cat_1(A,E,F))))))))))) & r1_tarski(u5_cat_1(B),u5_cat_1(A)) & (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (C = D -> k10_cat_1(B,C) = k10_cat_1(A,D)))))) & r1_tarski(u1_cat_1(B),u1_cat_1(A))))))) # label(d4_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3185 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_cat_2(C,A,B) & v2_cat_1(A) -> (all D (m1_subset_1(D,C) <-> m2_cat_2(D,A,B,C))))) # label(redefinition_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3186 $T # label(t57_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3187 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (k5_cat_2(A,B) = C <-> (all D (m2_cat_1(D,A,B) <-> r2_hidden(D,C))))))))) # label(d2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3188 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> m2_cat_1(k15_cat_1(B),B,A))))) # label(t19_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3189 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k8_cat_2(A,B)),C))))))) # label(t22_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3190 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k16_cat_2(A,B),k11_cat_2(A,B),A))) # label(dt_k16_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3191 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> m1_subset_1(C,u1_cat_1(A)))))))) # label(t12_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3192 (all A all B all C all D all E all F (v1_funct_2(E,A,D) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_1(E) & m1_fraenkel(D,B,C) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k1_cat_2(A,B,C,D,E,F) = k1_funct_1(E,F))) # label(redefinition_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3193 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(B) -> (exists D m2_cat_2(D,A,B,C)))) # label(existence_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3194 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (D = F & k3_cat_1(B,C) = k2_cat_1(B,D) & C = E -> k4_cat_1(B,C,D) = k4_cat_1(A,E,F)))))))))))))) # label(t17_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3195 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,C,B) & m2_relset_1(D,C,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,B) & v1_funct_2(E,C,B) -> (all F (m2_relset_1(F,k2_zfmisc_1(C,C),C) & v1_funct_1(F) -> (all G (v1_funct_2(G,B,C) & m2_relset_1(G,B,C) & v1_funct_1(G) -> (r1_cat_2(g1_cat_1(B,C,D,E,F,G),A) -> E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & k1_realset1(u5_cat_1(A),C) = F & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) & D = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) & C = k3_tarski(a_2_0_cat_2(A,B))))))))))))))))) # label(t31_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3196 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k3_cat_1(B,E) = k2_cat_1(B,F) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) = k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F))))))))))))))) # label(t39_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3197 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(B) -> m2_relset_1(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) & v1_funct_2(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) & v1_funct_1(k2_cat_2(A,B,C,D)))) # label(dt_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3198 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)) = u1_cat_1(k11_cat_2(A,B)) & k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)) = u4_cat_1(k11_cat_2(A,B)) & u6_cat_1(k11_cat_2(A,B)) = k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B)) & u5_cat_1(k11_cat_2(A,B)) = k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)) & k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)) = u3_cat_1(k11_cat_2(A,B)) & k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)) = u2_cat_1(k11_cat_2(A,B)))))) # label(t33_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3199 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k14_cat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)))))))))))) # label(d8_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3200 (all A (l1_cat_1(A) & v2_cat_1(A) -> (exists B (v2_cat_1(B) & v1_cat_1(B) & m3_cat_2(B,A))))) # label(rc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3201 (all A (v2_cat_1(A) & l1_cat_1(A) -> m3_cat_2(A,A))) # label(t18_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3202 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (C = D -> k2_cat_1(A,D) = k2_cat_1(B,C) & k3_cat_1(A,D) = k3_cat_1(B,C)))))))))) # label(t15_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3203 (all A all B all C all D all E all F (m1_cat_2(D,B,C) & v1_funct_2(E,A,D) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_1(E) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & -v1_xboole_0(A) -> m2_cat_2(k6_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3204 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k3_cat_1(A,C),k3_cat_1(B,D)) & k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k2_cat_1(A,C),k2_cat_1(B,D)))))))))) # label(t38_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3205 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (v9_cat_1(k8_cat_2(A,B),B,A) <-> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (D = F & C = E -> k6_cat_1(B,C,D) = k6_cat_1(A,E,F))))))))))))))) # label(t25_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3206 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),k2_cat_2(A,B,C,F),D),E))))))))))))) # label(t3_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3207 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> (exists C m1_cat_2(C,A,B)))) # label(existence_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3208 (all A (l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (m3_cat_2(A,B) & (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (D = F & E = C -> k6_cat_1(A,C,D) = k6_cat_1(B,E,F)))))))))) <-> r1_cat_2(A,B)))))) # label(d6_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3209 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> r1_tarski(u2_cat_1(B),u2_cat_1(A)))))) # label(t13_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3210 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(D,u2_cat_1(B)) & l1_cat_1(B) & l1_cat_1(A) -> k4_tarski(C,D) = k13_cat_2(A,B,C,D))) # label(redefinition_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3211 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k17_cat_2(A,B),k11_cat_2(A,B),B))) # label(dt_k17_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3212 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k3_cat_2(A,B,C,D) = k5_funct_5(D))) # label(redefinition_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3213 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> m2_cat_1(k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)),B,C))))))))))) # label(t44_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3214 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(B,A),C) & v1_funct_2(D,k2_zfmisc_1(B,A),C) -> v1_funct_1(k5_funct_5(D)) & v1_funct_2(k5_funct_5(D),A,k1_fraenkel(B,C)) & m2_relset_1(k5_funct_5(D),A,k1_fraenkel(B,C)))))))))) # label(t2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3215 $T # label(t20_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3216 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(k11_cat_2(A,B)) & v1_cat_1(k11_cat_2(A,B)))) # label(fc2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3217 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,B) & v1_funct_2(D,C,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,C,B) & v1_funct_2(E,C,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(C,C),C) -> (all G (v1_funct_2(G,B,C) & m2_relset_1(G,B,C) & v1_funct_1(G) -> (D = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) & F = k1_realset1(u5_cat_1(A),C) & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & C = k3_tarski(a_2_0_cat_2(A,B)) -> r1_cat_2(g1_cat_1(B,C,D,E,F,G),A)))))))))))))))) # label(t30_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3218 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_cat_1(G,B,C,D) -> (F = D & E = C -> m1_cat_1(G,A,E,F) | k1_xboole_0 = k6_cat_1(B,C,D)))))))))))))))) # label(t16_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3219 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_cat_2(k7_cat_2(A,B),A,B))) # label(dt_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3220 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(A),k12_cat_1(k11_cat_2(A,B),A,k16_cat_2(A,B)),k12_cat_2(A,B,C,D)) = C)))))))) # label(t59_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3221 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> l1_cat_1(B) & v2_cat_1(B))))) # label(dt_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3222 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> k18_cat_2(k11_cat_2(A,C),B,D,k14_cat_1(k11_cat_2(A,C),A,B,k16_cat_2(A,C),E),k14_cat_1(k11_cat_2(A,C),C,D,k17_cat_2(A,C),F)) = k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F))))))))))))) # label(t64_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3223 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k2_zfmisc_1(k6_cat_1(A,C,D),k6_cat_1(B,E,F)) = k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)))))))))))))) # label(t42_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3224 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> (all C (m1_cat_2(C,A,B) -> -v1_xboole_0(C))))) # label(dt_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3225 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> v1_funct_2(k3_funct_5(D),A,k1_fraenkel(B,C)) & m2_relset_1(k3_funct_5(D),A,k1_fraenkel(B,C)) & v1_funct_1(k3_funct_5(D)))))))))) # label(t1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3226 $T # label(t11_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3227 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(A),k16_cat_2(A,B),k13_cat_2(A,B,C,D)) = C)))))))) # label(t58_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3228 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(B)) & l1_cat_1(A) -> k4_tarski(C,D) = k12_cat_2(A,B,C,D))) # label(redefinition_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3229 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E)) = k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,D,F)) -> k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) = k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F))))))))))))))) # label(t40_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3230 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & v2_cat_1(C) -> m2_cat_1(k18_cat_2(A,B,C,D,E),A,k11_cat_2(B,C)))) # label(dt_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3231 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> m2_cat_1(k14_funct_3(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,k11_cat_2(B,C)))))))))))) # label(t62_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3232 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k9_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),A))))) # label(t54_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3233 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (C = k3_tarski(a_2_0_cat_2(A,B)) -> v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C)) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B) & v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)) & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & v1_funct_1(k1_realset1(u5_cat_1(A),C)) & v1_funct_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) & m2_relset_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & v1_funct_2(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & m2_relset_1(k1_realset1(u5_cat_1(A),C),k2_zfmisc_1(C,C),C) & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B)))))))) # label(t29_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3234 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k9_funct_3(u2_cat_1(A),u2_cat_1(B)) = k16_cat_2(A,B))))) # label(d10_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3235 (all A all B (m3_cat_2(B,A) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k8_cat_2(A,B),B,A))) # label(dt_k8_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3236 $T # label(t5_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3237 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> k5_cat_2(A,B) = k7_cat_2(A,B))) # label(redefinition_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3238 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k3_funct_5(D) = k2_cat_2(A,B,C,D))) # label(redefinition_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3239 (all A all B all C (v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) & -v1_xboole_0(C) -> ((exists D exists E (m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(E,u1_cat_1(B)) & r2_hidden(D,C) & r2_hidden(E,C) & k6_cat_1(B,D,E) = A)) <-> r2_hidden(A,a_2_0_cat_2(B,C))))) # label(fraenkel_a_2_0_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3240 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> C = k13_cat_1(B,A,k8_cat_2(A,B),C))))))) # label(t23_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3241 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k11_cat_2(B,C)),k12_cat_1(A,k11_cat_2(B,C),k18_cat_2(A,B,C,D,E)),F) = k12_cat_2(B,C,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F),k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,E),F)))))))))))))) # label(t63_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3242 (all A all B all C all D all E all F (-v1_xboole_0(C) & m1_fraenkel(D,B,C) & v1_funct_2(E,A,D) & m1_subset_1(F,A) & m1_relset_1(E,A,D) & v1_funct_1(E) & -v1_xboole_0(A) -> m2_fraenkel(k1_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3243 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,C)),u1_cat_1(k11_cat_2(B,D)),k12_cat_1(k11_cat_2(A,C),k11_cat_2(B,D),k19_cat_2(A,C,B,D,E,F)),k12_cat_2(A,C,G,H)) = k12_cat_2(B,D,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,E),G),k8_funct_2(u1_cat_1(C),u1_cat_1(D),k12_cat_1(C,D,F),H)))))))))))))))))) # label(t66_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3244 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,C,D) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> (all H (m1_cat_1(H,B,F,G) -> -(-m1_cat_1(k13_cat_2(A,B,E,H),k11_cat_2(A,B),k12_cat_2(A,B,C,F),k12_cat_2(A,B,D,G)) & k6_cat_1(B,F,G) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))))))) # label(t43_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3245 (all A (v2_cat_1(A) & l1_cat_1(A) -> (exists B m3_cat_2(B,A)))) # label(existence_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3246 (all A all B all C all D (v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k10_cat_2(A,B,C,D)) & m2_relset_1(k10_cat_2(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)))) # label(dt_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3247 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> k10_funct_3(u2_cat_1(A),u2_cat_1(B)) = k17_cat_2(A,B))))) # label(d11_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3248 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(k11_cat_2(A,B))) -> (exists D (m1_subset_1(D,u2_cat_1(A)) & (exists E (k13_cat_2(A,B,D,E) = C & m1_subset_1(E,u2_cat_1(B)))))))))))) # label(t37_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3249 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> C = k8_funct_2(u2_cat_1(B),u2_cat_1(A),k8_cat_2(A,B),C))))))) # label(t21_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3250 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k3_cat_2(A,B,C,D)) & m2_relset_1(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)) & v1_funct_2(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)))) # label(dt_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3251 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> g1_cat_1(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)),k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)),k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B))) = k11_cat_2(A,B))))) # label(d7_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3252 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,F,k10_cat_1(B,E))) = k8_funct_2(u2_cat_1(A),u2_cat_1(C),k15_cat_2(A,B,C,D,E),F))))))))))))) # label(t50_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3253 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_1(E) -> -((all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,F),k10_cat_1(B,G)) = k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,G),k10_cat_1(A,F)))))) & (all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F)))))) & (all F (m2_cat_1(F,k11_cat_2(B,A),C) -> -(all G (m1_subset_1(G,u2_cat_1(B)) -> (all H (m1_subset_1(H,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,G)),H),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,H)),G)) = k8_funct_2(u2_cat_1(k11_cat_2(B,A)),u2_cat_1(C),F,k13_cat_2(B,A,G,H))))))))))))))))))) # label(t52_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3254 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k13_cat_2(A,B,k10_cat_1(A,C),k10_cat_1(B,D)) = k10_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,D)))))))))) # label(t41_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3255 (all A all B all C all D all E (l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(D,k11_cat_2(A,B),C) & m1_subset_1(E,u1_cat_1(A)) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k14_cat_2(A,B,C,D,E),B,C))) # label(dt_k14_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3256 (all A all B all C all D all E all F (-v1_xboole_0(A) & v2_cat_1(C) & l1_cat_1(C) & v1_funct_1(E) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_2(E,A,D) & m1_cat_2(D,B,C) & l1_cat_1(B) & v2_cat_1(B) -> k1_funct_1(E,F) = k6_cat_2(A,B,C,D,E,F))) # label(redefinition_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3257 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(k11_cat_2(A,B)) & l1_cat_1(k11_cat_2(A,B)))) # label(dt_k11_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3258 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> k15_cat_1(B) = k8_cat_2(A,B))))) # label(d5_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3259 (all A all B all C all D (v2_cat_1(B) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k12_cat_2(A,B,C,D),u1_cat_1(k11_cat_2(A,B))))) # label(dt_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3260 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k4_cat_2(A,B,C) = k10_pboole(u2_cat_1(A),k10_cat_1(B,C)))))))) # label(d1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3261 (all A all B all C (v2_cat_1(B) & m1_subset_1(C,u1_cat_1(B)) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k4_cat_2(A,B,C),A,B))) # label(dt_k4_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3262 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> -v1_xboole_0(k5_cat_2(A,B)))) # label(fc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3263 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> m1_subset_1(C,u2_cat_1(A)))))))) # label(t14_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3264 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k4_cat_2(B,A,C)),D))))))))) # label(t7_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3265 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,k14_cat_2(A,B,C,D,E)),F) = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)))))))))))))) # label(t48_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3266 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(A),k4_cat_2(B,A,C),D) = k10_cat_1(A,C))))))))) # label(t6_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3267 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & v2_cat_1(C) & v2_cat_1(D) & m2_cat_1(F,B,D) & m2_cat_1(E,A,C) & l1_cat_1(D) & l1_cat_1(C) & l1_cat_1(B) -> k15_funct_3(E,F) = k19_cat_2(A,B,C,D,E,F))) # label(redefinition_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3268 (all A all B all C all D (v1_funct_1(C) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k10_cat_2(A,B,C,D) = k3_funct_4(C,D))) # label(redefinition_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3269 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(A) -> (all D (m2_cat_2(D,A,B,C) -> m2_cat_1(D,A,B))))) # label(dt_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3270 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(A),k12_cat_1(k2_oppcat_1(A),A,k11_oppcat_1(A)),B) = k4_oppcat_1(A,B))))) # label(t69_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3271 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> m1_oppcat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B))))))) # label(t58_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3272 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)))))))))) # label(t38_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3273 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_2(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_1(E) -> k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),u2_cat_1(C),k8_oppcat_1(A,B,D),E))))))))))) # label(t53_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3274 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k10_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)) = k5_oppcat_1(A,k10_cat_1(A,B)))))) # label(t21_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3275 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,k2_oppcat_1(A),B) -> m2_cat_1(k7_oppcat_1(A,B,C),A,B))))))) # label(t39_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3276 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) & v1_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) -> k9_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)) = C)))))) # label(t51_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3277 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))))))))) # label(t33_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3278 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A)) <-> v7_cat_1(B,A)))))) # label(t26_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3279 (all A (v2_cat_1(A) & l1_cat_1(A) -> k10_oppcat_1(A) = k9_oppcat_1(A,A,k15_cat_1(A)))) # label(d10_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3280 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)))))))))) # label(t32_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3281 (all A (l1_cat_1(A) & v2_cat_1(A) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = k2_oppcat_1(k2_oppcat_1(A)))) # label(t2_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3282 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)))))))))) # label(t62_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3283 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) & m1_subset_1(E,u1_cat_1(B)))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))) <-> m1_oppcat_1(C,A,B)))))))) # label(d7_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3284 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_1(k8_oppcat_1(A,B,C)) & m2_relset_1(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_2(k8_oppcat_1(A,B,C),u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)))) # label(dt_k8_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3285 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v3_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A)) <-> v4_cat_1(B,A)))))) # label(t23_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3286 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) -> k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) = k5_oppcat_1(A,k4_cat_1(A,B,C))))))))) # label(t17_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.38 3287 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)))))))))) # label(t45_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3288 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (all C (m1_oppcat_1(C,A,B) -> v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C))))) # label(dt_m1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3289 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k3_oppcat_1(A,B),u1_cat_1(k2_oppcat_1(A))))) # label(dt_k3_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3290 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C)) = k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) -> k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,C),k5_oppcat_1(A,B)) = k5_oppcat_1(A,k4_cat_1(A,B,C))))))))) # label(t18_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3291 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (r2_hidden(k5_oppcat_1(A,D),k6_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B))) <-> r2_hidden(D,k6_cat_1(A,B,C))))))))))) # label(t13_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3292 (all A (v2_cat_1(A) & l1_cat_1(A) -> m1_oppcat_1(k10_oppcat_1(A),A,k2_oppcat_1(A)))) # label(dt_k10_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3293 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(k3_oppcat_1(A,B),k2_oppcat_1(A)) <-> v6_cat_1(B,A)))))) # label(t27_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3294 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) -> (all D (v1_funct_2(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & m2_relset_1(D,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u2_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_oppcat_1(A,E)) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),D,E))) <-> D = k8_oppcat_1(A,B,C)))))))))) # label(d8_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3295 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k5_oppcat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k5_oppcat_1(A,D)))))))))) # label(t47_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3296 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m1_oppcat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t60_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3297 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v5_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A)) <-> v5_cat_1(B,A)))))) # label(t25_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3298 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> m1_subset_1(k6_oppcat_1(A,B),u2_cat_1(A)))) # label(dt_k6_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3299 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) -> k8_oppcat_1(A,B,C) = k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),u2_cat_1(B),k11_oppcat_1(A),C) & k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(B)),C,k10_oppcat_1(B)) = k9_oppcat_1(A,B,C))))))) # label(t70_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3300 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> m2_cat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)))))))) # label(t57_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3301 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> k6_oppcat_1(A,k10_cat_1(k2_oppcat_1(A),B)) = k10_cat_1(A,k4_oppcat_1(A,B)))))) # label(t22_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3302 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) & k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_cat_1(A,B))))) # label(t9_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3303 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> m1_oppcat_1(k9_oppcat_1(A,B,C),A,k2_oppcat_1(B)))))))) # label(t59_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3304 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)) = k8_oppcat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)))))))) # label(t50_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3305 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t46_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3306 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k6_oppcat_1(A,B) = k5_oppcat_1(k2_oppcat_1(A),B))))) # label(d5_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3307 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k4_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,F),k5_oppcat_1(A,E)) != k5_oppcat_1(A,k9_cat_1(A,B,C,D,E,F)) & k6_cat_1(A,C,D) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,B,C)))))))))))))) # label(t20_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3308 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k3_oppcat_1(A,D)))))))))) # label(t42_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3309 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,k2_oppcat_1(A),B) -> m1_oppcat_1(k7_oppcat_1(A,B,C),A,B))))))) # label(t35_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3310 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(A)),k12_cat_1(A,k2_oppcat_1(A),k10_oppcat_1(A)),B) = k3_oppcat_1(A,B))))) # label(t67_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3311 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) -> k8_oppcat_1(A,B,k7_oppcat_1(A,B,C)) = C)))))) # label(t49_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3312 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(A),k11_oppcat_1(A),B) = k6_oppcat_1(A,B))))) # label(t68_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3313 (all A all B all C all D (-v1_xboole_0(C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k1_oppcat_1(A,B,C,D)) & m2_relset_1(k1_oppcat_1(A,B,C,D),k2_zfmisc_1(B,A),C))) # label(dt_k1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3314 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k5_oppcat_1(A,B),u2_cat_1(k2_oppcat_1(A))))) # label(dt_k5_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3315 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k2_oppcat_1(A))) -> (k2_cat_1(k2_oppcat_1(A),C) = k3_cat_1(k2_oppcat_1(A),B) -> k4_cat_1(A,k6_oppcat_1(A,C),k6_oppcat_1(A,B)) = k6_oppcat_1(A,k4_cat_1(k2_oppcat_1(A),B,C))))))))) # label(t19_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3316 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D))))))))) # label(t37_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3317 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),k8_oppcat_1(A,B,C),k5_oppcat_1(A,D)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))) # label(t40_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3318 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k4_oppcat_1(A,k3_oppcat_1(A,B)))))) # label(t4_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3319 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> k4_oppcat_1(A,B) = k3_oppcat_1(k2_oppcat_1(A),B))))) # label(d3_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3320 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> m2_cat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)))))))) # label(t64_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3321 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u2_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,D) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),k7_oppcat_1(A,B,C),k6_oppcat_1(A,D)))))))))) # label(t28_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3322 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> B = k3_oppcat_1(A,k4_oppcat_1(A,B)))))) # label(t5_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3323 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k2_cat_1(k2_oppcat_1(A),B) = k3_cat_1(A,k6_oppcat_1(A,B)) & k2_cat_1(A,k6_oppcat_1(A,B)) = k3_cat_1(k2_oppcat_1(A),B))))) # label(t10_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3324 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> (all C (m1_subset_1(C,u1_cat_1(k2_oppcat_1(A))) -> (all D (m1_subset_1(D,u2_cat_1(k2_oppcat_1(A))) -> (r2_hidden(k6_oppcat_1(A,D),k6_cat_1(A,k4_oppcat_1(A,C),k4_oppcat_1(A,B))) <-> r2_hidden(D,k6_cat_1(k2_oppcat_1(A),B,C))))))))))) # label(t14_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3325 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k5_oppcat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = B)))) # label(t6_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3326 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),k4_oppcat_1(A,D)))))))))) # label(t30_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3327 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k6_oppcat_1(A,k5_oppcat_1(A,B)) = B)))) # label(t7_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3328 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))))))))))) # label(t34_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3329 (all A (l1_cat_1(A) & v2_cat_1(A) -> k11_oppcat_1(A) = k8_oppcat_1(A,A,k15_cat_1(A)))) # label(d11_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3330 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k3_oppcat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)))))) # label(t3_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3331 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_2(E,u2_cat_1(B),u2_cat_1(C)) -> k7_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(k2_oppcat_1(B)),u2_cat_1(k2_oppcat_1(C)),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,D)),k9_oppcat_1(k2_oppcat_1(B),C,k8_oppcat_1(B,C,E))) = k9_oppcat_1(k2_oppcat_1(A),C,k8_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E))))))))))))) # label(t55_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3332 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(k2_oppcat_1(A),k2_oppcat_1(B),k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C))),k3_oppcat_1(A,D)) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t63_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3333 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,k2_oppcat_1(A),B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,C),k3_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,k7_oppcat_1(A,B,C)),D))))))))) # label(t29_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3334 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) -> (all D (v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(D) -> (D = k7_oppcat_1(A,B,C) <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),D,E) = k8_funct_2(u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B),C,k5_oppcat_1(A,E))))))))))))) # label(d6_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3335 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k5_oppcat_1(A,B) = B)))) # label(d4_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3336 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v1_funct_2(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & m1_relset_1(C,u2_cat_1(k2_oppcat_1(A)),u2_cat_1(B)) & v1_funct_1(C) & l1_cat_1(A) -> v1_funct_1(k7_oppcat_1(A,B,C)) & m2_relset_1(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(k7_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(B)))) # label(dt_k7_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3337 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> m2_cat_1(k8_oppcat_1(A,B,C),k2_oppcat_1(A),B))))))) # label(t56_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3338 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) -> (all C (m1_subset_1(C,u1_cat_1(k2_oppcat_1(A))) -> (all D (m1_cat_1(D,k2_oppcat_1(A),B,C) -> (k1_xboole_0 != k6_cat_1(k2_oppcat_1(A),B,C) -> m1_cat_1(k6_oppcat_1(A,D),A,k4_oppcat_1(A,C),k4_oppcat_1(A,B))))))))))) # label(t16_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3339 (all A (v2_cat_1(A) & l1_cat_1(A) -> v1_cat_1(k2_oppcat_1(A)) & l1_cat_1(k2_oppcat_1(A)) & v2_cat_1(k2_oppcat_1(A)))) # label(dt_k2_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3340 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> k7_oppcat_1(A,B,k8_oppcat_1(A,B,C)) = C)))))) # label(t48_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3341 (all A (v2_cat_1(A) & l1_cat_1(A) -> k2_oppcat_1(A) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A)))) # label(d1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3342 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k5_oppcat_1(A,B) = k8_funct_2(u2_cat_1(A),u2_cat_1(k2_oppcat_1(A)),k10_oppcat_1(A),B))))) # label(t66_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3343 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)) = k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D))))))))) # label(t44_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3344 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> m1_oppcat_1(k9_oppcat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),k2_oppcat_1(A),k2_oppcat_1(B)))))))) # label(t65_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3345 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_oppcat_1(A,k3_cat_1(A,B)) & k3_cat_1(k2_oppcat_1(A),k5_oppcat_1(A,B)) = k3_oppcat_1(A,k2_cat_1(A,B)))))) # label(t11_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3346 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m1_oppcat_1(E,B,C) -> m1_oppcat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t61_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3347 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> B = k5_oppcat_1(A,k6_oppcat_1(A,B)))))) # label(t8_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3348 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k2_funct_4(D) = k1_oppcat_1(A,B,C,D))) # label(redefinition_k1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3349 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(k2_oppcat_1(A))) -> k4_oppcat_1(A,k2_cat_1(k2_oppcat_1(A),B)) = k3_cat_1(A,k6_oppcat_1(A,B)) & k4_oppcat_1(A,k3_cat_1(k2_oppcat_1(A),B)) = k2_cat_1(A,k6_oppcat_1(A,B)))))) # label(t12_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3350 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m1_oppcat_1(D,A,B) -> (all E (m1_oppcat_1(E,B,C) -> m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t36_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3351 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & v1_funct_1(C) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & l1_cat_1(B) & v2_cat_1(A) -> v1_funct_1(k9_oppcat_1(A,B,C)) & v1_funct_2(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) & m2_relset_1(k9_oppcat_1(A,B,C),u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))))) # label(dt_k9_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3352 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> (exists C m1_oppcat_1(C,A,B)))) # label(existence_m1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3353 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) & v1_funct_2(D,u2_cat_1(A),u2_cat_1(k2_oppcat_1(B))) -> (k9_oppcat_1(A,B,C) = D <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> k5_oppcat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(k2_oppcat_1(B)),D,E)))))))))))) # label(d9_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3354 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_oppcat_1(A,B) = B)))) # label(d2_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3355 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(k2_oppcat_1(A))) & l1_cat_1(A) -> m1_subset_1(k4_oppcat_1(A,B),u1_cat_1(A)))) # label(dt_k4_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3356 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_oppcat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))))) # label(t31_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3357 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(k2_oppcat_1(A))) -> k8_funct_2(u1_cat_1(k2_oppcat_1(A)),u1_cat_1(B),k12_cat_1(k2_oppcat_1(A),B,k8_oppcat_1(A,B,C)),D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k4_oppcat_1(A,D)))))))))) # label(t41_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3358 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(k2_oppcat_1(B)),k12_cat_1(A,k2_oppcat_1(B),k9_oppcat_1(A,B,C)),D) = k3_oppcat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t43_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3359 (all A (v2_cat_1(A) & l1_cat_1(A) -> m1_oppcat_1(k11_oppcat_1(A),k2_oppcat_1(A),A))) # label(dt_k11_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3360 (all A (l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))) & l1_cat_1(g1_cat_1(u1_cat_1(A),u2_cat_1(A),u4_cat_1(A),u3_cat_1(A),k1_oppcat_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u5_cat_1(A)),u6_cat_1(A))))) # label(t1_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3361 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v4_cat_1(k5_oppcat_1(A,B),k2_oppcat_1(A)) <-> v3_cat_1(B,A)))))) # label(t24_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3362 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_relset_1(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(D,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(D) -> (all E (v1_funct_2(E,u2_cat_1(B),u2_cat_1(C)) & m2_relset_1(E,u2_cat_1(B),u2_cat_1(C)) & v1_funct_1(E) -> k9_oppcat_1(A,C,k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E)) = k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(k2_oppcat_1(C)),D,k9_oppcat_1(B,C,E)))))))))))) # label(t54_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.39 3363 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> m1_cat_1(k5_oppcat_1(A,D),k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B))))))))))) # label(t15_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3364 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v1_cat_1(B) & l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(B),u2_cat_1(A)) & m2_relset_1(C,u2_cat_1(B),u2_cat_1(A)) -> k8_oppcat_1(k2_oppcat_1(B),A,k8_oppcat_1(B,A,C)) = C)))))) # label(t52_oppcat_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3365 (all A all B all C all D (m1_relset_1(C,A,B) & m1_subset_1(D,k1_zfmisc_1(A)) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k1_nattra_1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3366 (all A all B k8_cat_1(A,B) = k13_nattra_1(k8_cat_1(A,B))) # label(t54_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3367 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k10_cat_1(A,k13_cat_1(B,A,C,D)) = k5_nattra_1(B,A,C,C,k4_nattra_1(B,A,C),D))))))))) # label(t21_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3368 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_cat_1(C) & l1_cat_1(C) & v2_cat_1(C) -> (C = k12_nattra_1(A,B) <-> u1_cat_1(C) = k7_cat_2(A,B) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> (k3_cat_1(C,D) = k2_cat_1(C,E) -> r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C)))))))) & (all D (m1_subset_1(D,u1_cat_1(C)) -> (all E (m2_cat_1(E,A,B) -> (E = D -> k10_cat_1(C,D) = k4_tarski(k4_tarski(E,E),k7_nattra_1(A,B,E))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> -(r2_hidden(k13_cat_2(C,C,E,D),k1_relat_1(u5_cat_1(C))) & (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,A,B) -> (all H (m2_cat_1(H,A,B) -> (all I (m2_nattra_1(I,A,B,F,G) -> (all J (m2_nattra_1(J,A,B,G,H) -> -(D = k4_tarski(k4_tarski(F,G),I) & k4_tarski(k4_tarski(G,H),J) = E & k4_tarski(k4_tarski(F,H),k8_nattra_1(A,B,F,G,H,I,J)) = k1_funct_1(u5_cat_1(C),k13_cat_2(C,C,E,D)))))))))))))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> k1_mcart_1(k1_mcart_1(D)) = k2_cat_1(C,D) & k2_mcart_1(k1_mcart_1(D)) = k3_cat_1(C,D))) & u2_cat_1(C) = k11_nattra_1(A,B)))))))) # label(d18_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3369 $T # label(t29_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3370 (all A (l1_cat_1(A) & v2_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (exists C (k10_cat_1(A,C) = B & m1_subset_1(C,u1_cat_1(A)))))) <-> v2_nattra_1(A)))) # label(d19_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3371 (exists A (v2_nattra_1(A) & v2_cat_1(A) & l1_cat_1(A))) # label(rc1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3372 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) & -v1_xboole_0(C) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (all G (v1_funct_1(G) & m2_relset_1(G,k12_mcart_1(A,A,C,C),C) -> (G = k1_realset1(E,C) -> (all H (v1_funct_1(H) & m2_relset_1(H,k12_mcart_1(B,B,D,D),D) -> (k1_realset1(F,D) = H -> k1_realset1(k10_cat_2(A,B,E,F),k12_mcart_1(A,B,C,D)) = k2_nattra_1(A,B,C,D,G,H))))))))))))))))))) # label(t2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3373 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k3_nattra_1(A,B,C,D,D,k10_cat_1(A,D)) = k10_cat_1(B,E) -> k13_cat_1(A,B,C,D) = E))))))))))) # label(t14_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3374 $T # label(t38_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3375 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (v2_nattra_1(A) & v2_nattra_1(B) -> v2_nattra_1(k11_cat_2(A,B))))))) # label(t48_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3376 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,A,B,E,F) -> (all H (m2_nattra_1(H,A,B,C,D) -> (all I (m1_subset_1(I,u2_cat_1(k12_nattra_1(A,B))) -> (all J (m1_subset_1(J,u2_cat_1(k12_nattra_1(A,B))) -> (J = k4_tarski(k4_tarski(C,D),H) & k4_tarski(k4_tarski(E,F),G) = I -> (r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),F,C) <-> r2_hidden(k13_cat_2(k12_nattra_1(A,B),k12_nattra_1(A,B),J,I),k1_relat_1(u5_cat_1(k12_nattra_1(A,B)))))))))))))))))))))))))) # label(t41_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3377 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u2_cat_1(k12_nattra_1(A,B))) -> (k4_tarski(k4_tarski(C,D),E) = F -> k2_cat_1(k12_nattra_1(A,B),F) = C & D = k3_cat_1(k12_nattra_1(A,B),F)))))))))))))) # label(t39_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3378 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (-r1_xboole_0(k6_cat_1(A,B,C),k6_cat_1(A,D,E)) -> C = E & B = D))))))))))) # label(t17_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3379 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u2_cat_1(B),E,F) = k5_nattra_1(A,B,C,D,E,F)))))))))))))) # label(d5_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3380 (all A all B all C all D all E (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_nattra_1(E,A,B,C,D) & m2_cat_1(D,A,B) & l1_cat_1(A) -> m2_nattra_1(k10_nattra_1(A,B,C,D,E),A,B,D,C))) # label(dt_k10_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3381 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v1_cat_1(B) & m3_cat_2(B,A) & v2_nattra_1(B) -> (k13_nattra_1(A) = B <-> u2_cat_1(B) = a_1_0_nattra_1(A) & u1_cat_1(A) = u1_cat_1(B)))))) # label(d20_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3382 (all A all B all C all D all E all F all G (l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(E,A,B) & m1_nattra_1(G,A,B,D,E) & m1_nattra_1(F,A,B,C,D) & m2_cat_1(D,A,B) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m1_nattra_1(k6_nattra_1(A,B,C,D,E,F,G),A,B,C,E))) # label(dt_k6_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3383 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_nattra_1(F,A,B,C,D) -> (all G (m2_nattra_1(G,A,B,D,E) -> (all H (m1_subset_1(H,u2_cat_1(k12_nattra_1(A,B))) -> (all I (m1_subset_1(I,u2_cat_1(k12_nattra_1(A,B))) -> (k4_tarski(k4_tarski(D,E),G) = I & k4_tarski(k4_tarski(C,D),F) = H -> k4_tarski(k4_tarski(C,E),k8_nattra_1(A,B,C,D,E,F,G)) = k4_cat_1(k12_nattra_1(A,B),H,I)))))))))))))))))))) # label(t42_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3384 (all A all B all C (l1_cat_1(B) & m2_cat_1(C,A,B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_nattra_1(k4_nattra_1(A,B,C),A,B,C,C))) # label(dt_k4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3385 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_2(E,A,B) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(C) -> (F = E <-> r4_nattra_1(A,B,C,D,E,F)))) # label(redefinition_r4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3386 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,C,A) & m2_relset_1(E,C,A) -> (all F (m2_relset_1(F,D,B) & v1_funct_2(F,D,B) & v1_funct_1(F) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) & -v1_xboole_0(G) -> (all H (-v1_xboole_0(H) & m1_subset_1(H,k1_zfmisc_1(D)) -> k1_nattra_1(k2_zfmisc_1(C,D),k2_zfmisc_1(A,B),k9_cat_2(C,D,A,B,E,F),k12_mcart_1(C,D,G,H)) = k9_cat_2(G,H,A,B,k1_nattra_1(C,A,E,G),k1_nattra_1(D,B,F,H)))))))))))))))))) # label(t1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3387 (all A (v2_cat_1(A) & v2_nattra_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m1_nattra_1(D,B,A,C,C) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),D,k7_nattra_1(B,A,C)))))))))) # label(t50_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3388 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_cat_1(C,A,B,B) -> r2_hidden(C,k6_cat_1(A,B,B)))))))) # label(t3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3389 (all A all B all C all D (m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> r2_nattra_1(A,B,C,C))) # label(reflexivity_r2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3390 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> m3_cat_2(k8_cat_1(B,k10_cat_1(A,B)),A))))) # label(t7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3391 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r3_nattra_1(A,B,D,E) & r3_nattra_1(A,B,C,D) -> r3_nattra_1(A,B,C,E)))))))))))) # label(t32_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3392 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r3_nattra_1(A,B,C,D) -> r3_nattra_1(A,B,D,C)))))))))) # label(t31_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3393 (all A all B all C (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & l1_cat_1(A) -> k7_nattra_1(A,B,C) = k4_nattra_1(A,B,C))) # label(redefinition_k7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3394 (all A (v2_cat_1(A) & l1_cat_1(A) -> (exists B (v1_cat_1(B) & v2_nattra_1(B) & v2_cat_1(B) & m3_cat_2(B,A))))) # label(rc2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3395 (all A all B all C all D all E all F (-v1_xboole_0(C) & v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & v1_funct_2(F,C,D) & m1_relset_1(F,C,D) & v1_funct_2(E,A,B) & -v1_xboole_0(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> (r4_nattra_1(A,B,C,D,E,F) -> r4_nattra_1(A,B,C,D,F,E)))) # label(symmetry_r4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3396 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (r1_nattra_1(B,A,C,D) -> (all E (m1_nattra_1(E,B,A,C,D) -> (all F (m1_nattra_1(F,B,A,C,D) -> ((all G (m1_subset_1(G,u1_cat_1(B)) -> k5_nattra_1(B,A,C,D,E,G) = k5_nattra_1(B,A,C,D,F,G))) -> E = F)))))))))))))) # label(t20_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3397 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r2_nattra_1(A,B,C,D) -> (all E (m2_nattra_1(E,A,B,C,D) -> E = k8_nattra_1(A,B,C,D,D,E,k7_nattra_1(A,B,D)) & E = k8_nattra_1(A,B,C,C,D,k7_nattra_1(A,B,C),E)))))))))))) # label(t26_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3398 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) & r1_nattra_1(A,B,C,D) -> r1_nattra_1(A,B,C,E)))))))))))) # label(t19_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3399 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k3_nattra_1(B,A,C,D,D,k10_cat_1(B,D)) = k10_cat_1(A,k13_cat_1(B,A,C,D)))))))))) # label(t15_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3400 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> k3_nattra_1(A,B,C,D,E,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)))))))))))))) # label(d1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3401 (all A all B all C all D all E all F (-v1_xboole_0(B) & m1_relset_1(E,A,B) & v1_funct_1(F) & v1_funct_2(F,C,D) & m1_relset_1(F,C,D) & v1_funct_2(E,A,B) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> r4_nattra_1(A,B,C,D,E,E))) # label(reflexivity_r4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3402 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,A,B,C,D) -> (all H (m2_nattra_1(H,A,B,D,E) -> (r2_nattra_1(A,B,C,D) & r2_nattra_1(A,B,D,E) & r2_nattra_1(A,B,E,F) -> (all I (m2_nattra_1(I,A,B,E,F) -> k8_nattra_1(A,B,C,D,F,G,k8_nattra_1(A,B,D,E,F,H,I)) = k8_nattra_1(A,B,C,E,F,k8_nattra_1(A,B,C,D,E,G,H),I)))))))))))))))))))) # label(t28_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3403 (all A (l1_cat_1(A) & v2_nattra_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (r1_nattra_1(B,A,C,D) -> r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),C,D)))))))))) # label(t49_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3404 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (-v1_xboole_0(C) -> (m4_nattra_1(C,A,B) <-> (all D -((all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,A,B,E,F) -> -(k4_tarski(k4_tarski(E,F),G) = D & r2_nattra_1(A,B,E,F)))))))) & r2_hidden(D,C)))))))))) # label(d15_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3405 (all A all B all C all D all E all F (l1_cat_1(A) & v2_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m1_cat_1(F,A,D,E) & m1_subset_1(E,u1_cat_1(A)) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m1_cat_1(k3_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))) # label(dt_k3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3406 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & m1_subset_1(D,k1_zfmisc_1(A)) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> v1_funct_1(k1_nattra_1(A,B,C,D)) & v1_funct_2(k1_nattra_1(A,B,C,D),D,B) & m2_relset_1(k1_nattra_1(A,B,C,D),D,B))) # label(dt_k1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3407 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (r1_nattra_1(A,B,C,D) & r1_nattra_1(A,B,E,F) & r1_nattra_1(A,B,D,E) -> (all G (m1_nattra_1(G,A,B,C,D) -> (all H (m1_nattra_1(H,A,B,D,E) -> (all I (m1_nattra_1(I,A,B,E,F) -> k6_nattra_1(A,B,C,E,F,k6_nattra_1(A,B,C,D,E,G,H),I) = k6_nattra_1(A,B,C,D,F,G,k6_nattra_1(A,B,D,E,F,H,I))))))))))))))))))))) # label(t23_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3408 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_hidden(k4_tarski(k4_tarski(C,D),E),k11_nattra_1(A,B)) <-> r2_nattra_1(A,B,C,D)))))))))))) # label(t35_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3409 $T # label(t43_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3410 (all A all B all C all D all E all F (v2_cat_1(B) & m2_cat_1(D,A,B) & m1_subset_1(F,u1_cat_1(A)) & m1_nattra_1(E,A,B,C,D) & m2_cat_1(C,A,B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m1_cat_1(k5_nattra_1(A,B,C,D,E,F),B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))) # label(dt_k5_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3411 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> E = k6_nattra_1(A,B,C,D,D,E,k4_nattra_1(A,B,D)) & E = k6_nattra_1(A,B,C,C,D,k4_nattra_1(A,B,C),E)))))))))))) # label(t22_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3412 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> k7_relat_1(u3_cat_1(A),u2_cat_1(B)) = u3_cat_1(B) & k7_relat_1(u6_cat_1(A),u1_cat_1(B)) = u6_cat_1(B) & u5_cat_1(B) = k1_realset1(u5_cat_1(A),u2_cat_1(B)) & k7_relat_1(u4_cat_1(A),u2_cat_1(B)) = u4_cat_1(B))))) # label(t8_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3413 (all A all B all C all D (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & v2_cat_1(A) -> r3_nattra_1(A,B,C,C))) # label(reflexivity_r3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3414 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(A,B,C,D) -> (all F (m2_nattra_1(F,A,B,C,D) -> (all G (m2_nattra_1(G,A,B,D,E) -> k6_nattra_1(A,B,C,D,E,F,G) = k8_nattra_1(A,B,C,D,E,F,G)))))))))))))))) # label(d9_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3415 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m1_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) <-> (all F (m1_subset_1(F,u1_cat_1(A)) -> v5_cat_1(k5_nattra_1(A,B,C,D,E,F),B)))))))))))))) # label(d10_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3416 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) & v1_nattra_1(E,A,B,C,D) -> k10_nattra_1(A,B,C,D,E) = k9_nattra_1(A,B,C,D,E)))))))))))) # label(d13_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3417 (all A (v2_cat_1(A) & l1_cat_1(A) -> m3_cat_2(k13_nattra_1(A),A) & v2_nattra_1(k13_nattra_1(A)) & v1_cat_1(k13_nattra_1(A)))) # label(dt_k13_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3418 (all A all B all C all D (m2_cat_1(D,A,B) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> r1_nattra_1(A,B,C,C))) # label(reflexivity_r1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3419 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (v2_nattra_1(A) -> v2_nattra_1(k12_nattra_1(B,A))))))) # label(t51_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3420 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> m4_nattra_1(k11_nattra_1(A,B),A,B))) # label(dt_k11_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3421 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & m1_nattra_1(E,A,B,C,D) & l1_cat_1(B) & v2_cat_1(A) -> m1_nattra_1(k9_nattra_1(A,B,C,D,E),A,B,D,C))) # label(dt_k9_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3422 $T # label(t24_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3423 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m2_nattra_1(k7_nattra_1(A,B,C),A,B,C,C))) # label(dt_k7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.29/5.41 3424 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> -(-(all G (m1_cat_1(G,B,D,E) -> (all H (m1_cat_1(H,B,E,F) -> k9_cat_1(A,k13_cat_1(B,A,C,D),k13_cat_1(B,A,C,E),k13_cat_1(B,A,C,F),k3_nattra_1(B,A,C,D,E,G),k3_nattra_1(B,A,C,E,F,H)) = k3_nattra_1(B,A,C,D,F,k9_cat_1(B,D,E,F,G,H)))))) & k1_xboole_0 != k6_cat_1(B,E,F) & k1_xboole_0 != k6_cat_1(B,D,E)))))))))))))) # label(t13_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3425 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m4_nattra_1(C,A,B) -> (k11_nattra_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E ((exists F (m2_cat_1(F,A,B) & (exists G (m2_nattra_1(G,A,B,E,F) & r2_nattra_1(A,B,E,F) & k4_tarski(k4_tarski(E,F),G) = D)))) & m2_cat_1(E,A,B)))))))))))) # label(d16_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3426 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) -> (all F (m1_nattra_1(F,A,B,D,C) -> ((all G (m1_subset_1(G,u1_cat_1(A)) -> k5_nattra_1(A,B,D,C,F,G) = k11_cat_1(B,k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,G)))) <-> F = k9_nattra_1(A,B,C,D,E)))))))))))))))) # label(d12_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3427 (all A (l1_cat_1(A) & v2_cat_1(A) & v1_cat_1(A) -> (v2_nattra_1(A) -> A = k13_nattra_1(A)))) # label(t52_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3428 (all A (v2_cat_1(A) & l1_cat_1(A) -> (v2_nattra_1(A) <-> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (C != B -> k6_cat_1(A,B,C) = k1_xboole_0))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> (exists C (np__1 = k4_card_1(C) & k6_cat_1(A,B,B) = C & v1_finset_1(C)))))))) # label(t45_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3429 (all A (m1_subset_1(A,f1_s1_nattra_1) -> -r1_xboole_0(f2_s1_nattra_1,f3_s1_nattra_1(A)))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s1_nattra_1,f2_s1_nattra_1) & m2_relset_1(A,f1_s1_nattra_1,f2_s1_nattra_1) & (all B (m1_subset_1(B,f1_s1_nattra_1) -> r2_hidden(k8_funct_2(f1_s1_nattra_1,f2_s1_nattra_1,A,B),f3_s1_nattra_1(B)))))) # label(s1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3430 (all A all B all C all D (l1_cat_1(B) & m2_cat_1(D,A,B) & m2_cat_1(C,A,B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (all E (m3_nattra_1(E,A,B,C,D) -> m2_nattra_1(E,A,B,C,D))))) # label(dt_m3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3431 (all A (v2_nattra_1(A) & l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> v2_nattra_1(B))))) # label(t47_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3432 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(A,B,C,D) -> r2_nattra_1(A,B,C,E)))))))))))) # label(t25_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3433 (all A all B all C all D (l1_cat_1(A) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> (all E (m2_nattra_1(E,A,B,C,D) -> m1_nattra_1(E,A,B,C,D))))) # label(dt_m2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3434 (all A all B all C all D all E all F (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) & v1_funct_1(E) & v1_funct_1(F) & m1_relset_1(F,k12_mcart_1(B,B,D,D),D) & m1_relset_1(E,k12_mcart_1(A,A,C,C),C) & -v1_xboole_0(D) & -v1_xboole_0(A) -> k2_nattra_1(A,B,C,D,E,F) = k3_funct_4(E,F))) # label(redefinition_k2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3435 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) & v1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k5_nattra_1(A,B,D,C,k10_nattra_1(A,B,C,D,E),F) = k11_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k5_nattra_1(A,B,C,D,E,F))))))))))))))) # label(t30_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3436 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_cat_1(A),u2_cat_1(B)) & v1_funct_2(E,u1_cat_1(A),u2_cat_1(B)) -> ((all F (m1_subset_1(F,u1_cat_1(A)) -> m1_cat_1(k8_funct_2(u1_cat_1(A),u2_cat_1(B),E,F),B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))) <-> m1_nattra_1(E,A,B,C,D))))))))))))) # label(d3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3437 (all A (v1_cat_1(A) & v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) & v1_cat_1(B) -> (u1_cat_1(B) = u1_cat_1(A) & u2_cat_1(A) = u2_cat_1(B) -> B = A))))) # label(t10_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3438 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_nattra_1(D,A,B,C,C) -> (k4_nattra_1(A,B,C) = D <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u2_cat_1(B),D,E) = k10_cat_1(B,k13_cat_1(A,B,C,E))))))))))))) # label(d4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3439 (all A all B all C all D (v2_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (exists E m3_nattra_1(E,A,B,C,D)))) # label(existence_m3_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3440 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> m3_nattra_1(k7_nattra_1(A,B,C),A,B,C,C))))))) # label(t33_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3441 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r2_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> ((all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (k6_cat_1(A,F,G) != k1_xboole_0 -> (all H (m1_cat_1(H,A,F,G) -> k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,F),k3_nattra_1(A,B,D,F,G,H)) = k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k3_nattra_1(A,B,C,F,G,H),k5_nattra_1(A,B,C,D,E,G))))))))) <-> m2_nattra_1(E,A,B,C,D))))))))))))) # label(d8_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3442 $T # label(t37_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3443 (all A all B (v2_cat_1(B) & l1_cat_1(B) -> (r2_hidden(A,a_1_0_nattra_1(B)) <-> (exists C (m1_subset_1(C,u1_cat_1(B)) & k10_cat_1(B,C) = A))))) # label(fraenkel_a_1_0_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3444 (all A all B (l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (exists C m4_nattra_1(C,A,B)))) # label(existence_m4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3445 (all A all B all C (m1_subset_1(C,u2_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u2_cat_1(k8_cat_1(A,B))) -> C = D)))) # label(t4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3446 (all A all B v2_nattra_1(k8_cat_1(A,B))) # label(t46_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3447 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(k12_nattra_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k12_nattra_1(A,B))) -> (all E (m1_cat_1(E,k12_nattra_1(A,B),C,D) -> -(k1_xboole_0 != k6_cat_1(k12_nattra_1(A,B),C,D) & (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,A,B) -> (all H (m2_nattra_1(H,A,B,F,G) -> -(E = k4_tarski(k4_tarski(F,G),H) & G = D & F = C)))))))))))))))))) # label(t40_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3448 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & l1_cat_1(A) -> (exists E m2_nattra_1(E,A,B,C,D)))) # label(existence_m2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3449 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (all E (m2_cat_1(E,B,A) -> (r2_nattra_1(B,A,C,D) & r2_nattra_1(B,A,D,E) -> (all F (m2_nattra_1(F,B,A,C,D) -> (all G (m2_nattra_1(G,B,A,D,E) -> (all H (m1_subset_1(H,u1_cat_1(B)) -> k9_cat_1(A,k13_cat_1(B,A,C,H),k13_cat_1(B,A,D,H),k13_cat_1(B,A,E,H),k5_nattra_1(B,A,C,D,F,H),k5_nattra_1(B,A,D,E,G,H)) = k5_nattra_1(B,A,C,E,k8_nattra_1(B,A,C,D,E,F,G),H)))))))))))))))))) # label(t27_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3450 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k13_nattra_1(k11_cat_2(A,B)) = k11_cat_2(k13_nattra_1(A),k13_nattra_1(B)))))) # label(t55_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3451 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r3_nattra_1(A,B,D,E) & r3_nattra_1(A,B,C,D) -> (all F (m3_nattra_1(F,A,B,C,D) -> (all G (m3_nattra_1(G,A,B,D,E) -> m3_nattra_1(k8_nattra_1(A,B,C,D,E,F,G),A,B,C,E)))))))))))))))) # label(t34_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3452 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> (r4_nattra_1(A,B,C,D,E,F) <-> A = C & (all G (m1_subset_1(G,A) -> k8_funct_2(A,B,E,G) = k1_funct_1(F,G)))))))))))))))) # label(d17_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3453 (all A all B all C all D (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & v2_cat_1(A) -> (exists E m1_nattra_1(E,A,B,C,D)))) # label(existence_m1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3454 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r2_hidden(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k10_cat_1(A,B),k10_cat_1(A,B)),k10_cat_1(A,B)),u5_cat_1(A)))))) # label(t5_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3455 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) & (exists E (m1_nattra_1(E,A,B,C,D) & (all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,F,G) -> (all H (m1_cat_1(H,A,F,G) -> k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,C,G),k13_cat_1(A,B,D,G),k3_nattra_1(A,B,C,F,G,H),k5_nattra_1(A,B,C,D,E,G)) = k9_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F),k13_cat_1(A,B,D,G),k5_nattra_1(A,B,C,D,E,F),k3_nattra_1(A,B,D,F,G,H))))))))))) <-> r2_nattra_1(A,B,C,D)))))))))) # label(d7_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3456 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(B) -> (all E (m1_nattra_1(E,A,B,C,D) -> v1_funct_1(E) & m2_relset_1(E,u1_cat_1(A),u2_cat_1(B)) & v1_funct_2(E,u1_cat_1(A),u2_cat_1(B)))))) # label(dt_m1_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3457 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r3_nattra_1(A,B,C,D) <-> (exists E (m2_nattra_1(E,A,B,C,D) & v1_nattra_1(E,A,B,C,D))) & r2_nattra_1(A,B,C,D)))))))))) # label(d11_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3458 (all A all B u5_cat_1(k8_cat_1(A,B)) = k1_tarski(k4_tarski(k4_tarski(B,B),B))) # label(t6_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3459 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r3_nattra_1(A,B,C,D) -> (all E (m2_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) <-> m3_nattra_1(E,A,B,C,D))))))))))))) # label(d14_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3460 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) & r1_nattra_1(A,B,C,D) -> (all F (m1_nattra_1(F,A,B,C,D) -> (all G (m1_nattra_1(G,A,B,D,E) -> (all H (m1_nattra_1(H,A,B,C,E) -> (H = k6_nattra_1(A,B,C,D,E,F,G) <-> (all I (m1_subset_1(I,u1_cat_1(A)) -> k9_cat_1(B,k13_cat_1(A,B,C,I),k13_cat_1(A,B,D,I),k13_cat_1(A,B,E,I),k5_nattra_1(A,B,C,D,F,I),k5_nattra_1(A,B,D,E,G,I)) = k5_nattra_1(A,B,C,E,H,I))))))))))))))))))))) # label(d6_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3461 (all A (l1_cat_1(A) & v2_cat_1(A) -> k13_nattra_1(k13_nattra_1(A)) = k13_nattra_1(A))) # label(t53_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3462 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> (all C (m4_nattra_1(C,A,B) -> -v1_xboole_0(C))))) # label(dt_m4_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3463 (all A (v2_cat_1(A) & l1_cat_1(A) & v2_nattra_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k6_cat_1(A,B,B) = k1_tarski(k10_cat_1(A,B)))))) # label(t44_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3464 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> l1_cat_1(k12_nattra_1(A,B)) & v2_cat_1(k12_nattra_1(A,B)) & v1_cat_1(k12_nattra_1(A,B)))) # label(dt_k12_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3465 $T # label(t36_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3466 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_relset_1(E,k12_mcart_1(A,A,C,C),C) & v1_funct_1(F) & m1_relset_1(F,k12_mcart_1(B,B,D,D),D) & v1_funct_1(E) & -v1_xboole_0(D) & -v1_xboole_0(C) -> m2_relset_1(k2_nattra_1(A,B,C,D,E,F),k12_mcart_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k12_mcart_1(A,B,C,D),k12_mcart_1(A,B,C,D)),k12_mcart_1(A,B,C,D)) & v1_funct_1(k2_nattra_1(A,B,C,D,E,F)))) # label(dt_k2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3467 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(B,k13_cat_1(A,B,C,E),k13_cat_1(A,B,D,E))))))))))))) # label(d2_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3468 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,C,A) -> (all E (m2_cat_1(E,A,B) -> (all F (m1_subset_1(F,u1_cat_1(C)) -> (all G (m1_subset_1(G,u1_cat_1(C)) -> (k1_xboole_0 != k6_cat_1(C,F,G) -> (all H (m1_cat_1(H,C,F,G) -> k3_nattra_1(A,B,E,k13_cat_1(C,A,D,F),k13_cat_1(C,A,D,G),k3_nattra_1(C,A,D,F,G,H)) = k3_nattra_1(C,B,k14_cat_1(C,A,B,D,E),F,G,H)))))))))))))))))) # label(t11_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3469 $T # label(t18_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3470 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (all D (m1_cat_1(D,A,B,C) -> D = k3_nattra_1(A,A,k15_cat_1(A),B,C,D)))))))))) # label(t16_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3471 (all A all B all C all D all E all F all G (l1_cat_1(A) & l1_cat_1(B) & m2_cat_1(C,A,B) & m2_cat_1(D,A,B) & m2_cat_1(E,A,B) & m2_nattra_1(F,A,B,C,D) & m2_nattra_1(G,A,B,D,E) & v2_cat_1(B) & v2_cat_1(A) -> m2_nattra_1(k8_nattra_1(A,B,C,D,E,F,G),A,B,C,E))) # label(dt_k8_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3472 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u2_cat_1(A))) -> (all D (v1_funct_2(D,C,B) & m2_relset_1(D,C,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,C,B) & m2_relset_1(E,C,B) -> (k1_nattra_1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = D & E = k1_nattra_1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) -> (all F (m2_relset_1(F,k2_zfmisc_1(C,C),C) & v1_funct_1(F) -> (k1_realset1(u5_cat_1(A),C) = F -> (all G (v1_funct_1(G) & m2_relset_1(G,B,C) & v1_funct_2(G,B,C) -> (G = k1_nattra_1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) -> m3_cat_2(g1_cat_1(B,C,D,E,F,G),A)))))))))))))))))) # label(t9_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.41 3473 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (k6_cat_1(A,E,F) != k1_xboole_0 -> (all G (m1_cat_1(G,A,E,F) -> k3_nattra_1(A,B,C,E,F,G) = k3_nattra_1(A,B,D,E,F,G)))))))) -> C = D))))))))) # label(t12_nattra_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3474 (all A all B all C (l1_cat_1(A) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(B,u2_cat_1(A)) & v2_cat_1(A) -> v1_funct_1(k22_ens_1(A,B,C)) & v1_funct_2(k22_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) & m2_relset_1(k22_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))))) # label(dt_k22_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3475 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & v2_cat_1(A) -> v1_funct_2(k21_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & m2_relset_1(k21_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_1(k21_ens_1(A,B)))) # label(dt_k21_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3476 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_partfun1(k6_cat_1(A,B,C)) = k19_ens_1(A,C,k10_cat_1(A,B)))))))) # label(t44_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3477 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k1_xboole_0 = k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)) -> k1_xboole_0 = k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C))))))))) # label(t51_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3478 (all A all B (m1_subset_1(B,k2_ens_1(A)) & -v1_xboole_0(A) -> m1_subset_1(k4_ens_1(A,B),A))) # label(dt_k4_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3479 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r1_tarski(k7_ens_1(A,B,C),k2_ens_1(A)))))))) # label(t17_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3480 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k5_ens_1(A,B),k2_ens_1(A)))) # label(dt_k5_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3481 (all A all B all C all D (m1_subset_1(C,B) & m1_subset_1(D,B) & -v1_xboole_0(B) -> ((exists E (k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E) = A & r2_hidden(k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E),k2_ens_1(B)) & m1_subset_1(E,k1_ens_1(B)))) <-> r2_hidden(A,a_3_0_ens_1(B,C,D))))) # label(fraenkel_a_3_0_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3482 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k1_funct_1(k3_funct_5(k23_ens_1(A)),k10_cat_1(A,B)) = k20_ens_1(A,B) & k1_funct_1(k5_funct_5(k23_ens_1(A)),k10_cat_1(A,B)) = k21_ens_1(A,B))))) # label(t57_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3483 (all A (-v1_xboole_0(A) -> m2_relset_1(k10_ens_1(A),k2_zfmisc_1(k2_ens_1(A),k2_ens_1(A)),k2_ens_1(A)) & v1_funct_1(k10_ens_1(A)))) # label(dt_k10_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3484 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (v1_ens_1(B,A) <-> k2_relat_1(k2_mcart_1(B)) = k4_ens_1(A,B)))))) # label(d9_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3485 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A))) & v1_funct_2(B,u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A))) -> ((all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A)),B,k13_cat_2(A,A,C,D)) = k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,C),k2_cat_1(A,D)),k6_cat_1(A,k2_cat_1(A,C),k3_cat_1(A,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,C),k2_cat_1(A,D)),k6_cat_1(A,k2_cat_1(A,C),k3_cat_1(A,D))),k22_ens_1(A,C,D)))))) <-> k23_ens_1(A) = B))))) # label(d25_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3486 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m2_relset_1(D,k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & v1_funct_2(D,k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(E,k6_cat_1(A,B,k2_cat_1(A,C))) -> k1_funct_1(D,E) = k4_cat_1(A,E,C)))) <-> k18_ens_1(A,B,C) = D))))))))) # label(d20_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3487 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> -(k1_tarski(k1_xboole_0) != A & v6_cat_1(B,k12_ens_1(A)) & (all C B != k1_tarski(C))))))) # label(t34_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3488 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> -(k4_ens_1(A,B) = k1_xboole_0 & k1_xboole_0 != k3_ens_1(A,B)) & v1_funct_1(k2_mcart_1(B)) & m2_relset_1(k2_mcart_1(B),k3_ens_1(A,B),k4_ens_1(A,B)) & v1_funct_2(k2_mcart_1(B),k3_ens_1(A,B),k4_ens_1(A,B)))))) # label(t9_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3489 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> k6_ens_1(A,k5_ens_1(A,k3_ens_1(A,B)),B) = B & B = k6_ens_1(A,B,k5_ens_1(A,k4_ens_1(A,B))))))) # label(t14_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3490 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> k4_ens_1(A,B) = k2_mcart_1(k1_mcart_1(B)))))) # label(d5_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3491 (all A all B (l1_cat_1(B) & v2_cat_1(B) & -v1_xboole_0(A) -> m2_cat_1(k26_ens_1(A,B),k11_cat_2(k2_oppcat_1(B),B),k12_ens_1(A)))) # label(dt_k26_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3492 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))),k22_ens_1(A,B,C)),k2_ens_1(k17_ens_1(A))))))))) # label(t52_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3493 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> m1_subset_1(B,k2_ens_1(A)))))) # label(t25_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3494 (all A (-v1_xboole_0(A) -> k2_ens_1(A) = a_1_1_ens_1(A))) # label(d2_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3495 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> k16_ens_1(A,B) = B)))) # label(d18_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3496 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k2_ens_1(A)))) # label(fc2_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3497 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> k4_ens_1(A,k16_ens_1(A,B)) = k3_cat_1(k12_ens_1(A),B) & k3_ens_1(A,k16_ens_1(A,B)) = k2_cat_1(k12_ens_1(A),B))))) # label(t26_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3498 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(k4_tarski(k4_tarski(C,D),B),k2_ens_1(A)) -> (k1_xboole_0 = D -> C = k1_xboole_0) & v1_funct_1(B) & v1_funct_2(B,C,D) & m2_relset_1(B,C,D))))))) # label(t10_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3499 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k6_cat_1(A,k2_cat_1(A,C),B) = k1_xboole_0 -> k6_cat_1(A,k3_cat_1(A,C),B) = k1_xboole_0) & (k1_xboole_0 = k6_cat_1(A,B,k3_cat_1(A,C)) -> k6_cat_1(A,B,k2_cat_1(A,C)) = k1_xboole_0))))))) # label(t42_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3500 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> m1_subset_1(B,A))))) # label(t23_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3501 (all A (l1_cat_1(A) & v2_cat_1(A) -> -v1_xboole_0(k17_ens_1(A)))) # label(fc5_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3502 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> -((all C B != k1_tarski(C)) & v6_cat_1(B,k12_ens_1(A))))))) # label(t35_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3503 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (r2_hidden(D,k7_ens_1(A,B,C)) -> D = k4_tarski(k1_domain_1(A,A,B,C),k2_mcart_1(D))))))))))) # label(t16_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3504 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> k3_ens_1(A,k5_ens_1(A,B)) = B & B = k4_ens_1(A,k5_ens_1(A,B)) & k2_mcart_1(k5_ens_1(A,B)) = k6_partfun1(B))))) # label(t11_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3505 (all A all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) & -v1_xboole_0(A) -> m1_subset_1(k14_ens_1(A,B),A))) # label(dt_k14_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3506 (all A (v2_cat_1(A) & l1_cat_1(A) -> k17_ens_1(A) = a_1_3_ens_1(A))) # label(d19_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3507 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_ens_1(A),A) & v1_funct_2(B,k2_ens_1(A),A) & v1_funct_1(B) -> ((all C (m1_subset_1(C,k2_ens_1(A)) -> k8_funct_2(k2_ens_1(A),A,B,C) = k4_ens_1(A,C))) <-> k9_ens_1(A) = B))))) # label(d11_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3508 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_ens_1(A),A) & m2_relset_1(B,k2_ens_1(A),A) -> ((all C (m1_subset_1(C,k2_ens_1(A)) -> k3_ens_1(A,C) = k8_funct_2(k2_ens_1(A),A,B,C))) <-> k8_ens_1(A) = B))))) # label(d10_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3509 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)),k19_ens_1(A,B,C)),k2_ens_1(k17_ens_1(A))))))))) # label(t48_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3510 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r1_tarski(k17_ens_1(B),A) -> k26_ens_1(A,B) = k23_ens_1(B)))))) # label(d28_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3511 (all A all B (m1_subset_1(B,k2_ens_1(A)) & -v1_xboole_0(A) -> m1_subset_1(k15_ens_1(A,B),u2_cat_1(k12_ens_1(A))))) # label(dt_k15_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3512 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_ens_1(B)) <-> (exists C exists D (k1_funct_2(C,D) = A & m1_subset_1(D,B) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_0_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3513 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k8_funct_2(u1_cat_1(B),u1_cat_1(k12_ens_1(A)),k12_cat_1(B,k12_ens_1(A),k24_ens_1(A,B,C)),D) = k6_cat_1(B,C,D)))))))))) # label(t60_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3514 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,D) = k3_cat_1(A,E) & k2_cat_1(A,C) = k3_cat_1(A,B) -> k22_ens_1(A,k4_cat_1(A,B,C),k4_cat_1(A,E,D)) = k1_partfun1(k6_cat_1(A,k3_cat_1(A,C),k2_cat_1(A,E)),k6_cat_1(A,k2_cat_1(A,C),k3_cat_1(A,E)),k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,D)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,D)),k22_ens_1(A,C,E),k22_ens_1(A,B,D))))))))))))) # label(t56_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3515 (all A all B (l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & v2_cat_1(A) -> m2_relset_1(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_2(k20_ens_1(A,B),u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_1(k20_ens_1(A,B)))) # label(dt_k20_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3516 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,k2_ens_1(A)) & m1_subset_1(B,k2_ens_1(A)) -> m1_subset_1(k6_ens_1(A,B,C),k2_ens_1(A)))) # label(dt_k6_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3517 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k25_ens_1(A,B,C) = k15_cat_2(k2_oppcat_1(B),B,k12_ens_1(A),k26_ens_1(A,B),C)))))))) # label(t66_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3518 (all A (-v1_xboole_0(A) -> (all B (r2_hidden(B,k1_ens_1(A)) <-> (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & (D = k1_xboole_0 -> k1_xboole_0 = C) & v1_funct_2(B,C,D) & m2_relset_1(B,C,D) & v1_funct_1(B))))))))) # label(t1_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3519 (all A all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) & -v1_xboole_0(A) -> m1_subset_1(k16_ens_1(A,B),k2_ens_1(A)))) # label(dt_k16_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3520 (all A (-v1_xboole_0(A) -> g1_cat_1(A,k2_ens_1(A),k8_ens_1(A),k9_ens_1(A),k10_ens_1(A),k11_ens_1(A)) = k12_ens_1(A))) # label(d14_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3521 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (k4_ens_1(A,D) = C & k3_ens_1(A,D) = B <-> r2_hidden(D,k7_ens_1(A,B,C))))))))))) # label(t19_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3522 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v4_cat_1(B,k12_ens_1(A)) -> (all C (m1_subset_1(C,A) -> (all D all E -(r2_hidden(D,C) & E != D & r2_hidden(E,C))))) | v1_ens_1(k16_ens_1(A,B),A)))))) # label(t37_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3523 (all A (-v1_xboole_0(A) -> k3_tarski(a_1_2_ens_1(A)) = k2_ens_1(A))) # label(t18_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3524 $T # label(dt_k2_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3525 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,C) & v1_funct_2(D,B,C) -> ((C = k1_xboole_0 -> B = k1_xboole_0) -> r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(B,C)),k1_domain_1(A,A,B,C),D),k2_ens_1(A))))))))))) # label(t5_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3526 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> ((exists C k1_tarski(C) = B) -> v6_cat_1(B,k12_ens_1(A))))))) # label(t33_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3527 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,C) -> k19_ens_1(A,B,k4_cat_1(A,D,C)) = k1_partfun1(k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B),k6_cat_1(A,k3_cat_1(A,D),B),k6_cat_1(A,k2_cat_1(A,D),B),k19_ens_1(A,B,C),k19_ens_1(A,B,D))))))))))) # label(t46_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3528 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m1_subset_1(B,u1_cat_1(k12_ens_1(A))))))) # label(t22_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3529 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r1_tarski(k1_funct_2(B,C),k1_ens_1(A)))))))) # label(t2_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3530 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & m2_relset_1(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) -> ((all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),k2_ens_1(k17_ens_1(A)),C,D) = k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D))),k18_ens_1(A,B,D)))) <-> k20_ens_1(A,B) = C))))))) # label(d22_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3531 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> r2_hidden(k6_cat_1(A,B,C),k17_ens_1(A)))))))) # label(t41_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3532 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,k2_ens_1(A)) & v1_funct_2(B,A,k2_ens_1(A)) -> ((all C (m1_subset_1(C,A) -> k5_ens_1(A,C) = k8_funct_2(A,k2_ens_1(A),B,C))) <-> B = k11_ens_1(A)))))) # label(d13_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3533 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v2_funct_1(k2_mcart_1(k16_ens_1(A,B))) <-> v3_cat_1(B,k12_ens_1(A))))))) # label(t36_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3534 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (all C (m1_subset_1(C,k2_ens_1(A)) -> (k3_ens_1(A,C) = k4_ens_1(A,B) -> k6_ens_1(A,B,C) = k4_tarski(k1_domain_1(A,A,k3_ens_1(A,B),k4_ens_1(A,C)),k5_relat_1(k2_mcart_1(B),k2_mcart_1(C)))))))))) # label(d7_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3535 (all A all B all C (-v1_xboole_0(A) & l1_cat_1(B) & m1_subset_1(C,u1_cat_1(B)) & v2_cat_1(B) -> m2_cat_1(k24_ens_1(A,B,C),B,k12_ens_1(A)))) # label(dt_k24_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3536 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k8_funct_2(u2_cat_1(B),u2_cat_1(k12_ens_1(A)),k24_ens_1(A,B,C),D) = k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(B,C,k2_cat_1(B,D)),k6_cat_1(B,C,k3_cat_1(B,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B)),k6_cat_1(B,C,k2_cat_1(B,D)),k6_cat_1(B,C,k3_cat_1(B,D))),k18_ens_1(B,C,D))))))))))) # label(t59_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3537 (all A (-v1_xboole_0(A) -> k3_tarski(a_1_0_ens_1(A)) = k1_ens_1(A))) # label(d1_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3538 $T # label(dt_k1_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3539 (all A all B (l1_cat_1(B) & v2_cat_1(B) -> ((exists C exists D (A = k6_cat_1(B,C,D) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(B)))) <-> r2_hidden(A,a_1_3_ens_1(B))))) # label(fraenkel_a_1_3_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3540 (all A (-v1_xboole_0(A) -> v2_cat_1(g1_cat_1(A,k2_ens_1(A),k8_ens_1(A),k9_ens_1(A),k10_ens_1(A),k11_ens_1(A))) & l1_cat_1(g1_cat_1(A,k2_ens_1(A),k8_ens_1(A),k9_ens_1(A),k10_ens_1(A),k11_ens_1(A))))) # label(t21_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3541 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> B = k15_ens_1(A,B))))) # label(d17_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3542 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> k6_partfun1(k6_cat_1(A,B,C)) = k22_ens_1(A,k10_cat_1(A,B),k10_cat_1(A,C)))))))) # label(t54_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3543 $T # label(dt_k7_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3544 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> k18_ens_1(A,B,C) = k22_ens_1(A,k10_cat_1(A,B),C) & k22_ens_1(A,C,k10_cat_1(A,B)) = k19_ens_1(A,B,C))))))) # label(t53_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3545 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> B = k4_tarski(k1_domain_1(A,A,k3_ens_1(A,B),k4_ens_1(A,B)),k2_mcart_1(B)))))) # label(t8_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3546 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> a_3_0_ens_1(A,B,C) = k7_ens_1(A,B,C))))))) # label(d8_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3547 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (k1_xboole_0 = B -> v7_cat_1(B,k12_ens_1(A))))))) # label(t30_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3548 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (exists C (m1_subset_1(C,k1_ens_1(A)) & (exists D (m1_subset_1(D,A) & (exists E (k1_domain_1(k2_zfmisc_1(A,A),k1_ens_1(A),k1_domain_1(A,A,D,E),C) = B & v1_funct_1(C) & m2_relset_1(C,D,E) & v1_funct_2(C,D,E) & (E = k1_xboole_0 -> k1_xboole_0 = D) & m1_subset_1(E,A))))))))))) # label(t4_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3549 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_relset_1(D,B,C) & v1_funct_2(D,B,C) & v1_funct_1(D) -> ((C = k1_xboole_0 -> B = k1_xboole_0) -> r2_hidden(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(B,C)),k1_domain_1(A,A,B,C),D),k7_ens_1(A,B,C))))))))))) # label(t15_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3550 (all A all B (m1_subset_1(B,k2_ens_1(A)) & -v1_xboole_0(A) -> m1_subset_1(k3_ens_1(A,B),A))) # label(dt_k3_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3551 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> k1_mcart_1(k1_mcart_1(B)) = k3_ens_1(A,B))))) # label(d4_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3552 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(k2_ens_1(A),k2_ens_1(A)),k2_ens_1(A)) -> ((all C (m1_subset_1(C,k2_ens_1(A)) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (k3_ens_1(A,C) = k4_ens_1(A,D) <-> r2_hidden(k1_domain_1(k2_ens_1(A),k2_ens_1(A),C,D),k1_relat_1(B))))))) & (all C (m1_subset_1(C,k2_ens_1(A)) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (k4_ens_1(A,D) = k3_ens_1(A,C) -> k1_funct_1(B,k1_domain_1(k2_ens_1(A),k2_ens_1(A),C,D)) = k6_ens_1(A,D,C)))))) <-> k10_ens_1(A) = B))))) # label(d12_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3553 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v1_ens_1(k16_ens_1(A,B),A) -> v4_cat_1(B,k12_ens_1(A))))))) # label(t38_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3554 (all A (-v1_xboole_0(A) -> v1_funct_2(k8_ens_1(A),k2_ens_1(A),A) & m2_relset_1(k8_ens_1(A),k2_ens_1(A),A) & v1_funct_1(k8_ens_1(A)))) # label(dt_k8_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3555 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> k14_ens_1(A,B) = B)))) # label(d16_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3556 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (all C (m1_subset_1(C,k2_ens_1(A)) -> (k3_ens_1(A,B) = k4_ens_1(A,C) -> k3_ens_1(A,k6_ens_1(A,C,B)) = k3_ens_1(A,C) & k4_ens_1(A,B) = k4_ens_1(A,k6_ens_1(A,C,B)) & k5_relat_1(k2_mcart_1(C),k2_mcart_1(B)) = k2_mcart_1(k6_ens_1(A,C,B))))))))) # label(t12_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3557 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (all C (m1_subset_1(C,u1_cat_1(k12_ens_1(A))) -> k6_cat_1(k12_ens_1(A),B,C) = k7_ens_1(A,k14_ens_1(A,B),k14_ens_1(A,C)))))))) # label(t27_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3558 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_ens_1(A)) & v1_fraenkel(k1_ens_1(A)))) # label(fc1_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3559 (all A all B all C (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(A)) & l1_cat_1(A) -> v1_funct_2(k18_ens_1(A,B,C),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & m2_relset_1(k18_ens_1(A,B,C),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))) & v1_funct_1(k18_ens_1(A,B,C)))) # label(dt_k18_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3560 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> k13_ens_1(A,B) = B)))) # label(d15_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3561 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k6_cat_1(B,D,C) = k8_funct_2(u1_cat_1(B),u1_cat_1(k12_ens_1(A)),k12_cat_1(B,k12_ens_1(A),k25_ens_1(A,B,C)),D)))))))))) # label(t62_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3562 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (v7_cat_1(B,k12_ens_1(A)) -> B = k1_xboole_0))))) # label(t32_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3563 (all A (-v1_xboole_0(A) -> r1_tarski(k2_ens_1(A),k2_zfmisc_1(k2_zfmisc_1(A,A),k1_ens_1(A))))) # label(t6_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3564 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k12_ens_1(A))) -> (k2_cat_1(k12_ens_1(A),B) = k3_cat_1(k12_ens_1(A),C) -> k6_ens_1(A,k16_ens_1(A,C),k16_ens_1(A,B)) = k4_cat_1(k12_ens_1(A),C,B)))))))) # label(t28_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3565 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> r1_tarski(k1_ens_1(B),k1_ens_1(A)))))) # label(t3_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3566 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> k1_partfun1(k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C)),k19_ens_1(A,k2_cat_1(A,C),B),k18_ens_1(A,k2_cat_1(A,B),C)) = k22_ens_1(A,B,C))))))) # label(t55_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3567 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k2_ens_1(A)) -> v1_relat_1(k2_mcart_1(B)) & v1_funct_1(k2_mcart_1(B)))) # label(fc3_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3568 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> k18_ens_1(A,B,k10_cat_1(A,C)) = k6_partfun1(k6_cat_1(A,B,C)))))))) # label(t43_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3569 $T # label(d3_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3570 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) & v1_funct_2(D,k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) -> (D = k19_ens_1(A,B,C) <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(E,k6_cat_1(A,k3_cat_1(A,C),B)) -> k4_cat_1(A,C,E) = k1_funct_1(D,E))))))))))))) # label(d21_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3571 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> r1_tarski(k2_ens_1(B),k2_ens_1(A)))))) # label(t7_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3572 (all A all B (-v1_xboole_0(B) -> ((exists C exists D (k7_ens_1(B,C,D) = A & m1_subset_1(D,B) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_2_ens_1(B))))) # label(fraenkel_a_1_2_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3573 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,C) -> k1_partfun1(k6_cat_1(A,B,k2_cat_1(A,D)),k6_cat_1(A,B,k3_cat_1(A,D)),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C)),k18_ens_1(A,B,D),k18_ens_1(A,B,C)) = k18_ens_1(A,B,k4_cat_1(A,D,C))))))))))) # label(t45_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3574 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(B,B)),k1_domain_1(A,A,B,B),k6_partfun1(B)) = k5_ens_1(A,B))))) # label(d6_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3575 (all A (v2_cat_1(A) & l1_cat_1(A) -> v1_funct_2(k23_ens_1(A),u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A))) & m2_relset_1(k23_ens_1(A),u2_cat_1(k11_cat_2(A,A)),k2_ens_1(k17_ens_1(A))) & v1_funct_1(k23_ens_1(A)))) # label(dt_k23_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3576 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k13_ens_1(A,B),u1_cat_1(k12_ens_1(A))))) # label(dt_k13_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3577 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> m1_oppcat_1(k21_ens_1(B,C),B,k12_ens_1(A))))))))) # label(t50_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3578 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,B,k2_cat_1(A,C)),k6_cat_1(A,B,k3_cat_1(A,C))),k18_ens_1(A,B,C)),k2_ens_1(k17_ens_1(A))))))))) # label(t47_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3579 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) & v1_funct_2(D,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C)),k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,C))) -> (D = k22_ens_1(A,B,C) <-> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(E,k6_cat_1(A,k3_cat_1(A,B),k2_cat_1(A,C))) -> k4_cat_1(A,B,k4_cat_1(A,E,C)) = k1_funct_1(D,E))))))))))))) # label(d24_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3580 (all A all B all C (m1_subset_1(C,u1_cat_1(B)) & l1_cat_1(B) & v2_cat_1(B) & -v1_xboole_0(A) -> m1_oppcat_1(k25_ens_1(A,B,C),B,k12_ens_1(A)))) # label(dt_k25_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3581 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k21_ens_1(B,C) = k25_ens_1(A,B,C)))))))) # label(d27_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3582 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (v1_funct_2(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & m2_relset_1(C,u2_cat_1(A),k2_ens_1(k17_ens_1(A))) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u2_cat_1(A)) -> k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(A,k3_cat_1(A,D),B),k6_cat_1(A,k2_cat_1(A,D),B))),k1_domain_1(k1_zfmisc_1(u2_cat_1(A)),k1_zfmisc_1(u2_cat_1(A)),k6_cat_1(A,k3_cat_1(A,D),B),k6_cat_1(A,k2_cat_1(A,D),B)),k19_ens_1(A,B,D)) = k8_funct_2(u2_cat_1(A),k2_ens_1(k17_ens_1(A)),C,D))) <-> C = k21_ens_1(A,B)))))))) # label(d23_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3583 (all A all B all C (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(A)) & l1_cat_1(A) -> v1_funct_1(k19_ens_1(A,B,C)) & v1_funct_2(k19_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)) & m2_relset_1(k19_ens_1(A,B,C),k6_cat_1(A,k3_cat_1(A,C),B),k6_cat_1(A,k2_cat_1(A,C),B)))) # label(dt_k19_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3584 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> (all C (m1_subset_1(C,k2_ens_1(A)) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (k3_ens_1(A,B) = k4_ens_1(A,C) & k4_ens_1(A,B) = k3_ens_1(A,D) -> k6_ens_1(A,k6_ens_1(A,C,B),D) = k6_ens_1(A,C,k6_ens_1(A,B,D))))))))))) # label(t13_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3585 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,k2_ens_1(A)) -> (r2_hidden(D,k7_ens_1(A,B,C)) -> r2_hidden(k2_mcart_1(D),k1_funct_2(B,C))))))))))) # label(t20_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3586 (all A (-v1_xboole_0(A) -> v1_funct_2(k9_ens_1(A),k2_ens_1(A),A) & m2_relset_1(k9_ens_1(A),k2_ens_1(A),A) & v1_funct_1(k9_ens_1(A)))) # label(dt_k9_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3587 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(B,k3_cat_1(B,D),C),k6_cat_1(B,k2_cat_1(B,D),C))),k1_domain_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B)),k6_cat_1(B,k3_cat_1(B,D),C),k6_cat_1(B,k2_cat_1(B,D),C)),k19_ens_1(B,C,D)) = k8_funct_2(u2_cat_1(B),u2_cat_1(k12_ens_1(A)),k25_ens_1(A,B,C),D)))))))))) # label(t61_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3588 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> k5_ens_1(A,k14_ens_1(A,B)) = k10_cat_1(k12_ens_1(A),B))))) # label(t29_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3589 (all A (-v1_xboole_0(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k24_ens_1(A,B,C) = k20_ens_1(B,C)))))))) # label(d26_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3590 (all A all B (-v1_xboole_0(B) -> ((exists C exists D exists E (m1_subset_1(D,B) & (k1_xboole_0 = D -> k1_xboole_0 = C) & v1_funct_1(E) & v1_funct_2(E,C,D) & m2_relset_1(E,C,D) & k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E) = A & m1_subset_1(E,k1_ens_1(B)) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_1_ens_1(B))))) # label(fraenkel_a_1_1_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3591 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k14_cat_2(k2_oppcat_1(B),B,k12_ens_1(A),k26_ens_1(A,B),k3_oppcat_1(B,C)) = k24_ens_1(A,B,C)))))))) # label(t65_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3592 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k1_domain_1(k2_zfmisc_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B))),k1_zfmisc_1(k2_zfmisc_1(k6_cat_1(B,k3_cat_1(B,C),k2_cat_1(B,D)),k6_cat_1(B,k2_cat_1(B,C),k3_cat_1(B,D)))),k1_domain_1(k1_zfmisc_1(u2_cat_1(B)),k1_zfmisc_1(u2_cat_1(B)),k6_cat_1(B,k3_cat_1(B,C),k2_cat_1(B,D)),k6_cat_1(B,k2_cat_1(B,C),k3_cat_1(B,D))),k22_ens_1(B,C,D)) = k8_funct_2(u2_cat_1(k11_cat_2(k2_oppcat_1(B),B)),u2_cat_1(k12_ens_1(A)),k26_ens_1(A,B),k13_cat_2(k2_oppcat_1(B),B,k5_oppcat_1(B,C),D))))))))))) # label(t63_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3593 (all A (-v1_xboole_0(A) -> v2_cat_1(k12_ens_1(A)) & v1_cat_1(k12_ens_1(A)))) # label(fc4_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3594 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> r1_cat_2(k12_ens_1(B),k12_ens_1(A)))))) # label(t40_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3595 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> m2_cat_1(k20_ens_1(B,C),B,k12_ens_1(A))))))))) # label(t49_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3596 (all A (-v1_xboole_0(A) -> l1_cat_1(k12_ens_1(A)))) # label(dt_k12_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3597 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (r1_tarski(k17_ens_1(B),A) -> k6_cat_1(B,C,D) = k8_funct_2(u1_cat_1(k11_cat_2(k2_oppcat_1(B),B)),u1_cat_1(k12_ens_1(A)),k12_cat_1(k11_cat_2(k2_oppcat_1(B),B),k12_ens_1(A),k26_ens_1(A,B)),k12_cat_2(k2_oppcat_1(B),B,k3_oppcat_1(B,C),D))))))))))) # label(t64_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3598 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k12_ens_1(A))) -> (v4_cat_1(B,k12_ens_1(A)) -> v1_ens_1(k16_ens_1(A,B),A)))))) # label(t39_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3599 (all A (-v1_xboole_0(A) -> v1_funct_1(k11_ens_1(A)) & m2_relset_1(k11_ens_1(A),A,k2_ens_1(A)) & v1_funct_2(k11_ens_1(A),A,k2_ens_1(A)))) # label(dt_k11_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3600 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_cat_1(k12_ens_1(A))) -> (v7_cat_1(B,k12_ens_1(A)) & r2_hidden(k1_xboole_0,A) -> B = k1_xboole_0))))) # label(t31_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3601 $T # label(dt_k17_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3602 (all A (-v1_xboole_0(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r1_tarski(k17_ens_1(B),A) -> m2_cat_1(k23_ens_1(B),k11_cat_2(k2_oppcat_1(B),B),k12_ens_1(A))))))) # label(t58_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3603 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k2_ens_1(A)) -> m1_subset_1(B,u2_cat_1(k12_ens_1(A))))))) # label(t24_ens_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3604 (all A (v2_cat_1(A) & l1_cat_1(A) -> m2_cat_1(k1_isocat_1(A),A,A))) # label(dt_k1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3605 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (v8_cat_1(C,B,A) -> r4_nattra_1(u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),u2_cat_1(B),k2_isocat_1(B,A,B,C,k3_isocat_1(B,A,C)),k1_isocat_1(B)) & r4_nattra_1(u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),u2_cat_1(A),k2_isocat_1(A,B,A,k3_isocat_1(B,A,C),C),k1_isocat_1(A))))))))) # label(t16_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3606 $T # label(t51_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3607 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (r1_isocat_1(C,D) & r1_isocat_1(A,B) -> r1_isocat_1(k11_cat_2(A,C),k11_cat_2(B,D))))))))))) # label(t24_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3608 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (r1_nattra_1(A,B,D,E) & r1_nattra_1(B,C,F,G) -> r1_nattra_1(A,C,k14_cat_1(A,B,C,D,F),k14_cat_1(A,B,C,E,G))))))))))))))))) # label(t8_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3609 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_cat_1(H,B,C) -> (all I (m2_cat_1(I,C,D) -> (all J (m2_cat_1(J,C,D) -> (all K (m2_nattra_1(K,A,B,E,F) -> (all L (m2_nattra_1(L,B,C,G,H) -> (all M (m2_nattra_1(M,C,D,I,J) -> (r2_nattra_1(C,D,I,J) & r2_nattra_1(B,C,G,H) & r2_nattra_1(A,B,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k8_isocat_1(A,C,D,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,F,H),I,J,k8_isocat_1(A,B,C,E,F,G,H,K,L),M),k8_isocat_1(A,B,D,E,F,k2_isocat_1(B,C,D,G,I),k2_isocat_1(B,C,D,H,J),K,k8_isocat_1(B,C,D,G,H,I,J,L,M)))))))))))))))))))))))))))))) # label(t44_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3610 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> r2_isocat_1(A,A))) # label(reflexivity_r2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3611 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) -> (all F (m1_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> (all H (m1_subset_1(H,u1_cat_1(A)) -> k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k4_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H))))))))))))))))))) # label(t26_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3612 (all A all B all C all D all E all F all G (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(C) & m2_cat_1(F,A,B) & m1_nattra_1(G,B,C,D,E) & m2_cat_1(E,B,C) & m2_cat_1(D,B,C) & v2_cat_1(C) & l1_cat_1(A) -> m1_nattra_1(k5_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)))) # label(dt_k5_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3613 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (all F (m2_cat_1(F,C,A) -> (all G (m2_nattra_1(G,B,C,D,E) -> (r2_nattra_1(B,C,D,E) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,E,G,F),k8_isocat_1(B,C,A,D,E,F,F,G,k7_nattra_1(C,A,F)))))))))))))))))) # label(t46_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3614 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k8_isocat_1(A,B,B,C,D,k1_isocat_1(B),k1_isocat_1(B),E,k7_nattra_1(B,B,k1_isocat_1(B))),E)))))))))))) # label(t42_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3615 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,E,D,k7_nattra_1(B,C,E)),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))))))))))))) # label(t37_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3616 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (v5_cat_1(D,B) -> v5_cat_1(k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,D),A)))))))))) # label(t3_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3617 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (all C (m1_isocat_1(C,A,B) -> m2_cat_1(C,A,B))))) # label(dt_m1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3618 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v8_cat_1(C,A,B) -> r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k3_isocat_1(B,A,k3_isocat_1(A,B,C)),C)))))))) # label(t15_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3619 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) -> (all F (m1_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> k7_funct_2(u1_cat_1(A),u2_cat_1(B),u2_cat_1(C),F,G) = k4_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d5_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3620 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,C) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,C,D) -> (all H (m2_cat_1(H,D,B) -> (all I (m2_nattra_1(I,C,D,F,G) -> (r2_nattra_1(C,D,F,G) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k7_isocat_1(A,C,B,k2_isocat_1(C,D,B,F,H),k2_isocat_1(C,D,B,G,H),E,k6_isocat_1(C,D,B,F,G,I,H)),k6_isocat_1(A,D,B,k2_isocat_1(A,C,D,E,F),k2_isocat_1(A,C,D,E,G),k7_isocat_1(A,C,D,F,G,E,I),H))))))))))))))))))))) # label(t35_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3621 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v8_cat_1(C,A,B) -> v8_cat_1(k3_isocat_1(A,B,C),B,A)))))))) # label(t13_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3622 (all A (v2_cat_1(A) & l1_cat_1(A) -> m1_isocat_1(k1_isocat_1(A),A,A))) # label(t54_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3623 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (r2_nattra_1(B,A,C,D) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> k1_xboole_0 != k6_cat_1(A,k13_cat_1(B,A,C,E),k13_cat_1(B,A,D,E))))))))))))) # label(t30_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3624 (all A (l1_cat_1(A) & v2_cat_1(A) -> k15_cat_1(A) = k1_isocat_1(A))) # label(redefinition_k1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3625 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (r2_isocat_1(A,B) -> r2_isocat_1(B,A)))) # label(symmetry_r2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3626 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (r2_nattra_1(B,A,C,D) -> (all E (m2_nattra_1(E,B,A,C,D) -> (all F (m2_nattra_1(F,B,A,C,D) -> ((all G (m1_subset_1(G,u1_cat_1(B)) -> k5_nattra_1(B,A,C,D,F,G) = k5_nattra_1(B,A,C,D,E,G))) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),E,F))))))))))))))) # label(t31_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3627 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (r1_isocat_1(B,C) & r1_isocat_1(A,B) -> r1_isocat_1(A,C)))))))) # label(t20_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3628 $T # label(t5_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3629 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> r1_isocat_1(k11_cat_2(k11_cat_2(A,B),C),k11_cat_2(A,k11_cat_2(B,C))))))))) # label(t23_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3630 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> ((exists C ((exists D (r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) & r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A)) & m2_cat_1(D,B,A))) & m2_cat_1(C,A,B))) <-> r2_isocat_1(A,B)))))) # label(d10_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3631 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v8_cat_1(C,A,B) -> k2_funct_1(k12_cat_1(A,B,C)) = k12_cat_1(B,A,k3_isocat_1(A,B,C))))))))) # label(t14_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3632 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,C,A) -> (all H (m2_nattra_1(H,B,C,D,E) -> (all I (m2_nattra_1(I,B,C,E,F) -> (r2_nattra_1(B,C,E,F) & r2_nattra_1(B,C,D,E) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k6_isocat_1(B,C,A,D,F,k8_nattra_1(B,C,D,E,F,H,I),G),k8_nattra_1(B,A,k2_isocat_1(B,C,A,D,G),k2_isocat_1(B,C,A,E,G),k2_isocat_1(B,C,A,F,G),k6_isocat_1(B,C,A,D,E,H,G),k6_isocat_1(B,C,A,E,F,I,G)))))))))))))))))))))) # label(t32_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3633 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,C,D) -> (all H (m2_cat_1(H,C,D) -> (all I (m2_nattra_1(I,C,D,G,H) -> (r2_nattra_1(C,D,G,H) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(D),u1_cat_1(A),u2_cat_1(D),k7_isocat_1(A,B,D,k2_isocat_1(B,C,D,F,G),k2_isocat_1(B,C,D,F,H),E,k7_isocat_1(B,C,D,G,H,F,I)),k7_isocat_1(A,C,D,G,H,k2_isocat_1(A,B,C,E,F),I))))))))))))))))))))) # label(t34_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3634 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> r1_isocat_1(k11_cat_2(A,B),k11_cat_2(B,A)))))) # label(t22_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3635 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k15_funct_3(A,B))))))) # label(t1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3636 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,B,A) -> r4_nattra_1(u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),k14_cat_1(A,A,B,k15_cat_1(A),C),C) & r4_nattra_1(u2_cat_1(B),u2_cat_1(A),u2_cat_1(B),u2_cat_1(A),k14_cat_1(B,A,A,D,k15_cat_1(A)),D))))))))) # label(t4_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3637 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> r2_hidden(k5_nattra_1(A,B,C,D,E,F),k6_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))))))))))))))) # label(t7_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.42 3638 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (exists C m1_isocat_1(C,A,B)))) # label(existence_m1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3639 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r1_nattra_1(A,B,D,E) -> (all F (m2_cat_1(F,C,A) -> (all G (m1_nattra_1(G,A,B,D,E) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) = k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k5_isocat_1(C,A,B,D,E,F,G),H)))))))))))))))))) # label(t25_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3640 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m2_cat_1(k2_isocat_1(A,B,C,D,E),A,C))) # label(dt_k2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3641 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(C,A,B) -> m2_cat_1(k3_isocat_1(A,B,C),B,A))) # label(dt_k3_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3642 (all A all B all C all D all E all F all G (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(F,A,B) & m2_nattra_1(G,B,C,D,E) & m2_cat_1(D,B,C) & l1_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) -> m2_nattra_1(k7_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,F,D),k2_isocat_1(A,B,C,F,E)))) # label(dt_k7_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3643 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v8_cat_1(C,A,B) -> k3_isocat_1(A,B,C) = k2_funct_1(C)))))))) # label(d2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3644 $T # label(t18_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3645 (all A all B all C all D all E all F all G all H all I (l1_cat_1(B) & m2_nattra_1(H,A,B,D,E) & m2_nattra_1(I,B,C,F,G) & m2_cat_1(G,B,C) & m2_cat_1(F,B,C) & m2_cat_1(E,A,B) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & v2_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_nattra_1(k8_isocat_1(A,B,C,D,E,F,G,H,I),A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G)))) # label(dt_k8_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3646 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_cat_1(H,B,C) -> (r3_nattra_1(B,C,G,H) -> r3_nattra_1(A,C,k2_isocat_1(A,B,C,E,G),k2_isocat_1(A,B,C,E,H)) & r3_nattra_1(B,D,k2_isocat_1(B,C,D,G,F),k2_isocat_1(B,C,D,H,F))))))))))))))))))) # label(t48_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3647 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_nattra_1(H,A,B,D,E) -> (all I (m2_nattra_1(I,B,C,F,G) -> k8_isocat_1(A,B,C,D,E,F,G,H,I) = k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,F),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,H,F),k7_isocat_1(A,B,C,F,G,E,I)))))))))))))))))))) # label(d9_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3648 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,B,A) -> (all E (m2_cat_1(E,A,A) -> (r3_nattra_1(A,A,E,k1_isocat_1(A)) -> r3_nattra_1(A,B,k2_isocat_1(A,A,B,E,C),C) & r3_nattra_1(B,A,k2_isocat_1(B,A,A,D,E),D)))))))))))) # label(t49_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3649 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (r2_nattra_1(B,C,D,E) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_nattra_1(G,B,C,D,E) -> k5_isocat_1(A,B,C,D,E,F,G) = k7_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d8_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3650 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r2_isocat_1(A,B) -> (all C (m2_cat_1(C,A,B) -> (m1_isocat_1(C,A,B) <-> (exists D (r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A)) & r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) & m2_cat_1(D,B,A))))))))))) # label(d11_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3651 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v2_funct_1(C) -> v2_funct_1(k12_cat_1(A,B,C))))))))) # label(t12_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3652 (all A all B all C all D all E all F all G (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & m2_cat_1(G,B,C) & m1_nattra_1(F,A,B,D,E) & m2_cat_1(E,A,B) & m2_cat_1(D,A,B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) -> m1_nattra_1(k4_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)))) # label(dt_k4_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3653 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (all E (m2_nattra_1(E,B,A,C,D) -> (r2_nattra_1(B,A,C,D) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k7_isocat_1(B,B,A,C,D,k1_isocat_1(B),E),E)))))))))))) # label(t39_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3654 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) -> (all F (m2_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> (all H (m1_subset_1(H,u1_cat_1(A)) -> k5_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k6_isocat_1(A,B,C,D,E,F,G),H) = k3_nattra_1(B,C,G,k13_cat_1(A,B,D,H),k13_cat_1(A,B,E,H),k5_nattra_1(A,B,D,E,F,H))))))))))))))))))) # label(t28_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3655 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (v8_cat_1(C,B,A) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (D = k13_cat_1(B,A,C,E) & m1_subset_1(E,u1_cat_1(B))))))))))))) # label(t11_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3656 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (r1_isocat_1(A,B) -> r2_isocat_1(A,B)))))) # label(t50_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3657 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (r2_nattra_1(B,C,F,G) & r2_nattra_1(A,B,D,E) -> r2_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,E,G))))))))))))))))) # label(t27_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3658 $T # label(t19_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3659 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,B,C) -> (all E (m2_cat_1(E,B,C) -> (r1_nattra_1(B,C,D,E) -> (all F (m2_cat_1(F,A,B) -> (all G (m1_nattra_1(G,B,C,D,E) -> k7_funct_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(C),k12_cat_1(A,B,F),G) = k5_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d6_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3660 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,A,B) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_cat_1(H,B,C) -> (all I (m2_cat_1(I,B,C) -> (all J (m2_nattra_1(J,A,B,D,E) -> (all K (m2_nattra_1(K,A,B,E,F) -> (all L (m2_nattra_1(L,B,C,G,H) -> (all M (m2_nattra_1(M,B,C,H,I) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(B,C,H,I) & r2_nattra_1(B,C,G,H) & r2_nattra_1(A,B,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,F,G,I,k8_nattra_1(A,B,D,E,F,J,K),k8_nattra_1(B,C,G,H,I,L,M)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,H),k2_isocat_1(A,B,C,F,I),k8_isocat_1(A,B,C,D,E,G,H,J,L),k8_isocat_1(A,B,C,E,F,H,I,K,M)))))))))))))))))))))))))))))) # label(t47_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3661 (all A all B all C all D all E all F all G (v2_cat_1(B) & m2_cat_1(D,A,B) & m2_cat_1(G,B,C) & m2_nattra_1(F,A,B,D,E) & m2_cat_1(E,A,B) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> m2_nattra_1(k6_isocat_1(A,B,C,D,E,F,G),A,C,k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G)))) # label(dt_k6_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3662 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_nattra_1(G,B,C,E,F) -> (r2_nattra_1(B,C,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,F,D,G),k8_isocat_1(A,B,C,D,D,E,F,k7_nattra_1(A,B,D),G))))))))))))))))) # label(t45_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3663 (all A all B all C all D all E (v2_cat_1(B) & l1_cat_1(B) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) & l1_cat_1(C) & v2_cat_1(C) & l1_cat_1(A) & v2_cat_1(A) -> k5_relat_1(D,E) = k2_isocat_1(A,B,C,D,E))) # label(redefinition_k2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3664 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (v2_cat_1(D) & l1_cat_1(D) -> (all E (m2_cat_1(E,C,D) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,D,A) -> (all H (m2_cat_1(H,A,B) -> (all I (m2_nattra_1(I,C,D,E,F) -> (r2_nattra_1(C,D,E,F) -> r4_nattra_1(u1_cat_1(C),u2_cat_1(B),u1_cat_1(C),u2_cat_1(B),k6_isocat_1(C,D,B,E,F,I,k2_isocat_1(D,A,B,G,H)),k6_isocat_1(C,A,B,k2_isocat_1(C,D,A,E,G),k2_isocat_1(C,D,A,F,G),k6_isocat_1(C,D,A,E,F,I,G),H))))))))))))))))))))) # label(t36_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3665 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> r1_isocat_1(A,A))) # label(reflexivity_r1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3666 $T # label(t6_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3667 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_nattra_1(E,A,B,C,D) -> (r2_nattra_1(A,B,C,D) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(B),u1_cat_1(A),u2_cat_1(B),k6_isocat_1(A,B,B,C,D,E,k1_isocat_1(B)),E)))))))))))) # label(t40_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3668 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) -> (all F (m2_cat_1(F,C,A) -> (all G (m2_nattra_1(G,A,B,D,E) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k5_nattra_1(A,B,D,E,G,k13_cat_1(C,A,F,H)) = k5_nattra_1(C,B,k2_isocat_1(C,A,B,F,D),k2_isocat_1(C,A,B,F,E),k7_isocat_1(C,A,B,D,E,F,G),H)))))))))))))))))) # label(t29_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3669 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v8_cat_1(C,A,B) <-> k2_relat_1(C) = u2_cat_1(B) & v2_funct_1(C)))))))) # label(d3_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3670 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (r2_isocat_1(A,B) -> (all C (m1_isocat_1(C,A,B) -> (exists D (m1_isocat_1(D,B,A) & r3_nattra_1(B,B,k2_isocat_1(B,A,B,D,C),k1_isocat_1(B)) & r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A))))))))))) # label(t56_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3671 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (m2_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) & m1_subset_1(E,u1_cat_1(B)))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) & k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,E) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E)))))))))))))) # label(d1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3672 (all A all B (v2_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) -> (r1_isocat_1(A,B) -> r1_isocat_1(B,A)))) # label(symmetry_r1_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3673 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_nattra_1(H,A,B,D,E) -> (all I (m2_nattra_1(I,B,C,F,G) -> (r2_nattra_1(A,B,D,E) & r2_nattra_1(B,C,F,G) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k8_isocat_1(A,B,C,D,E,F,G,H,I),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k2_isocat_1(A,B,C,E,G),k7_isocat_1(A,B,C,F,G,D,I),k6_isocat_1(A,B,C,D,E,H,G)))))))))))))))))))))) # label(t41_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3674 $T # label(t52_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3675 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r2_isocat_1(A,B) -> (all C (m1_isocat_1(C,A,B) -> v9_cat_1(C,A,B) & v10_cat_1(C,A,B) & (all D (m1_subset_1(D,u1_cat_1(B)) -> (exists E (r1_cat_1(B,D,k13_cat_1(A,B,C,E)) & m1_subset_1(E,u1_cat_1(A))))))))))))) # label(t58_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3676 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (v8_cat_1(C,B,A) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (exists E (m1_subset_1(E,u2_cat_1(B)) & k8_funct_2(u2_cat_1(B),u2_cat_1(A),C,E) = D))))))))))) # label(t10_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3677 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k6_isocat_1(A,B,C,D,D,k7_nattra_1(A,B,D),E),k7_nattra_1(A,C,k2_isocat_1(A,B,C,D,E))))))))))))) # label(t38_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3678 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B all C r1_isocat_1(k11_cat_2(k8_cat_1(B,C),A),A)))) # label(t21_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3679 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,B) -> (r2_nattra_1(A,B,D,E) -> (all F (m2_nattra_1(F,A,B,D,E) -> (all G (m2_cat_1(G,B,C) -> k6_isocat_1(A,B,C,D,E,F,G) = k4_isocat_1(A,B,C,D,E,F,G)))))))))))))))) # label(d7_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3680 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,B,A) -> (all D (m2_cat_1(D,B,A) -> (all E (m2_nattra_1(E,B,A,C,D) -> (r2_nattra_1(B,A,C,D) -> r4_nattra_1(u1_cat_1(B),u2_cat_1(A),u1_cat_1(B),u2_cat_1(A),k8_isocat_1(B,B,A,k1_isocat_1(B),k1_isocat_1(B),C,D,k7_nattra_1(B,B,k1_isocat_1(B)),E),E)))))))))))) # label(t43_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3681 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (r2_isocat_1(A,B) & r2_isocat_1(B,C) -> (all D (m1_isocat_1(D,A,B) -> (all E (m1_isocat_1(E,B,C) -> m1_isocat_1(k2_isocat_1(A,B,C,D,E),A,C)))))))))))) # label(t55_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3682 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,A,B) -> (r1_nattra_1(A,B,C,D) -> (all E (m1_nattra_1(E,A,B,C,D) -> (v1_nattra_1(E,A,B,C,D) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> r1_cat_1(B,k13_cat_1(A,B,C,F),k13_cat_1(A,B,D,F)))))))))))))))) # label(t9_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3683 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (r2_isocat_1(B,C) & r2_isocat_1(A,B) -> r2_isocat_1(A,C)))))))) # label(t53_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3684 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m2_cat_1(D,B,A) -> (r3_nattra_1(A,A,k2_isocat_1(A,B,A,C,D),k1_isocat_1(A)) -> v10_cat_1(C,A,B)))))))))) # label(t57_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3685 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v8_cat_1(E,B,C) & v8_cat_1(D,A,B) -> v8_cat_1(k2_isocat_1(A,B,C,D,E),A,C)))))))))))) # label(t17_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3686 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m2_cat_1(F,B,C) -> (all G (m2_cat_1(G,B,C) -> (all H (m2_nattra_1(H,B,C,E,F) -> (all I (m2_nattra_1(I,B,C,F,G) -> (r2_nattra_1(B,C,F,G) & r2_nattra_1(B,C,E,F) -> r4_nattra_1(u1_cat_1(A),u2_cat_1(C),u1_cat_1(A),u2_cat_1(C),k7_isocat_1(A,B,C,E,G,D,k8_nattra_1(B,C,E,F,G,H,I)),k8_nattra_1(A,C,k2_isocat_1(A,B,C,D,E),k2_isocat_1(A,B,C,D,F),k2_isocat_1(A,B,C,D,G),k7_isocat_1(A,B,C,E,F,D,H),k7_isocat_1(A,B,C,F,G,D,I)))))))))))))))))))))) # label(t33_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3687 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> ((exists C (m2_cat_1(C,A,B) & v8_cat_1(C,A,B))) <-> r1_isocat_1(A,B)))))) # label(d4_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3688 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k2_relat_1(k17_cat_2(B,A)) = u2_cat_1(A) & k2_relat_1(k16_cat_2(A,B)) = u2_cat_1(A))))) # label(t2_isocat_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3689 (all A all B all C all D (l1_cat_1(A) & v2_cat_1(B) & m1_subset_1(D,u1_cat_1(A)) & m1_oppcat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> m1_subset_1(k5_yoneda_1(A,B,C,D),u1_cat_1(B)))) # label(dt_k5_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3690 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k2_yoneda_1(A,B) = k20_ens_1(A,B))))) # label(d2_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3691 (all A all B (v2_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m2_nattra_1(k3_yoneda_1(A,B),A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))))) # label(dt_k3_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3692 (all A (l1_cat_1(A) & v2_cat_1(A) -> k12_ens_1(k17_ens_1(A)) = k1_yoneda_1(A))) # label(d1_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3693 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (m1_subset_1(D,u2_cat_1(k1_yoneda_1(A))) -> (all E (m1_subset_1(E,u2_cat_1(k1_yoneda_1(A))) -> (k3_cat_1(k1_yoneda_1(A),D) = k2_cat_1(k1_yoneda_1(A),E) & E = k4_tarski(k12_cat_2(k1_yoneda_1(A),k1_yoneda_1(A),k2_cat_1(k1_yoneda_1(A),E),k3_cat_1(k1_yoneda_1(A),E)),C) & D = k4_tarski(k12_cat_2(k1_yoneda_1(A),k1_yoneda_1(A),k2_cat_1(k1_yoneda_1(A),D),k3_cat_1(k1_yoneda_1(A),D)),B) -> k4_cat_1(k1_yoneda_1(A),D,E) = k4_tarski(k12_cat_2(k1_yoneda_1(A),k1_yoneda_1(A),k2_cat_1(k1_yoneda_1(A),D),k3_cat_1(k1_yoneda_1(A),E)),k5_relat_1(B,C))))))))))))) # label(t1_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3694 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> m2_cat_1(k2_yoneda_1(A,B),A,k1_yoneda_1(A)))) # label(dt_k2_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 5.37/5.43 3695 (all A (v2_cat_1(A) & l1_cat_1(A) -> m1_oppcat_1(k4_yoneda_1(A),A,k12_nattra_1(A,k1_yoneda_1(A))))) # label(dt_k4_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 81.06/81.10 3696 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m2_nattra_1(C,A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> k4_tarski(k4_tarski(k6_cat_1(A,k3_cat_1(A,B),D),k6_cat_1(A,k2_cat_1(A,B),D)),k22_ens_1(A,B,k10_cat_1(A,D))) = k5_nattra_1(A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B)),C,D))) <-> k3_yoneda_1(A,B) = C))))))) # label(d3_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 81.06/81.10 3697 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> m2_cat_1(k20_ens_1(A,B),A,k1_yoneda_1(A)))))) # label(t2_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 81.06/81.10 3698 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> r2_nattra_1(A,k1_yoneda_1(A),k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))))))) # label(t3_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 81.06/81.10 3699 (all A (v2_cat_1(A) & l1_cat_1(A) -> v2_cat_1(k1_yoneda_1(A)) & l1_cat_1(k1_yoneda_1(A)))) # label(dt_k1_yoneda_1) # label(axiom) # label(non_clause). [assumption]. 81.06/81.10 3700 -(all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k4_tarski(k4_tarski(k2_yoneda_1(A,k3_cat_1(A,B)),k2_yoneda_1(A,k2_cat_1(A,B))),k3_yoneda_1(A,B)),u2_cat_1(k12_nattra_1(A,k1_yoneda_1(A)))))))) # label(t4_yoneda_1) # label(negated_conjecture) # label(non_clause). [assumption]. 81.06/81.10 81.06/81.10 ============================== end of process non-clausal formulas === 81.06/81.10 81.06/81.10 ============================== PROCESS INITIAL CLAUSES =============== 81.06/81.10 81.06/81.10 ============================== PREDICATE ELIMINATION ================= 81.06/81.10 3701 p1_s1_xboole_0(A) | -r2_hidden(A,c6) # label(s1_xboole_0) # label(axiom). [clausify(44)]. 81.06/81.10 3702 -r2_hidden(A,f1_s1_xboole_0) | -p1_s1_xboole_0(A) | r2_hidden(A,c6) # label(s1_xboole_0) # label(axiom). [clausify(44)]. 81.06/81.10 3703 r2_hidden(A,c12) | -p1_s1_subset_1(A) | -r2_hidden(A,f1_s1_subset_1) # label(s1_subset_1) # label(axiom). [clausify(426)]. 81.06/81.10 3704 -r2_hidden(A,c12) | p1_s1_subset_1(A) # label(s1_subset_1) # label(axiom). [clausify(426)]. 81.06/81.10 3705 -m1_subset_1(A,f1_s3_subset_1) | p1_s3_subset_1(A) | -r2_hidden(A,c13) # label(s3_subset_1) # label(axiom). [clausify(456)]. 81.06/81.10 3706 -m1_subset_1(A,f1_s3_subset_1) | -p1_s3_subset_1(A) | r2_hidden(A,c13) # label(s3_subset_1) # label(axiom). [clausify(456)]. 81.06/81.10 3707 r2_hidden(k4_tarski(A,B),c15) | -r2_hidden(B,f2_s1_relat_1) | -p1_s1_relat_1(A,B) | -r2_hidden(A,f1_s1_relat_1) # label(s1_relat_1) # label(axiom). [clausify(477)]. 81.06/81.10 3708 -r2_hidden(k4_tarski(A,B),c15) | p1_s1_relat_1(A,B) # label(s1_relat_1) # label(axiom). [clausify(477)]. 81.06/81.10 3709 -v1_relat_1(A) | v2_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)) # label(d9_relat_1) # label(axiom). [clausify(519)]. 81.06/81.10 3710 -v1_relat_1(A) | -v2_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)) # label(d9_relat_1) # label(axiom). [clausify(519)]. 81.06/81.10 3711 -v1_funct_1(A) | -v2_relat_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)) # label(fc6_funct_1) # label(axiom). [clausify(843)]. 81.06/81.10 Derived: -v1_funct_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)) | -v1_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3711,b,3709,b)]. 81.06/81.10 3712 -v1_relat_1(A) | -v1_funct_1(A) | -v2_relat_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)) # label(d15_funct_1) # label(axiom). [clausify(864)]. 81.06/81.10 Derived: -v1_relat_1(A) | -v1_funct_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)) | -v1_relat_1(A) | r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3712,c,3709,b)]. 81.06/81.10 3713 -v1_relat_1(A) | -v1_funct_1(A) | v2_relat_1(A) | v1_xboole_0(k1_funct_1(A,f160(A))) # label(d15_funct_1) # label(axiom). [clausify(864)]. 81.06/81.10 Derived: -v1_relat_1(A) | -v1_funct_1(A) | v1_xboole_0(k1_funct_1(A,f160(A))) | -v1_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3713,c,3710,b)]. 81.06/81.10 Derived: -v1_relat_1(A) | -v1_funct_1(A) | v1_xboole_0(k1_funct_1(A,f160(A))) | -v1_funct_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)). [resolve(3713,c,3711,b)]. 99.42/99.53 Derived: -v1_relat_1(A) | -v1_funct_1(A) | v1_xboole_0(k1_funct_1(A,f160(A))) | -v1_relat_1(A) | -v1_funct_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)). [resolve(3713,c,3712,c)]. 99.42/99.53 3714 -v1_relat_1(A) | -v1_funct_1(A) | v2_relat_1(A) | r2_hidden(f160(A),k1_relat_1(A)) # label(d15_funct_1) # label(axiom). [clausify(864)]. 99.42/99.53 Derived: -v1_relat_1(A) | -v1_funct_1(A) | r2_hidden(f160(A),k1_relat_1(A)) | -v1_relat_1(A) | -r2_hidden(k1_xboole_0,k2_relat_1(A)). [resolve(3714,c,3710,b)]. 99.42/99.53 Derived: -v1_relat_1(A) | -v1_funct_1(A) | r2_hidden(f160(A),k1_relat_1(A)) | -v1_funct_1(A) | -v1_relat_1(A) | v1_setfam_1(k2_relat_1(A)). [resolve(3714,c,3711,b)]. 99.42/99.53 Derived: -v1_relat_1(A) | -v1_funct_1(A) | r2_hidden(f160(A),k1_relat_1(A)) | -v1_relat_1(A) | -v1_funct_1(A) | -v1_xboole_0(k1_funct_1(A,B)) | -r2_hidden(B,k1_relat_1(A)). [resolve(3714,c,3712,c)]. 99.42/99.53 3715 v2_relat_1(c31) # label(rc5_funct_1) # label(axiom). [clausify(877)]. 99.42/99.53 Derived: -v1_relat_1(c31) | -r2_hidden(k1_xboole_0,k2_relat_1(c31)). [resolve(3715,a,3710,b)]. 99.42/99.53 Derived: -v1_funct_1(c31) | -v1_relat_1(c31) | v1_setfam_1(k2_relat_1(c31)). [resolve(3715,a,3711,b)]. 99.42/99.53 Derived: -v1_relat_1(c31) | -v1_funct_1(c31) | -v1_xboole_0(k1_funct_1(c31,A)) | -r2_hidden(A,k1_relat_1(c31)). [resolve(3715,a,3712,c)]. 99.42/99.53 3716 v3_ordinal1(A) | -v1_ordinal1(A) | -v2_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(916)]. 99.42/99.53 3717 -v3_ordinal1(A) | v2_ordinal1(k3_tarski(A)) # label(fc4_ordinal1) # label(axiom). [clausify(895)]. 99.42/99.53 3718 -v1_relat_1(A) | -v1_funct_1(A) | -v5_ordinal1(A) | v2_ordinal1(k1_relat_1(A)) # label(fc5_ordinal1) # label(axiom). [clausify(898)]. 99.42/99.53 3719 -v1_xboole_0(A) | v2_ordinal1(A) # label(cc3_ordinal1) # label(axiom). [clausify(901)]. 99.42/99.53 3720 -v3_ordinal1(A) | v2_ordinal1(A) # label(d4_ordinal1) # label(axiom). [clausify(916)]. 99.42/99.53 Derived: v3_ordinal1(A) | -v1_ordinal1(A) | -v1_xboole_0(A). [resolve(3716,c,3719,b)]. 99.42/99.53 3721 -v3_ordinal1(A) | v2_ordinal1(A) # label(cc1_ordinal1) # label(axiom). [clausify(924)]. 99.42/99.53 3722 v2_ordinal1(c43) # label(rc2_ordinal1) # label(axiom). [clausify(934)]. 99.42/99.53 Derived: v3_ordinal1(c43) | -v1_ordinal1(c43). [resolve(3722,a,3716,c)]. 99.42/99.53 3723 -v2_ordinal1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B) # label(d3_ordinal1) # label(axiom). [clausify(943)]. 99.42/99.53 Derived: -r2_hidden(A,k3_tarski(B)) | -r2_hidden(C,k3_tarski(B)) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v3_ordinal1(B). [resolve(3723,a,3717,b)]. 99.42/99.53 Derived: -r2_hidden(A,k1_relat_1(B)) | -r2_hidden(C,k1_relat_1(B)) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v1_relat_1(B) | -v1_funct_1(B) | -v5_ordinal1(B). [resolve(3723,a,3718,d)]. 99.42/99.53 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v1_xboole_0(B). [resolve(3723,a,3719,b)]. 99.42/99.53 Derived: -r2_hidden(A,B) | -r2_hidden(C,B) | r2_hidden(A,C) | C = A | r2_hidden(C,A) | -v3_ordinal1(B). [resolve(3723,a,3720,b)]. 99.42/99.53 Derived: -r2_hidden(A,c43) | -r2_hidden(B,c43) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3723,a,3722,a)]. 99.42/99.53 3724 v2_ordinal1(A) | r2_hidden(f182(A),A) # label(d3_ordinal1) # label(axiom). [clausify(943)]. 99.42/99.53 Derived: r2_hidden(f182(A),A) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3724,a,3716,c)]. 99.42/99.53 Derived: r2_hidden(f182(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3724,a,3723,a)]. 99.42/99.53 3725 v2_ordinal1(A) | r2_hidden(f183(A),A) # label(d3_ordinal1) # label(axiom). [clausify(943)]. 99.42/99.53 Derived: r2_hidden(f183(A),A) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3725,a,3716,c)]. 99.42/99.53 Derived: r2_hidden(f183(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3725,a,3723,a)]. 99.42/99.53 3726 v2_ordinal1(A) | -r2_hidden(f182(A),f183(A)) # label(d3_ordinal1) # label(axiom). [clausify(943)]. 99.42/99.53 Derived: -r2_hidden(f182(A),f183(A)) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3726,a,3716,c)]. 99.42/99.53 Derived: -r2_hidden(f182(A),f183(A)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3726,a,3723,a)]. 104.58/104.63 3727 v2_ordinal1(A) | f183(A) != f182(A) # label(d3_ordinal1) # label(axiom). [clausify(943)]. 104.58/104.63 Derived: f183(A) != f182(A) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3727,a,3716,c)]. 104.58/104.63 Derived: f183(A) != f182(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3727,a,3723,a)]. 104.58/104.63 3728 v2_ordinal1(A) | -r2_hidden(f183(A),f182(A)) # label(d3_ordinal1) # label(axiom). [clausify(943)]. 104.58/104.63 Derived: -r2_hidden(f183(A),f182(A)) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3728,a,3716,c)]. 104.58/104.63 Derived: -r2_hidden(f183(A),f182(A)) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3728,a,3723,a)]. 104.58/104.63 3729 v2_ordinal1(c45) # label(rc3_ordinal1) # label(axiom). [clausify(951)]. 104.58/104.63 Derived: -r2_hidden(A,c45) | -r2_hidden(B,c45) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3729,a,3723,a)]. 104.58/104.63 3730 v2_ordinal1(k1_xboole_0) # label(fc2_ordinal1_AndRHS_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom). [assumption]. 104.58/104.63 Derived: -r2_hidden(A,k1_xboole_0) | -r2_hidden(B,k1_xboole_0) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3730,a,3723,a)]. 104.58/104.63 3731 v2_ordinal1(c48) # label(rc1_ordinal1) # label(axiom). [clausify(972)]. 104.58/104.63 Derived: v3_ordinal1(c48) | -v1_ordinal1(c48). [resolve(3731,a,3716,c)]. 104.58/104.63 Derived: -r2_hidden(A,c48) | -r2_hidden(B,c48) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3731,a,3723,a)]. 104.58/104.63 3732 -v2_ordinal1(A) | -v1_ordinal1(A) | v3_ordinal1(A) # label(cc2_ordinal1) # label(axiom). [clausify(973)]. 104.58/104.63 Derived: -v1_ordinal1(k3_tarski(A)) | v3_ordinal1(k3_tarski(A)) | -v3_ordinal1(A). [resolve(3732,a,3717,b)]. 104.58/104.63 Derived: -v1_ordinal1(k1_relat_1(A)) | v3_ordinal1(k1_relat_1(A)) | -v1_relat_1(A) | -v1_funct_1(A) | -v5_ordinal1(A). [resolve(3732,a,3718,d)]. 104.58/104.63 Derived: -v1_ordinal1(c45) | v3_ordinal1(c45). [resolve(3732,a,3729,a)]. 104.58/104.63 Derived: -v1_ordinal1(k1_xboole_0) | v3_ordinal1(k1_xboole_0). [resolve(3732,a,3730,a)]. 104.58/104.63 3733 -v3_ordinal1(A) | v2_ordinal1(k1_ordinal1(A)) # label(fc3_ordinal1) # label(axiom). [clausify(975)]. 104.58/104.63 Derived: -v3_ordinal1(A) | -r2_hidden(B,k1_ordinal1(A)) | -r2_hidden(C,k1_ordinal1(A)) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3733,b,3723,a)]. 104.58/104.63 3734 v2_ordinal1(c110) # label(rc1_ordinal2) # label(axiom). [clausify(1994)]. 104.58/104.63 Derived: -r2_hidden(A,c110) | -r2_hidden(B,c110) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3734,a,3723,a)]. 104.58/104.63 3735 -v1_funct_1(A) | -v1_ordinal2(A) | -v3_ordinal1(B) | -v5_ordinal1(A) | -v1_relat_1(A) | v2_ordinal1(k1_funct_1(A,B)) # label(fc3_ordinal2) # label(axiom). [clausify(2003)]. 104.58/104.63 Derived: -v1_funct_1(A) | -v1_ordinal2(A) | -v3_ordinal1(B) | -v5_ordinal1(A) | -v1_relat_1(A) | -r2_hidden(C,k1_funct_1(A,B)) | -r2_hidden(D,k1_funct_1(A,B)) | r2_hidden(C,D) | D = C | r2_hidden(D,C). [resolve(3735,f,3723,a)]. 104.58/104.63 3736 v2_ordinal1(k5_ordinal2) # label(fc1_ordinal2_AndRHS_AndLHS) # label(axiom). [assumption]. 104.58/104.63 Derived: -r2_hidden(A,k5_ordinal2) | -r2_hidden(B,k5_ordinal2) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3736,a,3723,a)]. 104.58/104.63 3737 v2_ordinal1(f567(A)) # label(rc2_finset_1) # label(axiom). [clausify(2164)]. 104.58/104.63 Derived: -r2_hidden(A,f567(B)) | -r2_hidden(C,f567(B)) | r2_hidden(A,C) | C = A | r2_hidden(C,A). [resolve(3737,a,3723,a)]. 104.58/104.63 3738 -m1_subset_1(A,k5_numbers) | v2_ordinal1(A) # label(cc3_card_1) # label(axiom). [clausify(2286)]. 104.58/104.63 Derived: -m1_subset_1(A,k5_numbers) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3738,b,3723,a)]. 104.58/104.63 3739 -v1_card_1(A) | v2_ordinal1(A) # label(cc1_card_1) # label(axiom). [clausify(2315)]. 104.58/104.63 Derived: -v1_card_1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3739,b,3723,a)]. 104.58/104.63 3740 -v3_ordinal1(A) | v2_ordinal1(k3_card_1(A)) # label(fc1_card_1) # label(axiom). [clausify(2325)]. 104.58/104.63 Derived: -v3_ordinal1(A) | v3_ordinal1(k3_card_1(A)) | -v1_ordinal1(k3_card_1(A)). [resolve(3740,b,3716,c)]. 104.58/104.63 Derived: -v3_ordinal1(A) | -r2_hidden(B,k3_card_1(A)) | -r2_hidden(C,k3_card_1(A)) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3740,b,3723,a)]. 118.08/118.15 3741 -v1_finset_1(A) | v2_ordinal1(k1_card_1(A)) # label(fc2_card_1) # label(axiom). [clausify(2332)]. 118.08/118.15 Derived: -v1_finset_1(A) | -r2_hidden(B,k1_card_1(A)) | -r2_hidden(C,k1_card_1(A)) | r2_hidden(B,C) | C = B | r2_hidden(C,B). [resolve(3741,b,3723,a)]. 118.08/118.15 3742 -m1_subset_1(A,k5_numbers) | v2_ordinal1(A) # label(cc2_card_1) # label(axiom). [clausify(2334)]. 118.08/118.15 Derived: -m1_subset_1(A,k5_numbers) | v3_ordinal1(A) | -v1_ordinal1(A). [resolve(3742,b,3716,c)]. 118.08/118.15 3743 v2_ordinal1(c194) # label(rc2_card_1) # label(axiom). [clausify(2354)]. 118.08/118.15 Derived: v3_ordinal1(c194) | -v1_ordinal1(c194). [resolve(3743,a,3716,c)]. 118.08/118.15 Derived: -r2_hidden(A,c194) | -r2_hidden(B,c194) | r2_hidden(A,B) | B = A | r2_hidden(B,A). [resolve(3743,a,3723,a)]. 118.08/118.15 3744 v6_ordinal1(A) | r2_hidden(f179(A),A) # label(d9_ordinal1) # label(axiom). [clausify(926)]. 118.08/118.15 3745 -v6_ordinal1(A) | r2_hidden(f177(A),A) | v1_relat_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(920)]. 118.08/118.15 3746 -v6_ordinal1(A) | r2_hidden(f177(A),A) | v5_ordinal1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(920)]. 118.08/118.15 3747 -v6_ordinal1(A) | r2_hidden(f177(A),A) | v1_funct_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(920)]. 118.08/118.15 3748 -v6_ordinal1(A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v1_relat_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(920)]. 118.08/118.15 3749 -v6_ordinal1(A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v5_ordinal1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(920)]. 118.08/118.15 3750 -v6_ordinal1(A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v1_funct_1(k3_tarski(A)) # label(t49_ordinal1) # label(axiom). [clausify(920)]. 118.08/118.15 3751 -v6_ordinal1(A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r3_xboole_0(C,B) # label(d9_ordinal1) # label(axiom). [clausify(926)]. 118.08/118.15 Derived: r2_hidden(f179(A),A) | r2_hidden(f177(A),A) | v1_relat_1(k3_tarski(A)). [resolve(3744,a,3745,a)]. 118.08/118.15 Derived: r2_hidden(f179(A),A) | r2_hidden(f177(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(3744,a,3746,a)]. 118.08/118.15 Derived: r2_hidden(f179(A),A) | r2_hidden(f177(A),A) | v1_funct_1(k3_tarski(A)). [resolve(3744,a,3747,a)]. 118.08/118.15 Derived: r2_hidden(f179(A),A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v1_relat_1(k3_tarski(A)). [resolve(3744,a,3748,a)]. 118.08/118.15 Derived: r2_hidden(f179(A),A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v5_ordinal1(k3_tarski(A)). [resolve(3744,a,3749,a)]. 118.08/118.15 Derived: r2_hidden(f179(A),A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v1_funct_1(k3_tarski(A)). [resolve(3744,a,3750,a)]. 118.08/118.15 Derived: r2_hidden(f179(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r3_xboole_0(C,B). [resolve(3744,a,3751,a)]. 118.08/118.15 3752 v6_ordinal1(A) | r2_hidden(f178(A),A) # label(d9_ordinal1) # label(axiom). [clausify(926)]. 118.08/118.15 Derived: r2_hidden(f178(A),A) | r2_hidden(f177(A),A) | v1_relat_1(k3_tarski(A)). [resolve(3752,a,3745,a)]. 118.08/118.15 Derived: r2_hidden(f178(A),A) | r2_hidden(f177(A),A) | v5_ordinal1(k3_tarski(A)). [resolve(3752,a,3746,a)]. 118.08/118.15 Derived: r2_hidden(f178(A),A) | r2_hidden(f177(A),A) | v1_funct_1(k3_tarski(A)). [resolve(3752,a,3747,a)]. 118.08/118.15 Derived: r2_hidden(f178(A),A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v1_relat_1(k3_tarski(A)). [resolve(3752,a,3748,a)]. 118.08/118.15 Derived: r2_hidden(f178(A),A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v5_ordinal1(k3_tarski(A)). [resolve(3752,a,3749,a)]. 118.08/118.15 Derived: r2_hidden(f178(A),A) | -v1_relat_1(f177(A)) | -v5_ordinal1(f177(A)) | -v1_funct_1(f177(A)) | v1_funct_1(k3_tarski(A)). [resolve(3752,a,3750,a)]. 118.08/118.15 Derived: r2_hidden(f178(A),A) | -r2_hidden(B,A) | -r2_hidden(C,A) | r3_xboole_0(C,B). [resolve(3752,a,3751,a)]. 118.08/118.15 3753 v6_ordinal1(A) | -r3_xboole_0(f178(A),f179(A)) # label(d9_ordinal1) # label(axiom). [clausify(926)]. 118.08/118.15 Derived: -r3_xboole_0(f178(A),f179(A)) | r2_hidden(f177(A),A) | v1_relat_1(k3_tarski(A)). [resolve(3753,a,3745,a)]. 118.08/118.15 Derived: -r3_xboole_0(f178(A),f179(A)) | r2_hidden(f177(A),A) | v5_ordinal1(k3_tarski(A)). [Cputime limit exceeded (core dumped) 180.07/180.10 EOF