0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.14/0.34 % Computer : n005.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1200 0.14/0.34 % DateTime : Tue Jul 13 16:08:49 EDT 2021 0.14/0.34 % CPUTime : 6.27/6.26 ============================== Prover9 =============================== 6.27/6.26 Prover9 (32) version 2009-11A, November 2009. 6.27/6.26 Process 12542 was started by sandbox2 on n005.cluster.edu, 6.27/6.26 Tue Jul 13 16:08:54 2021 6.27/6.26 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_12366_n005.cluster.edu". 6.27/6.26 ============================== end of head =========================== 6.27/6.26 6.27/6.26 ============================== INPUT ================================= 6.27/6.26 6.27/6.26 % Reading from file /tmp/Prover9_12366_n005.cluster.edu 6.27/6.26 6.27/6.26 set(prolog_style_variables). 6.27/6.26 set(auto2). 6.27/6.26 % set(auto2) -> set(auto). 6.27/6.26 % set(auto) -> set(auto_inference). 6.27/6.26 % set(auto) -> set(auto_setup). 6.27/6.26 % set(auto_setup) -> set(predicate_elim). 6.27/6.26 % set(auto_setup) -> assign(eq_defs, unfold). 6.27/6.26 % set(auto) -> set(auto_limits). 6.27/6.26 % set(auto_limits) -> assign(max_weight, "100.000"). 6.27/6.26 % set(auto_limits) -> assign(sos_limit, 20000). 6.27/6.26 % set(auto) -> set(auto_denials). 6.27/6.26 % set(auto) -> set(auto_process). 6.27/6.26 % set(auto2) -> assign(new_constants, 1). 6.27/6.26 % set(auto2) -> assign(fold_denial_max, 3). 6.27/6.26 % set(auto2) -> assign(max_weight, "200.000"). 6.27/6.26 % set(auto2) -> assign(max_hours, 1). 6.27/6.26 % assign(max_hours, 1) -> assign(max_seconds, 3600). 6.27/6.26 % set(auto2) -> assign(max_seconds, 0). 6.27/6.26 % set(auto2) -> assign(max_minutes, 5). 6.27/6.26 % assign(max_minutes, 5) -> assign(max_seconds, 300). 6.27/6.26 % set(auto2) -> set(sort_initial_sos). 6.27/6.26 % set(auto2) -> assign(sos_limit, -1). 6.27/6.26 % set(auto2) -> assign(lrs_ticks, 3000). 6.27/6.26 % set(auto2) -> assign(max_megs, 400). 6.27/6.26 % set(auto2) -> assign(stats, some). 6.27/6.26 % set(auto2) -> clear(echo_input). 6.27/6.26 % set(auto2) -> set(quiet). 6.27/6.26 % set(auto2) -> clear(print_initial_clauses). 6.27/6.26 % set(auto2) -> clear(print_given). 6.27/6.26 assign(lrs_ticks,-1). 6.27/6.26 assign(sos_limit,10000). 6.27/6.26 assign(order,kbo). 6.27/6.26 set(lex_order_vars). 6.27/6.26 clear(print_given). 6.27/6.26 6.27/6.26 % formulas(sos). % not echoed (5549 formulas) 6.27/6.26 6.27/6.26 ============================== end of input ========================== 6.27/6.26 6.27/6.26 % From the command line: assign(max_seconds, 1200). 6.27/6.26 6.27/6.26 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 6.27/6.26 6.27/6.26 % Formulas that are not ordinary clauses: 6.27/6.26 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 2 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 3 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 4 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 5 (all A all B ((all C (A = C <-> r2_hidden(C,B))) <-> B = k1_tarski(A))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 6 (all A all B k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 7 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 8 (all A all B -((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,C) & r2_hidden(D,B))))) & r2_hidden(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 9 (all A all B ((all C (r2_hidden(C,B) <-> (exists D (r2_hidden(C,D) & r2_hidden(D,A))))) <-> B = k3_tarski(A))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 10 (all A exists B ((all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & (all E (r1_tarski(E,C) -> r2_hidden(E,D))))))) & (all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 11 (all A all B (r2_tarski(A,B) <-> (exists C ((all D -((all E -(r2_hidden(k4_tarski(E,D),C) & r2_hidden(E,A))) & r2_hidden(D,B))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),C) & r2_hidden(k4_tarski(D,E),C) -> (D = F <-> E = G))) & (all D -((all E -(r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 12 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 13 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 14 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 15 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 16 (all A all B all C (p1_s1_tarski(A,C) & p1_s1_tarski(A,B) -> B = C)) -> (exists A all B ((exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))) <-> r2_hidden(B,A))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 17 (all A all B ((all C (r2_hidden(C,A) -> r2_hidden(C,B))) <-> r1_tarski(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 18 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 19 (all A all B all C ((all D (r2_hidden(D,C) <-> D = B | D = A)) <-> k2_tarski(A,B) = C)) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 21 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 22 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 23 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 24 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 25 (all A all B k5_xboole_0(B,A) = k5_xboole_0(A,B)) # label(commutativity_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 26 (all A all B ((all C (p1_s3_xboole_0(C) <-> r2_hidden(C,A))) & (all C (p1_s3_xboole_0(C) <-> r2_hidden(C,B))) -> A = B)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 27 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 28 (all A ((all B -r2_hidden(B,A)) <-> A = k1_xboole_0)) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 29 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (r2_hidden(A,f1_s2_xboole_0) <-> p1_s2_xboole_0(A))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 30 (all A all B all C -(r1_xboole_0(A,B) & r2_hidden(C,k2_xboole_0(A,B)) & -(-r2_hidden(C,A) & r2_hidden(C,B)) & -(r2_hidden(C,A) & -r2_hidden(C,B)))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 31 (all A all B (r1_tarski(B,A) | r1_tarski(A,B) <-> r3_xboole_0(A,B))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 32 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 33 (all A all B (r1_xboole_0(A,B) <-> k1_xboole_0 = k3_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 34 (all A all B (r1_xboole_0(A,B) -> r1_xboole_0(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 35 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 36 (all A all B (r1_tarski(B,A) & r1_tarski(A,B) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 37 (all A all B (r2_xboole_0(A,B) -> -r2_xboole_0(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 38 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 39 (exists A all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_xboole_0) & p1_s1_xboole_0(B))) # label(s1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 40 (all A all B all C ((all D ((r2_hidden(D,C) <-> r2_hidden(D,B)) <-> -r2_hidden(D,A))) -> k5_xboole_0(B,C) = A)) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 41 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 42 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 43 (all A (A = k1_xboole_0 <-> v1_xboole_0(A))) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 44 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 45 (all A all B (r2_xboole_0(A,B) <-> r1_tarski(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 46 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -((all C -(r2_hidden(C,A) & r2_hidden(C,B))) & -r1_xboole_0(A,B)))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 47 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 48 (all A all B k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 49 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 50 (all A all B (-(r1_xboole_0(A,B) & (exists C r2_hidden(C,k3_xboole_0(A,B)))) & -((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 51 (all A all B k3_xboole_0(A,B) = k3_xboole_0(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 52 (all A all B all C (k4_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> -r2_hidden(D,B) & r2_hidden(D,A))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 53 (all A all B (r3_xboole_0(A,B) -> r3_xboole_0(B,A))) # label(symmetry_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 54 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 55 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 56 (all A all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))) <-> k2_xboole_0(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 57 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,B) & r2_hidden(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 58 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 59 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 60 (all A all B all C (-(r2_hidden(A,C) <-> r2_hidden(A,B)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 61 (all A all B -(v1_xboole_0(B) & A != B & v1_xboole_0(A))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 62 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 63 (all A A = k4_xboole_0(A,k1_xboole_0)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 65 (all A A = k2_xboole_0(A,k1_xboole_0)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 66 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 67 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 68 (all A all B -(v1_xboole_0(B) & r2_hidden(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 69 (all A all B all C all D all E all F all G all H (k5_enumset1(A,B,C,D,E,F,G) = H <-> (all I (r2_hidden(I,H) <-> -(D != I & I != F & I != G & I != E & C != I & I != B & I != A))))) # label(d5_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 70 (all A all B all C all D all E (k2_enumset1(A,B,C,D) = E <-> (all F (-(C != F & F != D & B != F & A != F) <-> r2_hidden(F,E))))) # label(d2_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 71 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k6_enumset1(A,A,A,A,B,C,D,E)) # label(t86_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 72 $T # label(dt_k3_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 73 $T # label(t115_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 74 (all A all B all C all D all E all F all G all H k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t63_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 75 $T # label(t28_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 76 (all A all B all C all D k5_enumset1(A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t85_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 77 $T # label(t39_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 78 (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]. 6.27/6.26 79 (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]. 6.27/6.26 80 $T # label(t18_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 81 (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]. 6.27/6.26 82 $T # label(t24_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 83 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H))) # label(t67_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 84 (all A all B all C all D all E all F all G all H all I (k6_enumset1(A,B,C,D,E,F,G,H) = I <-> (all J (-(B != J & J != H & J != G & J != F & E != J & J != D & J != C & J != A) <-> r2_hidden(J,I))))) # label(d6_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 85 (all A all B all C all D all E k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E)) = k3_enumset1(A,B,C,D,E)) # label(t48_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 86 (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]. 6.27/6.26 87 $T # label(dt_k2_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 88 (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]. 6.27/6.26 89 $T # label(t27_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 90 $T # label(t22_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 91 (all A all B all C all D all E k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E)) = k3_enumset1(A,B,C,D,E)) # label(t50_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 92 $T # label(t36_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 93 (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]. 6.27/6.26 94 (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]. 6.27/6.26 95 $T # label(t7_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 96 $T # label(t3_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 97 $T # label(t121_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 98 (all A all B all C all D all E all F all G (G = k4_enumset1(A,B,C,D,E,F) <-> (all H (r2_hidden(H,G) <-> -(A != H & H != D & F != H & E != H & C != H & H != B))))) # label(d4_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 99 $T # label(t10_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 100 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A)) # label(t125_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 101 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D))) # label(t44_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 102 (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]. 6.27/6.26 103 (all A all B all C all D k2_enumset1(B,C,A,D) = k2_enumset1(A,B,C,D)) # label(t110_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 104 $T # label(t37_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 105 (all A all B all C all D k2_enumset1(B,D,C,A) = k2_enumset1(A,B,C,D)) # label(t113_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 106 (all A all B all C k1_enumset1(A,C,B) = k1_enumset1(A,B,C)) # label(t98_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 107 $T # label(t20_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 108 $T # label(t38_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 109 $T # label(t14_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 110 (all A k1_tarski(A) = k3_enumset1(A,A,A,A,A)) # label(t87_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 111 $T # label(t5_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 112 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F))) # label(t52_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 113 $T # label(t17_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 114 $T # label(t26_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 115 (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]. 6.27/6.26 116 $T # label(t35_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 117 (all A all B all C all D k3_enumset1(A,A,B,C,D) = k2_enumset1(A,B,C,D)) # label(t72_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 118 (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]. 6.27/6.26 119 (all A all B all C all D all E all F all G all H k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H)) # label(t66_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 120 $T # label(t16_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 121 (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]. 6.27/6.26 122 $T # label(t21_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 123 (all A all B all C all D all E all F all G k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) = k5_enumset1(A,B,C,D,E,F,G)) # label(t59_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 124 $T # label(dt_k5_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 125 (all A all B all C all D all E all F k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F))) # label(t51_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 126 (all A all B all C all D all E all F k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) = k4_enumset1(A,B,C,D,E,F)) # label(t55_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 127 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 128 (all A k1_tarski(A) = k2_enumset1(A,A,A,A)) # label(t82_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 129 $T # label(t101_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 130 (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]. 6.27/6.26 131 $T # label(t33_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 132 (all A all B all C k4_enumset1(A,A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t84_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 133 (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]. 6.27/6.26 134 $T # label(t6_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 135 (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]. 6.27/6.26 136 (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]. 6.27/6.26 137 $T # label(t29_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 138 (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]. 6.27/6.26 139 $T # label(t11_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 140 (all A k1_tarski(A) = k1_enumset1(A,A,A)) # label(t76_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 141 $T # label(t32_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 142 (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]. 6.27/6.26 143 (all A k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A)) # label(t96_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 144 $T # label(t19_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 145 $T # label(t97_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 146 (all A k2_tarski(A,A) = k1_tarski(A)) # label(t69_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 147 (all A all B k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B)) # label(t41_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 148 (all A all B all C k1_enumset1(C,B,A) = k1_enumset1(A,B,C)) # label(t102_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 149 (all A k1_tarski(A) = k5_enumset1(A,A,A,A,A,A,A)) # label(t94_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 150 (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]. 6.27/6.26 151 (all A all B all C all D k2_enumset1(A,C,B,D) = k2_enumset1(A,B,C,D)) # label(t104_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 152 (all A all B all C all D k2_enumset1(C,B,A,D) = k2_enumset1(A,B,C,D)) # label(t116_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 153 $T # label(t120_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 154 (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]. 6.27/6.26 155 $T # label(t9_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 156 $T # label(t13_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 157 (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]. 6.27/6.26 158 (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]. 6.27/6.26 159 (all A all B k2_tarski(A,B) = k3_enumset1(A,A,A,A,B)) # label(t83_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 160 (all A all B all C k3_enumset1(A,A,A,B,C) = k1_enumset1(A,B,C)) # label(t78_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 161 (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]. 6.27/6.26 162 $T # label(t30_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 163 $T # label(t1_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 164 (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]. 6.27/6.26 165 (all A all B k2_enumset1(A,A,A,B) = k2_tarski(A,B)) # label(t77_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 166 (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]. 6.27/6.26 167 (all A all B all C all D k2_enumset1(A,C,D,B) = k2_enumset1(A,B,C,D)) # label(t105_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 168 $T # label(t124_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 169 (all A all B all C all D all E all F ((all G (-(G != A & B != G & G != C & D != G & G != E) <-> r2_hidden(G,F))) <-> k3_enumset1(A,B,C,D,E) = F)) # label(d3_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 170 (all A all B k2_tarski(A,B) = k1_enumset1(A,A,B)) # label(t70_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 171 $T # label(dt_k4_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 172 (all A all B all C all D (k1_enumset1(A,B,C) = D <-> (all E (r2_hidden(E,D) <-> -(E != C & E != B & E != A))))) # label(d1_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 173 (all A all B all C all D all E all F all G all H k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H))) # label(t64_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 174 (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]. 6.27/6.26 175 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k4_enumset1(A,A,B,C,D,E)) # label(t73_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 176 $T # label(t2_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 177 $T # label(t15_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 178 (all A all B all C all D k2_enumset1(A,B,C,D) = k4_enumset1(A,A,A,B,C,D)) # label(t79_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 179 $T # label(dt_k6_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 180 $T # label(t34_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 181 $T # label(t8_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 182 (all A all B all C k1_enumset1(A,B,C) = k5_enumset1(A,A,A,A,A,B,C)) # label(t89_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 183 $T # label(t25_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 184 (all A all B all C all D all E k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E))) # label(t49_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 185 (all A all B all C k1_enumset1(B,A,C) = k1_enumset1(A,B,C)) # label(t99_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 186 $T # label(t23_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 187 (all A all B all C all D k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(A,B,C,D)) # label(t45_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 188 (all A k1_tarski(A) = k4_enumset1(A,A,A,A,A,A)) # label(t91_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 189 (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]. 6.27/6.26 190 $T # label(t4_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 191 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(A,B,D,C)) # label(t103_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 192 (all A all B all C all D all E all F all G k6_enumset1(A,A,B,C,D,E,F,G) = k5_enumset1(A,B,C,D,E,F,G)) # label(t75_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 193 $T # label(t12_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 194 $T # label(t122_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 195 $T # label(t31_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 196 (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]. 6.27/6.26 197 (all A all B all C all D k2_enumset1(A,B,C,D) = k2_enumset1(C,B,D,A)) # label(t117_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 198 (all A all B all C all D all E k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E)) = k3_enumset1(A,B,C,D,E)) # label(t47_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 199 (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]. 6.27/6.26 200 (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]. 6.27/6.26 201 (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]. 6.27/6.26 202 $T # label(t40_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 203 $T # label(t114_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 204 $T # label(t106_enumset1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 205 (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]. 6.27/6.26 206 (all A all B all C all D (k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B) -> A = k1_xboole_0 | k1_xboole_0 = B | B = D & C = A)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 207 (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]. 6.27/6.26 208 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 | k1_tarski(A) = k4_xboole_0(k1_tarski(A),B))) # label(t69_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 209 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 210 (all A all B k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 211 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 212 (all A all B all C all D k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D))) = k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 213 (all A all B -((all C -(B != C & r2_hidden(C,A))) & k1_xboole_0 != A & A != k1_tarski(B))) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 214 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 215 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 216 (all A all B (A = k1_tarski(B) | k1_xboole_0 = A <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 217 (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]. 6.27/6.26 218 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 219 (all A all B all C -((all D all E k4_tarski(D,E) != A) & r2_hidden(A,k2_zfmisc_1(B,C)))) # label(t102_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 220 (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]. 6.27/6.26 221 (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]. 6.27/6.26 222 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 223 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 224 (all A k3_tarski(k1_zfmisc_1(A)) = A) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 225 (all A all B (k2_zfmisc_1(B,B) = k2_zfmisc_1(A,A) -> A = B)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 226 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 227 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 228 (all A all B all C -(k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_tarski(B) != k4_xboole_0(k2_tarski(A,B),C) & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(A) & k1_xboole_0 != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 229 (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]. 6.27/6.26 230 (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]. 6.27/6.26 231 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 232 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> C = B)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 233 (all A all B all C -(-r2_hidden(A,B) & -r2_hidden(C,B) & -r1_xboole_0(k2_tarski(A,C),B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 234 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 235 (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]. 6.27/6.26 236 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 237 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 238 (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]. 6.27/6.26 239 (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]. 6.27/6.26 240 (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]. 6.27/6.26 241 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 242 (all A all B all C -(r1_tarski(k1_tarski(A),k2_tarski(B,C)) & C != A & A != B)) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 243 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <-> r2_hidden(A,C) & r2_hidden(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 244 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> A = B)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 245 (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]. 6.27/6.26 246 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(A != k1_xboole_0 & A != k2_tarski(B,C) & A != k1_tarski(C) & A != k1_tarski(B)))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 247 (all A all B k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 248 (all A all B all C (k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) & k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 249 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 250 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 251 (all A all B all C -(B != C & B != k1_xboole_0 & k1_xboole_0 != C & k1_tarski(A) = k2_xboole_0(B,C))) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.26 252 (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]. 6.27/6.26 253 (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]. 6.27/6.27 254 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 255 (all A all B k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k3_xboole_0(A,B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 256 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) & (all C -((all D all E C != k4_tarski(D,E)) & r2_hidden(C,A))) -> A = B)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 257 (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]. 6.27/6.27 258 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 259 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 260 (all A all B all C -(-r1_tarski(B,C) & (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C))) & k1_xboole_0 != A)) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 261 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 262 (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]. 6.27/6.27 263 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))) <-> r2_hidden(A,C) & B = D)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 264 (all A all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(A,C) & r1_tarski(B,D) | k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 265 (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]. 6.27/6.27 266 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 <-> r2_hidden(A,B))) # label(t68_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 267 (all A A = k3_tarski(k1_tarski(A))) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 268 (all A all B all C all D all E -((all F all G -(k4_tarski(F,G) = A & r2_hidden(G,k3_xboole_0(C,E)) & r2_hidden(F,k3_xboole_0(B,D)))) & r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,C),k2_zfmisc_1(D,E))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 269 (all A all B all C all D -(C != A & A != D & k2_tarski(C,D) = k2_tarski(A,B))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 270 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 271 (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]. 6.27/6.27 272 (all A all B all C -(-(k1_xboole_0 = C & k1_tarski(A) = B) & -(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_tarski(A) = B & C = k1_tarski(A)) & k2_xboole_0(B,C) = k1_tarski(A))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 273 (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]. 6.27/6.27 274 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 275 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 276 (all A all B ((all C all D (r2_hidden(k4_tarski(C,D),A) -> r2_hidden(k4_tarski(C,D),B))) & (all C -(r2_hidden(C,A) & (all D all E C != k4_tarski(D,E)))) -> r1_tarski(A,B))) # label(t111_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 277 (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]. 6.27/6.27 278 (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]. 6.27/6.27 279 (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]. 6.27/6.27 280 (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]. 6.27/6.27 281 (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]. 6.27/6.27 282 (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]. 6.27/6.27 283 (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]. 6.27/6.27 284 (all A all B (k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 285 (all A all B (B != A -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 286 (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]. 6.27/6.27 287 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 288 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) & r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 289 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(k2_tarski(B,C) != A & A != k1_tarski(C) & A != k1_tarski(B) & k1_xboole_0 != A))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 290 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 291 (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]. 6.27/6.27 292 (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]. 6.27/6.27 293 (all A all B (k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A) -> k1_xboole_0 = B | A = B | k1_xboole_0 = A)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 294 (all A all B all C all D (D = B & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),k1_tarski(D))))) # label(t34_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 295 (all A all B all C (k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_tarski(A,B),k4_tarski(A,C)) & k2_tarski(k4_tarski(A,C),k4_tarski(B,C)) = k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 296 (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]. 6.27/6.27 297 (all A all B (r1_tarski(A,k2_zfmisc_1(B,A)) | r1_tarski(A,k2_zfmisc_1(A,B)) -> k1_xboole_0 = A)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 298 (all A all B all C (-r2_hidden(B,C) & -r2_hidden(A,C) <-> k2_tarski(A,B) = k4_xboole_0(k2_tarski(A,B),C))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 299 (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]. 6.27/6.27 300 (all A all B (k1_tarski(B) = k3_xboole_0(A,k1_tarski(B)) -> r2_hidden(B,A))) # label(t51_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 301 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 302 (all A all B (k4_xboole_0(A,k1_tarski(B)) = A <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 303 (all A all B all C (k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) -> r2_hidden(A,C))) # label(t63_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 304 (all A all B all C all D (r1_xboole_0(A,B) | r1_xboole_0(C,D) -> r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t127_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 305 (all A all B all C all D -(A != C & A != D & r1_tarski(k2_tarski(A,B),k2_tarski(C,D)))) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 306 (all A all B (k1_zfmisc_1(A) = B <-> (all C (r1_tarski(C,A) <-> r2_hidden(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 307 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & (all G all H (r2_hidden(k4_tarski(G,H),A) <-> r2_hidden(k4_tarski(G,H),D))) & r1_tarski(D,k2_zfmisc_1(E,F)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 308 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 309 (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]. 6.27/6.27 310 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 311 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 312 (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]. 6.27/6.27 313 (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]. 6.27/6.27 314 (all A all B all C (r2_hidden(A,B) -> r2_hidden(C,B) & A != C | k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 315 (all A all B all C all D k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 316 (all A all B all C (r2_hidden(A,B) & A != C <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 317 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 318 (all A all B -(k1_xboole_0 = k4_xboole_0(A,k1_tarski(B)) & A != k1_xboole_0 & A != k1_tarski(B))) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 319 (all A all B (k1_xboole_0 = k4_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t21_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 320 (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]. 6.27/6.27 321 (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]. 6.27/6.27 322 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 323 (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]. 6.27/6.27 324 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 325 (all A all B (A != B <-> k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 326 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 327 (all A all B all C all D -(r2_hidden(D,A) & (all E all F -(r2_hidden(E,B) & D = k4_tarski(E,F) & r2_hidden(F,C))) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 328 (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]. 6.27/6.27 329 (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]. 6.27/6.27 330 (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]. 6.27/6.27 331 (all A exists B ((all C -(-r2_tarski(C,B) & -r2_hidden(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & (all C all D (r1_tarski(D,C) & r2_hidden(C,B) -> r2_hidden(D,B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 332 (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]. 6.27/6.27 333 (all A all B all C all D ((all E all F (r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) <-> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(C,D)))) -> k2_zfmisc_1(C,D) = k2_zfmisc_1(A,B))) # label(t108_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 334 (all A all B all C ((B = A | r2_hidden(B,C)) & -r2_hidden(A,C) <-> k1_tarski(A) = k4_xboole_0(k2_tarski(A,B),C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 335 (all A all B all C (k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t120_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 336 (all A all B k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B)) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 337 (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]. 6.27/6.27 338 (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]. 6.27/6.27 339 (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]. 6.27/6.27 340 (all A k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A))) # label(t30_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 341 (all A all B (A != k1_xboole_0 -> k1_xboole_0 != k2_zfmisc_1(k1_tarski(B),A) & k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 342 (all A all B all C all D (r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <-> A = C & r2_hidden(B,D))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 343 (all A all B k1_xboole_0 != k2_xboole_0(k1_tarski(A),B)) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 344 (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]. 6.27/6.27 345 (all A all B -(A = B & r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 346 (all A all B all C all D (k4_tarski(C,D) = k4_tarski(A,B) -> A = C & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 347 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 348 (all A all B all C (k2_zfmisc_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & k4_tarski(E,F) = D & r2_hidden(F,B))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 349 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 350 (all A all B (k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 351 (all A all B (r2_hidden(A,B) -> B = k2_xboole_0(k1_tarski(A),B))) # label(t46_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 352 (all A all B (k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B)) -> r3_xboole_0(A,B))) # label(t82_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 353 (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]. 6.27/6.27 354 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 355 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (all C (m2_subset_1(C,A,B) -> m1_subset_1(C,A))))) # label(dt_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 356 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k5_subset_1(A,C,B))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 357 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 358 (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]. 6.27/6.27 359 (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]. 6.27/6.27 360 (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]. 6.27/6.27 361 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_xboole_0(B,C) = k7_subset_1(A,B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 362 (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]. 6.27/6.27 363 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r1_tarski(B,C) & r1_xboole_0(D,C) -> r1_tarski(B,k3_subset_1(A,D))))))))) # label(t47_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 364 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 365 (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]. 6.27/6.27 366 (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]. 6.27/6.27 367 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 368 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 369 (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]. 6.27/6.27 370 (all A (A != k1_xboole_0 -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 371 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) | r2_hidden(E,D) <-> r2_hidden(E,B)))) -> B = k4_subset_1(A,C,D)))))))) # label(t15_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 372 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,k3_subset_1(A,C)) <-> r1_tarski(B,C)))))) # label(t44_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 373 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 374 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 375 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f3_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f2_s4_subset_1)))) -> f2_s4_subset_1 = f3_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 376 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r2_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 377 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 378 (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]. 6.27/6.27 379 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 380 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,D) & r2_hidden(E,C)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 381 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k7_subset_1(A,B,C)) = k4_subset_1(A,k5_subset_1(A,B,C),k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C))))))) # label(t34_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 382 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),C) = k3_subset_1(A,k6_subset_1(A,B,C)))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 383 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k4_xboole_0(B,C) = k6_subset_1(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 384 (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]. 6.27/6.27 385 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,C) & -r2_hidden(E,D) <-> r2_hidden(E,B)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 386 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (A != k1_xboole_0 -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 387 (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]. 6.27/6.27 388 (all A k1_xboole_0 = k1_subset_1(A)) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 389 (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]. 6.27/6.27 390 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,C) <-> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B))))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 391 (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]. 6.27/6.27 392 (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]. 6.27/6.27 393 (all A all B ((v1_xboole_0(A) -> (m1_subset_1(B,A) <-> v1_xboole_0(B))) & (-v1_xboole_0(A) -> (m1_subset_1(B,A) <-> r2_hidden(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 394 (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]. 6.27/6.27 395 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,B),B) <-> k2_subset_1(A) = B))) # label(t39_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 396 (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) -> (all H (m1_subset_1(H,A) -> (k1_xboole_0 != A -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 397 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k5_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 398 (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]. 6.27/6.27 399 (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]. 6.27/6.27 400 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 401 (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]. 6.27/6.27 402 (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]. 6.27/6.27 403 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 404 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,B) = B)) # label(idempotence_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 405 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 406 (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]. 6.27/6.27 407 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> -(r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = k3_subset_1(A,C)))))) # label(t53_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 408 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k5_subset_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 409 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> -(k1_xboole_0 != B & (all C (m1_subset_1(C,A) -> -r2_hidden(C,B)))))) # label(t10_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 410 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 411 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = k4_xboole_0(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 412 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(B) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 413 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 414 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 415 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 416 (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]. 6.27/6.27 417 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 418 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,C) & r2_hidden(B,k3_subset_1(A,C))))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 419 (exists A ((all B (m1_subset_1(B,f1_s3_subset_1) -> (r2_hidden(B,A) <-> p1_s3_subset_1(B)))) & m1_subset_1(A,k1_zfmisc_1(f1_s3_subset_1)))) # label(s3_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 420 (all A k3_subset_1(A,k2_subset_1(A)) = k1_subset_1(A)) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 421 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 422 (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]. 6.27/6.27 423 (all A (v1_xboole_0(k1_subset_1(A)) & m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 424 (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]. 6.27/6.27 425 (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]. 6.27/6.27 426 (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]. 6.27/6.27 427 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 428 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(A) -> (exists C m2_subset_1(C,A,B)))) # label(existence_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 429 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 430 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 431 (exists A ((all B (r2_hidden(B,A) <-> p1_s1_subset_1(B) & r2_hidden(B,f1_s1_subset_1))) & m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 432 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 433 (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]. 6.27/6.27 434 (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]. 6.27/6.27 435 (all A k2_subset_1(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 436 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 437 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> k3_subset_1(A,C) = B))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 438 (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]. 6.27/6.27 439 (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)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 440 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,B,k3_subset_1(A,C)) = k6_subset_1(A,B,C))))) # label(t32_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 441 (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]. 6.27/6.27 442 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (r1_subset_1(A,B) <-> r1_xboole_0(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 443 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 444 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 445 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = C))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 446 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,k3_subset_1(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 447 (all A (-$T -> (all B (m1_subset_1(B,A) -> k8_subset_1(A) = B)))) # label(d6_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 448 (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]. 6.27/6.27 449 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 450 (all A exists B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 451 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 452 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 453 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A))))))))))) # label(t58_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 454 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) <-> r1_xboole_0(B,C)))))) # label(t43_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 455 (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]. 6.27/6.27 456 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (k1_xboole_0 != A -> m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A))))))))) # label(t57_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 457 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 458 (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)))) -> k3_subset_1(A,C) = B))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 459 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 460 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (k1_subset_1(A) = B <-> r1_tarski(B,k3_subset_1(A,B))))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 461 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 462 (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]. 6.27/6.27 463 (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]. 6.27/6.27 464 (all A all B ((all C (r2_hidden(C,A) -> r1_tarski(B,C))) -> r1_tarski(B,k1_setfam_1(A)) | A = k1_xboole_0)) # label(t6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 465 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> (r2_hidden(B,k8_setfam_1(A,C)) <-> (all D (r2_hidden(D,C) -> r2_hidden(B,D))))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 466 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 467 (all A (-v1_xboole_0(A) & v1_setfam_1(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 468 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 469 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> B = C))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 470 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 471 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 472 (all A all B all C (C = k2_setfam_1(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & D = k2_xboole_0(E,F))))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 473 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),C) <-> r1_tarski(B,k7_setfam_1(A,C))))))) # label(t52_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 474 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 475 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 476 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 477 (all A all B all C (r1_tarski(A,C) & r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 478 (all A all B all C (r1_setfam_1(C,k2_tarski(A,B)) -> (all D -(r2_hidden(D,C) & -r1_tarski(D,A) & -r1_tarski(D,B))))) # label(t25_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 479 (all A all B all C ((all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) & r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 480 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(k1_xboole_0 != B & k7_setfam_1(A,B) = k1_xboole_0))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 481 (all A all B all C (k3_setfam_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k3_xboole_0(E,F) & r2_hidden(E,A))))))) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 482 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_xboole_0 -> A = k8_setfam_1(A,B)) & (k1_xboole_0 != B -> k8_setfam_1(A,B) = k6_setfam_1(A,B)))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 483 (all A all B r1_tarski(k1_setfam_1(k4_setfam_1(A,B)),k4_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t41_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 484 (all A (-r2_hidden(k1_xboole_0,A) <-> v1_setfam_1(A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 485 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 486 (all A all B -(B != k1_xboole_0 & -r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & k1_xboole_0 != A)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 487 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 488 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) <-> r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B))))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 489 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 490 (all A all B (r2_hidden(A,B) -> r1_tarski(k1_setfam_1(B),A))) # label(t4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 491 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 492 (all A all B -(k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 493 (all A all B (r2_setfam_1(B,A) -> k1_xboole_0 = A | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)))) # label(t19_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 494 (all A all B ((A = k1_xboole_0 -> (B = k1_xboole_0 <-> k1_setfam_1(A) = B)) & (A != k1_xboole_0 -> ((all C ((all D (r2_hidden(D,A) -> r2_hidden(C,D))) <-> r2_hidden(C,B))) <-> B = k1_setfam_1(A))))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 495 (all A all B (B != k1_xboole_0 -> k2_xboole_0(A,k1_setfam_1(B)) = k1_setfam_1(k2_setfam_1(k1_tarski(A),B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 496 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(k3_subset_1(A,D),B))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 497 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 498 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 499 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 500 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 501 (all A all B (B != k1_xboole_0 -> k1_setfam_1(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k3_tarski(B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 502 (all A all B (v1_setfam_1(B) & v1_setfam_1(A) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 503 (all A (-v2_setfam_1(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,A))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 504 (all A all B all C ((all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k4_xboole_0(E,F) & r2_hidden(E,A))))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 505 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)) = k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 506 (all A all B (k1_xboole_0 != B -> k4_xboole_0(A,k1_setfam_1(B)) = k3_tarski(k4_setfam_1(k1_tarski(A),B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 507 (all A all B all C (r2_hidden(C,A) & r1_tarski(k3_tarski(A),B) -> r1_tarski(C,B))) # label(t56_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 508 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 509 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 510 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(B) = k5_setfam_1(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 511 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 512 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 513 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 514 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 515 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 516 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 517 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,C) = k7_setfam_1(A,B) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 518 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 519 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 520 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k6_subset_1(A,k2_subset_1(A),k5_setfam_1(A,B)) = k6_setfam_1(A,k7_setfam_1(A,B))))) # label(t47_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 521 (all A all B k3_setfam_1(A,B) = k3_setfam_1(B,A)) # label(commutativity_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 522 (all A all B ((all C -(r2_hidden(C,A) & (all D -(r2_hidden(D,B) & r1_tarski(C,D))))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 523 (all A ((all B (-v1_xboole_0(B) -> -r2_hidden(B,A))) <-> v2_setfam_1(A))) # label(d11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 524 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 525 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 526 (all A all B (v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 527 (all A (r2_hidden(k1_xboole_0,A) -> k1_xboole_0 = k1_setfam_1(A))) # label(t5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 528 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> B = k7_setfam_1(A,k7_setfam_1(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 529 (all A (r1_setfam_1(A,k1_xboole_0) -> k1_xboole_0 = A)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 530 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 531 (all A all B k3_tarski(k3_setfam_1(k1_tarski(A),B)) = k3_xboole_0(A,k3_tarski(B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.27 532 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 533 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 534 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k5_setfam_1(A,k7_setfam_1(A,B)) = k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 535 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 536 (all A all B k3_xboole_0(k3_tarski(A),k3_tarski(B)) = k3_tarski(k3_setfam_1(A,B))) # label(t39_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 537 (all A all B k1_setfam_1(k2_tarski(A,B)) = k3_xboole_0(A,B)) # label(t12_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 538 (all A all B all C (r1_setfam_1(A,B) & r1_setfam_1(B,C) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 539 (all A all B ((all C -((all D -(r2_hidden(D,A) & r1_tarski(D,C))) & r2_hidden(C,B))) <-> r2_setfam_1(A,B))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 540 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 541 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(k7_setfam_1(A,B),k7_setfam_1(A,C)) -> r1_tarski(B,C)))))) # label(t51_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 542 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 543 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r1_tarski(B,C) -> r1_tarski(k8_setfam_1(A,C),k8_setfam_1(A,B))))))) # label(t59_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 544 (all A all B k2_setfam_1(A,B) = k2_setfam_1(B,A)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 545 (all A all B all C (r1_xboole_0(A,C) & r2_hidden(A,B) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 546 (all A k1_setfam_1(k1_tarski(A)) = A) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 547 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 548 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 549 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k6_setfam_1(A,B) = k1_setfam_1(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 550 (all A all B (-r1_xboole_0(A,B) -> k1_setfam_1(k3_setfam_1(A,B)) = k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)))) # label(t34_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 551 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 552 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 553 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | A = k1_xboole_0)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 554 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_tarski(A) -> k1_tarski(k1_xboole_0) = k7_setfam_1(A,B)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 555 (all A all B (r1_setfam_1(B,k1_tarski(A)) -> (all C (r2_hidden(C,B) -> r1_tarski(C,A))))) # label(t24_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 556 (all A all B (r1_setfam_1(A,B) -> r1_tarski(k3_tarski(A),k3_tarski(B)))) # label(t18_setfam_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 557 (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]. 6.27/6.28 558 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 559 (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]. 6.27/6.28 560 (all A all B all C -(m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) & r2_hidden(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 561 (all A all B all C (r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 562 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 563 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B))))))) # label(t106_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 564 (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]. 6.27/6.28 565 (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]. 6.27/6.28 566 (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]. 6.27/6.28 567 (all A k1_xboole_0 = k8_relat_1(A,k1_xboole_0)) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 568 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 569 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 570 (all A all B (v1_relat_1(B) -> k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))) = k7_relat_1(B,A))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 571 (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]. 6.27/6.28 572 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 573 (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]. 6.27/6.28 574 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 575 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> A = k1_xboole_0))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 576 (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]. 6.27/6.28 577 (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]. 6.27/6.28 578 (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]. 6.27/6.28 579 (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]. 6.27/6.28 580 (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]. 6.27/6.28 581 (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]. 6.27/6.28 582 (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]. 6.27/6.28 583 (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]. 6.27/6.28 584 (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]. 6.27/6.28 585 (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]. 6.27/6.28 586 (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]. 6.27/6.28 587 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 588 (all A all B all C all D (v1_relat_1(D) -> (r2_hidden(k4_tarski(A,B),k5_relat_1(k6_relat_1(C),D)) <-> r2_hidden(A,C) & r2_hidden(k4_tarski(A,B),D)))) # label(t74_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 589 (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]. 6.27/6.28 590 (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]. 6.27/6.28 591 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 592 (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]. 6.27/6.28 593 (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]. 6.27/6.28 594 (all A all B (v1_relat_1(B) -> k3_xboole_0(k2_relat_1(B),A) = k2_relat_1(k8_relat_1(A,B)))) # label(t119_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 595 (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]. 6.27/6.28 596 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k3_relat_1(A),k3_relat_1(B)))))) # label(t33_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 597 (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]. 6.27/6.28 598 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t107_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 599 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t26_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 600 (all A (k2_relat_1(k6_relat_1(A)) = A & k1_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 601 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 602 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 603 (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]. 6.27/6.28 604 (all A k7_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 605 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k7_relat_1(A,k1_relat_1(k7_relat_1(B,k1_relat_1(A)))) = k7_relat_1(A,k1_relat_1(B)))))) # label(t189_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 606 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 607 (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]. 6.27/6.28 608 (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]. 6.27/6.28 609 (all A all B (v3_relat_1(A) & v1_relat_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v3_relat_1(k7_relat_1(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 610 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,k1_relat_1(C)) & r2_hidden(A,B)))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 611 (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]. 6.27/6.28 612 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(B,k6_relat_1(A)),B) & r1_tarski(k5_relat_1(k6_relat_1(A),B),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 613 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k5_relat_1(B,k6_relat_1(A)) = B))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 614 (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]. 6.27/6.28 615 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 616 (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]. 6.27/6.28 617 (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]. 6.27/6.28 618 (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]. 6.27/6.28 619 (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]. 6.27/6.28 620 (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]. 6.27/6.28 621 (all A (v1_relat_1(A) -> k2_relat_1(A) = k9_relat_1(A,k1_relat_1(A)))) # label(t146_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 622 (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]. 6.27/6.28 623 (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]. 6.27/6.28 624 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) <-> k1_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 625 (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]. 6.27/6.28 626 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 627 (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]. 6.27/6.28 628 (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]. 6.27/6.28 629 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k4_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_relat_1(A),k4_relat_1(B)))))) # label(t40_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 630 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 631 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 632 (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]. 6.27/6.28 633 (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]. 6.27/6.28 634 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 635 (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]. 6.27/6.28 636 (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]. 6.27/6.28 637 (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]. 6.27/6.28 638 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 639 (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]. 6.27/6.28 640 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_relat_1(k5_relat_1(A,B)) = k9_relat_1(B,k2_relat_1(A)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 641 (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]. 6.27/6.28 642 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (C = k5_relat_1(A,B) <-> (all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 643 (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]. 6.27/6.28 644 (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]. 6.27/6.28 645 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 646 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 647 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k7_relat_1(k5_relat_1(B,C),A) = k5_relat_1(k7_relat_1(B,A),C))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 648 (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]. 6.27/6.28 649 (all A all B (v1_relat_1(B) -> -(-v3_relat_1(k7_relat_1(B,A)) & v3_relat_1(B)))) # label(t190_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 650 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 651 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 652 (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]. 6.27/6.28 653 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 654 (all A (v1_relat_1(A) -> (all B all C (k10_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 655 (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]. 6.27/6.28 656 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & r1_tarski(C,D) -> k7_relat_1(B,C) = k7_relat_1(A,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 657 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k3_xboole_0(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 658 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(A,k5_relat_1(B,C)) = k5_relat_1(k5_relat_1(A,B),C))))))) # label(t55_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 659 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k8_relat_1(A,k8_relat_1(A,B)))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 660 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 661 (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]. 6.27/6.28 662 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,C) = k7_relat_1(A,C) & k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(A,k2_xboole_0(C,D)) = k7_relat_1(B,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 663 (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]. 6.27/6.28 664 (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]. 6.27/6.28 665 (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]. 6.27/6.28 666 (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]. 6.27/6.28 667 (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]. 6.27/6.28 668 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (k8_relat_1(A,B) = C <-> (all D all E (r2_hidden(k4_tarski(D,E),B) & r2_hidden(E,A) <-> r2_hidden(k4_tarski(D,E),C)))))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 669 (all A (v1_relat_1(A) -> A = k5_relat_1(k6_relat_1(k1_relat_1(A)),A))) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 670 (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]. 6.27/6.28 671 (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]. 6.27/6.28 672 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 673 (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]. 6.27/6.28 674 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 675 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(D,C),A) <-> r2_hidden(k4_tarski(C,D),B))) <-> k4_relat_1(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 676 (all A (v1_relat_1(A) -> k2_relat_1(k4_relat_1(A)) = k1_relat_1(A) & k1_relat_1(k4_relat_1(A)) = k2_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 677 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (k1_relat_1(B) = A & r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k5_relat_1(B,D) = k6_relat_1(A) -> C = D))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 678 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 679 (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]. 6.27/6.28 680 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> B = k7_relat_1(B,A)))) # label(t97_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 681 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 682 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k1_xboole_0 = k9_relat_1(B,A)))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 683 (all A (v1_relat_1(A) -> A = k8_relat_1(k2_relat_1(A),A))) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 684 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 685 (all A (v1_relat_1(A) -> A = k4_relat_1(k4_relat_1(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 686 (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]. 6.27/6.28 687 (all A all B all C all D all E (v1_relat_1(E) -> (E = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) -> k2_relat_1(E) = k2_tarski(B,D) & k1_relat_1(E) = k2_tarski(A,C)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 688 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 689 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 690 (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]. 6.27/6.28 691 (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]. 6.27/6.28 692 (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]. 6.27/6.28 693 (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]. 6.27/6.28 694 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 695 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_relat_1(A)) = A)) # label(t98_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 696 (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]. 6.27/6.28 697 (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]. 6.27/6.28 698 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 699 (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]. 6.27/6.28 700 (all A (v1_relat_1(A) <-> (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 701 (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]. 6.27/6.28 702 (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]. 6.27/6.28 703 (all A k9_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 704 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(k2_xboole_0(A,B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 705 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 706 (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]. 6.27/6.28 707 (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]. 6.27/6.28 708 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 709 (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]. 6.27/6.28 710 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k9_relat_1(C,A),k9_relat_1(D,B))))))) # label(t158_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 711 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(C,B) & r1_tarski(k1_relat_1(C),A) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 712 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(C,A) & C = D <-> r2_hidden(k4_tarski(C,D),B))) <-> k6_relat_1(A) = B))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 713 (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]. 6.27/6.28 714 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 715 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 716 (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]. 6.27/6.28 717 (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]. 6.27/6.28 718 (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]. 6.27/6.28 719 (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]. 6.27/6.28 720 (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]. 6.27/6.28 721 (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]. 6.27/6.28 722 (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]. 6.27/6.28 723 (all A (v1_xboole_0(A) -> v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 724 (exists A (v1_relat_1(A) & (all B all C (p1_s1_relat_1(B,C) & r2_hidden(C,f2_s1_relat_1) & r2_hidden(B,f1_s1_relat_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 725 (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]. 6.27/6.28 726 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k2_relat_1(k8_relat_1(A,B))))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 727 (all A (v1_relat_1(A) -> r1_tarski(k1_relat_1(A),k3_relat_1(A)) & r1_tarski(k2_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 728 (all A all B all C (v1_relat_1(C) -> k3_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C))) # label(t135_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 729 (all A (v1_relat_1(A) -> k1_relat_1(A) = k10_relat_1(A,k2_relat_1(A)))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 730 (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]. 6.27/6.28 731 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 732 (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]. 6.27/6.28 733 (all A (v1_relat_1(A) -> k7_relat_1(A,k1_xboole_0) = k1_xboole_0)) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 734 (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]. 6.27/6.28 735 (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]. 6.27/6.28 736 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & r1_tarski(A,k2_relat_1(B)) & k10_relat_1(B,A) = k1_xboole_0))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 737 (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]. 6.27/6.28 738 (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]. 6.27/6.28 739 (all A all B (v1_xboole_0(A) & v1_relat_1(B) -> v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 740 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 741 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 742 (all A (v1_relat_1(A) -> (all B all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(k4_tarski(D,E),A) & r2_hidden(D,B))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 743 (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]. 6.27/6.28 744 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 745 (all A all B all C (v1_relat_1(C) -> k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k4_xboole_0(A,B),C))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 746 (all A (v1_relat_1(A) -> (k1_xboole_0 = k2_relat_1(A) | k1_relat_1(A) = k1_xboole_0 -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 747 (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]. 6.27/6.28 748 (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]. 6.27/6.28 749 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 750 (all A (v1_relat_1(A) -> k3_relat_1(k4_relat_1(A)) = k3_relat_1(A))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 751 (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]. 6.27/6.28 752 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 753 (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]. 6.27/6.28 754 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 755 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 756 (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]. 6.27/6.28 757 (all A (v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D ((exists E (r2_hidden(E,B) & r2_hidden(k4_tarski(E,D),A))) <-> r2_hidden(D,C))))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 758 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k2_xboole_0(A,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 759 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(A),k1_relat_1(B)) -> k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A)))))) # label(t46_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 760 (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]. 6.27/6.28 761 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k7_relat_1(B,A) = k1_xboole_0))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 762 (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]. 6.27/6.28 763 (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]. 6.27/6.28 764 (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]. 6.27/6.28 765 (all A (v1_xboole_0(A) -> v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 766 (all A all B (v1_relat_1(B) -> k10_relat_1(B,A) = k10_relat_1(B,k3_xboole_0(k2_relat_1(B),A)))) # label(t168_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 767 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 768 (all A all B (v1_relat_1(B) -> k5_relat_1(B,k6_relat_1(A)) = k8_relat_1(A,B))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 769 (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]. 6.27/6.28 770 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 771 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k8_relat_1(A,B)))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 772 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 773 (all A (v1_xboole_0(A) -> v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 774 (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]. 6.27/6.28 775 (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]. 6.27/6.28 776 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 777 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 778 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(k5_relat_1(B,C),A) = k10_relat_1(B,k10_relat_1(C,A)))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 779 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(D,B) & r2_hidden(k4_tarski(D,A),C))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 780 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 781 (all A (v1_relat_1(A) -> (all B (k1_relat_1(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 782 (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]. 6.27/6.28 783 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k2_relat_1(k7_relat_1(B,A)))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 784 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 785 (all A all B (v1_relat_1(B) -> -(k9_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k1_relat_1(B)) & k1_xboole_0 != A))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 786 (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]. 6.27/6.28 787 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 788 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(C,k9_relat_1(B,A)) = k9_relat_1(k5_relat_1(B,C),A))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 789 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 790 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k3_xboole_0(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k3_xboole_0(A,B)))))) # label(t39_relat_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 791 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B) & v2_funct_1(A)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 792 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 793 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)))) -> k5_relat_1(A,B) = C))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 794 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 795 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 796 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 797 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k5_relat_1(C,A) = k5_relat_1(B,A) & k1_relat_1(C) = k1_relat_1(B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> B = C)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 798 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (k9_relat_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & k1_funct_1(A,E) = D)))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 799 (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]. 6.27/6.28 800 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 801 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.28 802 (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]. 6.27/6.28 803 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D (r2_hidden(D,k1_relat_1(B)) & r2_hidden(C,k1_relat_1(A)) -> (D = k1_funct_1(A,C) <-> k1_funct_1(B,D) = C))) & k1_relat_1(B) = k2_relat_1(A) & k2_relat_1(B) = k1_relat_1(A) & v2_funct_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 804 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r2_hidden(A,k1_relat_1(B)) -> A = k1_funct_1(k2_funct_1(B),k1_funct_1(B,A)) & A = k1_funct_1(k5_relat_1(B,k2_funct_1(B)),A)))) # label(t56_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 805 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k9_relat_1(B,k1_tarski(A)) = k1_tarski(k1_funct_1(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 806 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((-r2_hidden(B,k1_relat_1(A)) -> (C = k1_xboole_0 <-> k1_funct_1(A,B) = C)) & (r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> r2_hidden(k4_tarski(B,C),A))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 807 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> A = k1_relat_1(B) & (all C (r2_hidden(C,A) -> C = k1_funct_1(B,C)))))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 808 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B)))) <-> v3_relat_1(A)))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 809 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) & r2_hidden(A,k1_relat_1(C)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 810 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 811 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_funct_1(A)) & v1_relat_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 812 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 813 (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]. 6.27/6.29 814 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 815 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 816 (exists A (v1_relat_1(A) & f1_s4_funct_1 = k1_relat_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> k1_funct_1(A,B) = f2_s4_funct_1(B))) & v1_funct_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 817 (all A ((all B all C all D (r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) -> D = C)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 818 (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]. 6.27/6.29 819 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A) & k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 820 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k3_xboole_0(B,C)) = k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 821 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -((all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))) & r2_hidden(B,k2_relat_1(A)))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 822 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 823 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 824 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 825 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) -> k1_funct_1(B,k1_funct_1(C,A)) = k1_funct_1(k5_relat_1(C,B),A)))))) # label(t22_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 826 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 827 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 828 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 829 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 830 (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]. 6.27/6.29 831 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 832 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & k2_relat_1(A) = k1_relat_1(B) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 833 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 834 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 835 (all A (v1_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 836 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 837 (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,C) & p1_s2_funct_1(A,B) -> C = B)) & (all A -((all B -p1_s2_funct_1(A,B)) & r2_hidden(A,f1_s2_funct_1))) -> (exists A (k1_relat_1(A) = f1_s2_funct_1 & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 838 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 839 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & k1_relat_1(A) = k1_relat_1(B) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 840 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(C,A) = B <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & k1_relat_1(B) = k3_xboole_0(k1_relat_1(C),A)))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 841 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & k1_funct_1(C,A) = B <-> r2_hidden(k4_tarski(A,B),C)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 842 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t71_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 843 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(C,B) = k1_funct_1(k5_relat_1(k6_relat_1(A),C),B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 844 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(B) & r1_tarski(k2_relat_1(C),A) & B = k5_relat_1(C,B) & v2_funct_1(B) & k1_relat_1(C) = A -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 845 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 846 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 847 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 848 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 849 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k3_xboole_0(k1_relat_1(B),A) = k1_relat_1(k5_relat_1(k6_relat_1(A),B)))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 850 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(B)))))) # label(t47_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 851 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 852 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & v2_funct_1(B) -> k5_relat_1(k2_funct_1(B),k2_funct_1(A)) = k2_funct_1(k5_relat_1(A,B))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 853 (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]. 6.27/6.29 854 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 855 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 856 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k1_relat_1(A) = k2_relat_1(B) & k5_relat_1(B,A) = k6_relat_1(k2_relat_1(A)) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 857 (all A all B -(-(A = k1_xboole_0 & B != k1_xboole_0) & (all C (v1_funct_1(C) & v1_relat_1(C) -> -(k1_relat_1(C) = B & r1_tarski(k2_relat_1(C),A)))))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 858 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A))))))) # label(t23_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 859 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C (r2_hidden(B,k1_relat_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) & r2_hidden(C,k1_relat_1(A)) -> B = C)) <-> v2_funct_1(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 860 (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]. 6.27/6.29 861 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(A) & k2_relat_1(k5_relat_1(B,A)) = k2_relat_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 862 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A))) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 863 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 864 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 865 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 866 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(k8_relat_1(A,B)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k8_relat_1(A,B)),k2_relat_1(B)))) # label(t89_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 867 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(B) = A & k1_relat_1(C) = A -> C = B))))) -> k1_xboole_0 = A)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 868 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 869 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_relat_1(C) = k1_tarski(A) & k1_tarski(A) = k2_relat_1(B) & k1_relat_1(B) = k1_relat_1(C) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 870 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k2_funct_1(A)) & k2_relat_1(k2_funct_1(A)) = k1_relat_1(A)))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 871 (all A all B (v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) <-> k10_relat_1(B,k1_tarski(A)) != k1_xboole_0))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 872 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,C) = k5_relat_1(B,D) & k1_relat_1(D) = A & k1_relat_1(C) = A -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 873 (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]. 6.27/6.29 874 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D ((r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C -> r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D) & (r2_hidden(C,k2_relat_1(A)) & k1_funct_1(B,C) = D -> r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C))) & k2_relat_1(A) = k1_relat_1(B) <-> B = k2_funct_1(A))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 875 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 876 (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]. 6.27/6.29 877 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 878 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 879 (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]. 6.27/6.29 880 (all A (v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 881 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k5_relat_1(B,D) = k5_relat_1(B,C) & k1_relat_1(D) = A & k1_relat_1(C) = A & k2_relat_1(B) = A -> C = D))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 882 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k10_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 883 (all A all B (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 884 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k10_relat_1(C,A),k10_relat_1(C,B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,B)))) # label(t158_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 885 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 886 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 887 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 888 (all A (A != k1_xboole_0 -> (all B exists C (v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = A & v1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 889 (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]. 6.27/6.29 890 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 891 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 892 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k3_xboole_0(A,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 893 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 894 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 895 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 896 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A) <-> r2_hidden(B,k1_relat_1(k5_relat_1(C,k6_relat_1(A))))))) # label(t40_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 897 (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]. 6.27/6.29 898 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(C,B) = k1_funct_1(k8_relat_1(A,C),B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 899 (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]. 6.27/6.29 900 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & (all D (r2_hidden(D,k1_relat_1(B)) <-> r2_hidden(D,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,D),A))) <-> k8_relat_1(A,C) = B))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 901 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 902 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 903 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 904 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 905 (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]. 6.27/6.29 906 (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]. 6.27/6.29 907 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k2_relat_1(A) & A = k5_relat_1(A,B) -> B = k6_relat_1(k1_relat_1(B))))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 908 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 909 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 910 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> r1_tarski(k10_relat_1(B,k9_relat_1(B,A)),A)))) # label(t152_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 911 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k7_relat_1(C,A))) -> k1_funct_1(C,B) = k1_funct_1(k7_relat_1(C,A),B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 912 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 913 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> A = k1_funct_1(B,k1_funct_1(k2_funct_1(B),A)) & A = k1_funct_1(k5_relat_1(k2_funct_1(B),B),A)))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 914 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> D = C)) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))) -> v1_funct_1(A) & v1_relat_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 915 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 916 (all A all B (r2_hidden(B,A) -> B = k1_funct_1(k6_relat_1(A),B))) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 917 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 918 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 919 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,C) = k8_relat_1(B,k8_relat_1(A,C)) & k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t97_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 920 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 921 (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]. 6.27/6.29 922 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 923 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 924 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 925 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 926 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 927 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 928 (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]. 6.27/6.29 929 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 930 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k1_tarski(k1_funct_1(B,A)) = k2_relat_1(B)))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 931 (all A all B all C (v1_relat_1(C) -> k10_relat_1(k7_relat_1(C,A),B) = k3_xboole_0(A,k10_relat_1(C,B)))) # label(t139_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 932 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k10_relat_1(k2_funct_1(B),A) = k9_relat_1(B,A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 933 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 934 (exists A (v1_relat_1(A) & (all B (r2_hidden(B,f1_s3_funct_1) -> f2_s3_funct_1(B) = k1_funct_1(A,B))) & k1_relat_1(A) = f1_s3_funct_1 & v1_funct_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 935 (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]. 6.27/6.29 936 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 937 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 938 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 939 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 940 (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]. 6.27/6.29 941 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k9_relat_1(B,k10_relat_1(B,A)) = A))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 942 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 943 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 944 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 945 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 946 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (v1_funct_1(B) & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) & v1_relat_1(B))) -> v2_funct_1(A)))) # label(t53_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 947 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_funct_1(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 948 (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]. 6.27/6.29 949 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 950 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),B) <-> r2_hidden(D,C))) <-> C = k10_relat_1(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 951 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> k2_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A) & k1_relat_1(k5_relat_1(k2_funct_1(A),A)) = k2_relat_1(A)))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 952 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 953 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 954 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) & r1_tarski(A,k1_relat_1(C)) & v2_funct_1(C) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 955 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (B = k2_relat_1(A) <-> (all C ((exists D (r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D))) <-> r2_hidden(C,B))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 956 (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]. 6.27/6.29 957 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> B = C)) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C) <-> r2_hidden(k4_tarski(B,C),A))) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 958 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 959 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 960 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 961 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) <-> (all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C)))))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 962 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(k5_relat_1(B,A)) = k1_relat_1(B) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 963 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(B,A) -> r2_hidden(k1_funct_1(C,B),k2_relat_1(k7_relat_1(C,A)))))) # label(t73_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 964 (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]. 6.27/6.29 965 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k6_relat_1(k1_relat_1(A)) = k5_relat_1(A,k2_funct_1(A)) & k5_relat_1(k2_funct_1(A),A) = k6_relat_1(k2_relat_1(A))))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 966 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 967 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) -> k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B)) = k9_relat_1(C,k2_tarski(A,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 968 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 969 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 970 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 971 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 972 (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]. 6.27/6.29 973 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 974 (all A all B (v1_relat_1(B) -> ((all C -(k10_relat_1(B,k1_tarski(C)) = k1_xboole_0 & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 975 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(B,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,B),A)))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 976 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> ((all C -(r2_hidden(C,A) & (all D -(C = k1_funct_1(B,D) & r2_hidden(D,k1_relat_1(B)))))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 977 (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]. 6.27/6.29 978 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 979 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 980 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k9_relat_1(k6_relat_1(A),B) = B)) # label(t162_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 981 (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]. 6.27/6.29 982 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 983 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 984 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 985 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 986 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 987 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r1_tarski(k5_relat_1(A,A),A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 988 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 989 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v5_relat_2(k4_relat_1(A))))) # label(t36_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 990 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 991 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(A) & v3_relat_2(B) -> v3_relat_2(k2_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k4_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 992 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(A) -> v2_relat_2(k4_xboole_0(A,B))))))) # label(t33_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 993 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 994 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 995 (all A (v1_relat_1(A) -> (v4_relat_2(A) -> v4_relat_2(k4_relat_1(A))))) # label(t40_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 996 (all A (v1_relat_1(A) -> (r2_relat_2(A,k3_relat_1(A)) <-> v2_relat_2(A)))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 997 (all A (v1_relat_1(A) -> (r1_relat_2(A,k3_relat_1(A)) <-> v1_relat_2(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 998 (all A (v1_relat_1(A) -> (r4_relat_2(A,k3_relat_1(A)) <-> v4_relat_2(A)))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 999 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k1_relat_1(k4_relat_1(A)) = k1_relat_1(A)))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1000 (all A (v1_relat_1(A) -> (v8_relat_2(A) <-> r8_relat_2(A,k3_relat_1(A))))) # label(d16_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1001 (all A (v1_relat_1(A) -> (v7_relat_2(A) -> v6_relat_2(A) & v1_relat_2(A)))) # label(t46_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1002 (all A (v1_relat_1(A) -> (r1_xboole_0(k6_relat_1(k3_relat_1(A)),A) <-> v2_relat_2(A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1003 (all A (v1_relat_1(A) -> (v8_relat_2(A) -> v8_relat_2(k4_relat_1(A))))) # label(t42_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1004 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) <-> (all C (r2_hidden(C,B) -> r2_hidden(k4_tarski(C,C),A))))))) # label(d1_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1005 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k2_xboole_0(A,B)) & v1_relat_2(k3_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1006 (all A (v1_relat_1(A) -> (v2_relat_2(A) & v8_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1007 (all A (v1_relat_1(A) -> (v2_relat_2(A) -> v2_relat_2(k4_relat_1(A))))) # label(t28_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1008 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1009 (all A (v1_relat_1(A) -> (v5_relat_2(A) <-> r5_relat_2(A,k3_relat_1(A))))) # label(d13_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1010 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1011 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> v1_relat_2(k4_relat_1(A))))) # label(t27_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1012 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1013 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1014 (all A (v1_relat_1(A) -> (v3_relat_2(A) -> v3_relat_2(k4_relat_1(A))))) # label(t34_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1015 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1016 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1017 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) -> v5_relat_2(k4_xboole_0(A,B))))))) # label(t38_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1018 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1019 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1020 (all A (v1_relat_1(A) -> (A = k4_relat_1(A) <-> v3_relat_2(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1021 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(k4_tarski(C,C),A) & r2_hidden(C,B))) <-> r2_relat_2(A,B))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1022 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A))) <-> r5_relat_2(A,B))))) # label(d5_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1023 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1024 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1025 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_relat_2(B) & v2_relat_2(A) -> v2_relat_2(k2_xboole_0(A,B)) & v2_relat_2(k3_xboole_0(A,B))))))) # label(t32_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1026 (all A (v1_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)))) # label(t24_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1027 (all A (v1_relat_1(A) -> (r3_relat_2(A,k3_relat_1(A)) <-> v3_relat_2(A)))) # label(d11_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1028 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v4_relat_2(A) -> v4_relat_2(k3_xboole_0(A,B)) & v4_relat_2(k4_xboole_0(A,B))))))) # label(t41_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1029 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1030 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1031 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r6_relat_2(A,k3_relat_1(A))))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1032 (all A all B (v1_relat_1(B) -> (r4_relat_2(B,A) <-> r5_relat_2(k4_xboole_0(B,k6_relat_1(A)),A)))) # label(t19_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1033 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(D,B) & C != D & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B))) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1034 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(A) & v8_relat_2(B) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1035 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1036 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) <-> (all C all D (r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1037 (all A (v1_relat_1(A) -> (v3_relat_2(A) & v8_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1038 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1039 (all A (v1_relat_1(A) -> (v6_relat_2(A) <-> r1_tarski(k4_xboole_0(k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A)),k6_relat_1(k3_relat_1(A))),k2_xboole_0(A,k4_relat_1(A)))))) # label(t45_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1040 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v4_relat_2(A) & v2_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1041 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1042 (all A (v1_relat_1(A) -> (all B (r7_relat_2(A,B) <-> (all C all D -(-r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) & r2_hidden(C,B))))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1043 (all A (v1_relat_1(A) -> (r1_tarski(k3_xboole_0(A,k4_relat_1(A)),k6_relat_1(k1_relat_1(A))) <-> v4_relat_2(A)))) # label(t39_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1044 (all A (v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1045 (all A (v1_relat_1(A) -> (r1_tarski(k6_relat_1(k3_relat_1(A)),A) <-> v1_relat_2(A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1046 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> r7_relat_2(A,k3_relat_1(A))))) # label(d15_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1047 (all A (v1_relat_1(A) -> (v7_relat_2(A) <-> k2_xboole_0(A,k4_relat_1(A)) = k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))))) # label(t47_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1048 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(A) & v5_relat_2(B) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.27/6.29 1049 (all A all B (v1_relat_1(B) -> (r5_relat_2(B,A) -> r4_relat_2(k2_xboole_0(B,k6_relat_1(A)),A)))) # label(t20_relat_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1050 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> (r1_ordinal1(A,B) <-> r1_tarski(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1051 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1052 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1053 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1054 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1055 (all A (v3_ordinal1(A) -> v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1056 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) <-> v5_ordinal1(A)))) # label(d7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1057 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1058 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1059 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> A = B | r2_hidden(A,B))) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1060 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1061 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> B = A)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1062 (all A all B (v3_ordinal1(B) -> -(r1_tarski(A,B) & (all C (v3_ordinal1(C) -> -(r2_hidden(C,A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D))))))) & k1_xboole_0 != A))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1063 (all A -(all B (v3_ordinal1(B) <-> r2_hidden(B,A)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1064 (all A exists B ((all C (v3_ordinal1(C) -> (-r2_hidden(C,A) -> r1_ordinal1(B,C)))) & -r2_hidden(B,A) & v3_ordinal1(B))) # label(t39_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1065 (all A ((all B (r2_hidden(B,A) -> v3_ordinal1(B) & r1_tarski(B,A))) -> v3_ordinal1(A))) # label(t31_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1066 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r1_ordinal1(k1_ordinal1(A),B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1067 (all A all B all C all D -(r2_hidden(D,A) & r2_hidden(C,D) & r2_hidden(B,C) & r2_hidden(A,B))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1068 (all A all B all C all D all E -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(E,A) & r2_hidden(D,E))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1069 (all A all B (m1_ordinal1(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1070 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1071 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1072 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & -v1_xboole_0(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1073 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A (v3_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))) & p1_s1_ordinal1(A))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1074 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1075 (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]. 6.36/6.30 1076 (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]. 6.36/6.30 1077 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1078 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> r1_ordinal1(A,B) | r1_ordinal1(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1079 (all A (v3_ordinal1(A) <-> v1_ordinal1(A) & v2_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1080 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1081 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1082 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v1_relat_1(k3_tarski(A)) & v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1083 (exists A (v1_relat_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1084 (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]. 6.36/6.30 1085 (all A all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1086 (all A (v1_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r1_tarski(A,B) & r2_hidden(B,C) -> r2_hidden(A,C)))))))) # label(t22_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1087 (exists A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1088 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r3_xboole_0(B,C))) <-> v6_ordinal1(A))) # label(d9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1089 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1090 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1091 (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]. 6.36/6.30 1092 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1093 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1094 (all A (v3_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A)))) <-> v4_ordinal1(A)))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1095 (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]. 6.36/6.30 1096 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1097 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_xboole_0(A,B) & B != A & -r2_xboole_0(B,A)))))) # label(t50_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1098 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1099 (all A (v3_ordinal1(A) -> v2_ordinal1(A) & v1_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1100 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v3_ordinal1(B) & v5_ordinal1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1101 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1102 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1103 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1104 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1105 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1106 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1107 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1108 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r1_ordinal1(A,B) | r2_hidden(B,A))))) # label(t26_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1109 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(B,A) & -r2_hidden(B,C) & C != B & -r2_hidden(C,B) & r2_hidden(C,A))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1110 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1111 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1112 (all A (v1_xboole_0(A) -> v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1113 (all A all B all C -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,A))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1114 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(A,B) & A != B & -r2_hidden(B,A)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1115 (all A all B all C all D all E all F -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,A) & r2_hidden(C,D))) # label(t6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1116 (all A (v3_ordinal1(A) -> -((all B (v3_ordinal1(B) -> k1_ordinal1(B) != A)) & -v4_ordinal1(A)) & -((exists B (v3_ordinal1(B) & k1_ordinal1(B) = A)) & v4_ordinal1(A)))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1117 (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]. 6.36/6.30 1118 (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]. 6.36/6.30 1119 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1120 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (all B (v3_ordinal1(B) -> (all C (v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,f1_s4_ordinal1) & C = k2_ordinal1(A,B) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v1_funct_1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1121 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1122 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1123 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1124 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1125 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v2_ordinal1(k1_relat_1(A)) & v3_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1126 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1127 (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]. 6.36/6.30 1128 k1_relat_1(f3_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & B = k2_ordinal1(f3_s3_ordinal1,A) -> f2_s3_ordinal1(B) = k1_funct_1(f3_s3_ordinal1,A)))))) & k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> f2_s3_ordinal1(B) = k1_funct_1(f4_s3_ordinal1,A)))))) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1129 (all A (A = k3_tarski(A) <-> v4_ordinal1(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1130 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1131 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> f3_s5_ordinal1(k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & B = f3_s5_ordinal1(C))) <-> f2_s5_ordinal1(A) = B)))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f2_s5_ordinal1(A) = k1_funct_1(f1_s5_ordinal1,A)))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1132 (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]. 6.36/6.30 1133 (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]. 6.36/6.30 1134 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1135 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1136 (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]. 6.36/6.30 1137 (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]. 6.36/6.30 1138 (all A (-v1_xboole_0(A) -> k6_relat_1(A) != k1_xboole_0)) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1139 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1140 (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]. 6.36/6.30 1141 (all A all B all C (m1_relset_1(C,A,B) <-> m2_relset_1(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1142 (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]. 6.36/6.30 1143 (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]. 6.36/6.30 1144 (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]. 6.36/6.30 1145 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1146 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1147 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k4_xboole_0(C,D) = k3_relset_1(A,B,C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1148 (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]. 6.36/6.30 1149 (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]. 6.36/6.30 1150 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1151 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> C = k1_xboole_0))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1152 (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]. 6.36/6.30 1153 (all A all B all C (m1_relset_1(C,A,B) -> C = k6_relset_1(A,B,k6_relset_1(A,B,C)))) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1154 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1155 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(C,f2_s1_relset_1) & p1_s1_relset_1(B,C) & r2_hidden(B,f1_s1_relset_1))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1156 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1157 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1158 (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]. 6.36/6.30 1159 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1160 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> ((exists E (r2_hidden(k4_tarski(E,D),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1161 (all A all B all C all D (m2_relset_1(D,A,B) -> -((all E all F -(C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B))) & r2_hidden(C,D)))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1162 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1163 (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]. 6.36/6.30 1164 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1165 (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]. 6.36/6.30 1166 (all A all B all C (m1_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k1_relat_1(C))) # label(redefinition_k4_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1167 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1168 (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]. 6.36/6.30 1169 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,C) = k4_relat_1(C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1170 (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]. 6.36/6.30 1171 (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]. 6.36/6.30 1172 (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]. 6.36/6.30 1173 (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]. 6.36/6.30 1174 (all A all B all C (m2_relset_1(C,A,B) -> (r1_tarski(k6_relat_1(B),C) -> k5_relset_1(A,B,C) = B & r1_tarski(B,k4_relset_1(A,B,C))))) # label(t32_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1175 (all A all B all C (m1_relset_1(C,A,B) <-> r1_tarski(C,k2_zfmisc_1(A,B)))) # label(d1_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1176 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(k6_relat_1(A),B) & B = k5_relat_1(B,k6_relat_1(A)))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1177 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D))) <-> r2_hidden(E,k11_relset_1(A,C,D,B))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1178 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1179 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C)))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1180 (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]. 6.36/6.30 1181 (all A all B all C (m1_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k2_relat_1(C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1182 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1183 (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]. 6.36/6.30 1184 (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]. 6.36/6.30 1185 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) -> (all E (m2_relset_1(E,B,C) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,C) -> ((exists H (m1_subset_1(H,B) & r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E))) <-> r2_hidden(k4_tarski(F,G),k7_relset_1(A,B,B,C,D,E))))))))))))))))) # label(t51_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1186 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C)))) & r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1187 (all A all B all C all D (m1_relset_1(C,A,B) -> k9_relat_1(C,D) = k10_relset_1(A,B,C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1188 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1189 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1190 (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]. 6.36/6.30 1191 (all A all B all C (v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> m2_relset_1(C,A,B)))) # label(t11_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1192 (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]. 6.36/6.30 1193 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1194 (all A all B all C (m2_relset_1(C,B,A) -> ((all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B))) <-> B = k4_relset_1(B,A,C)))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1195 (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]. 6.36/6.30 1196 (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]. 6.36/6.30 1197 (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]. 6.36/6.30 1198 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1199 (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]. 6.36/6.30 1200 (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]. 6.36/6.30 1201 (all A all B all C all D (m1_relset_1(D,A,B) -> k8_relat_1(C,D) = k9_relset_1(A,B,C,D))) # label(redefinition_k9_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1202 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1203 (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]. 6.36/6.30 1204 (exists A (m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1) & (all B (m1_subset_1(B,f1_s2_relset_1) -> (all C (m1_subset_1(C,f2_s2_relset_1) -> (p1_s2_relset_1(B,C) <-> r2_hidden(k4_tarski(B,C),A)))))))) # label(s2_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1205 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1206 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> r1_tarski(B,k5_relset_1(B,A,C)) & B = k4_relset_1(B,A,C)))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1207 (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]. 6.36/6.30 1208 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1209 (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]. 6.36/6.30 1210 (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]. 6.36/6.30 1211 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k1_relset_1(A,B,C,D),A,B))) # label(dt_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1212 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k10_relset_1(A,B,C,A) & k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1213 (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]. 6.36/6.30 1214 (all A all B all C (m2_relset_1(C,A,B) -> k5_relset_1(A,B,C) = k4_relset_1(B,A,k6_relset_1(A,B,C)) & k4_relset_1(A,B,C) = k5_relset_1(B,A,k6_relset_1(A,B,C)))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1215 (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]. 6.36/6.30 1216 (all A all B all C all D (m1_relset_1(C,A,B) -> k7_relat_1(C,D) = k8_relset_1(A,B,C,D))) # label(redefinition_k8_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1217 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,A) -> (all E (m1_subset_1(E,A) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(F,E),D))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1218 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1219 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1220 (all A all B all C (m2_relset_1(C,B,A) -> k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) = k4_relset_1(B,A,C) & k5_relset_1(B,A,C) = k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1221 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1222 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1223 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1224 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1225 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1226 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1227 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1228 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1229 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(B,C) & r1_tarski(A,C))) <-> r1_partfun1(A,B)))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1230 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1231 (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]. 6.36/6.30 1232 (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]. 6.36/6.30 1233 (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]. 6.36/6.30 1234 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1235 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(C = k1_funct_1(D,E) & r2_hidden(E,k4_relset_1(A,B,D)))))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1236 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1237 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1238 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) & k4_relset_1(A,B,D) = k4_relset_1(A,B,C) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1239 (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]. 6.36/6.30 1240 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1241 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1242 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k4_relset_1(k1_xboole_0,A,B) = k1_xboole_0 & k2_relat_1(B) = k1_xboole_0)) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1243 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> v1_funct_1(D) & m2_relset_1(D,C,B)))) # label(t30_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1244 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k3_partfun1(C,A,B),k3_partfun1(D,A,B))))))) # label(t81_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1245 (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]. 6.36/6.30 1246 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_xboole_0(A,B) = C -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,D) = k1_funct_1(A,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1247 (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]. 6.36/6.30 1248 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),C,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t43_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1249 (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]. 6.36/6.30 1250 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) -> k1_funct_1(k3_partfun1(D,B,C),A) = k1_funct_1(D,A)))) # label(t80_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1251 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> B = k1_funct_1(D,C)))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1252 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> k3_partfun1(k5_relat_1(D,E),C,B) = k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B))))))) # label(t93_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1253 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (k4_relset_1(A,k1_tarski(B),D) = k4_relset_1(A,k1_tarski(B),C) -> C = D))))) # label(t74_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1254 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1255 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1256 (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]. 6.36/6.30 1257 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (-r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_partfun1(C,D)))))) # label(t185_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1258 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1259 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1260 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> m2_relset_1(k7_relat_1(k8_relat_1(A,C),B),B,A) & v1_funct_1(k7_relat_1(k8_relat_1(A,C),B)))) # label(t47_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1261 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1262 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1263 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1264 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1265 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> m2_relset_1(k3_partfun1(A,B,C),B,C) & v1_funct_1(k3_partfun1(A,B,C)))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1266 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,k1_relat_1(D)) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1267 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1268 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1269 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v2_funct_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A)))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1270 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1271 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1272 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_partfun1 & (all B (r2_hidden(B,f1_s1_partfun1) -> (p1_s1_partfun1(B) -> f2_s1_partfun1(B) = k1_funct_1(A,B)) & (-p1_s1_partfun1(B) -> f3_s1_partfun1(B) = k1_funct_1(A,B)))) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1273 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1274 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1275 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1276 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)) = A)) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1277 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1278 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> m2_relset_1(D,A,C) & v1_funct_1(D)))) # label(t29_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1279 (all A all B all C all D all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_tarski(B,D) & r1_tarski(A,C) -> m2_relset_1(E,C,D) & v1_funct_1(E)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1280 (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]. 6.36/6.30 1281 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1282 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1283 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1284 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1285 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(k4_relset_1(A,B,D),C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1286 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> k2_partfun1(A,B,k3_partfun1(D,A,B),C) = k3_partfun1(D,k3_xboole_0(A,C),B))) # label(t96_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1287 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k3_partfun1(A,B,C) = k7_relat_1(k8_relat_1(C,A),B)))) # label(d3_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1288 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1289 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1290 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A ((all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> k1_funct_1(A,B) = f3_s3_partfun1(B))) & (all B (p1_s3_partfun1(B) & r2_hidden(B,f1_s3_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & v1_funct_1(A))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1291 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1292 (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]. 6.36/6.30 1293 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1294 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1295 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1296 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1297 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1298 (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]. 6.36/6.30 1299 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0))) # label(t176_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1300 (all A k6_partfun1(A) = k6_relat_1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1301 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1302 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1303 (all A exists B (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v3_relat_2(B) & v1_relat_2(B) & v1_relat_1(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1304 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1305 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & v1_funct_1(F) & m1_relset_1(E,A,B) & v1_funct_1(E) -> m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) & v1_funct_1(k1_partfun1(A,B,C,D,E,F)))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1306 (all A (v8_relat_2(A) & v3_relat_2(A) & v1_relat_1(A) -> v1_relat_2(A) & v1_relat_1(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1307 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1308 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1309 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((exists C (v1_funct_1(C) & C = k2_xboole_0(A,B) & v1_relat_1(C))) <-> r1_partfun1(A,B)))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1310 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1311 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> (k1_xboole_0 != A -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.30 1312 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & r1_partfun1(C,D) & (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(C,E) & r1_partfun1(D,E) & v1_partfun1(E,A,B))))))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1313 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t57_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1314 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1315 (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]. 6.36/6.31 1316 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C))) <-> r1_partfun1(A,B))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1317 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)) & r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1318 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1319 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1320 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1321 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v2_funct_1(B))) # label(t59_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1322 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1323 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(D,C) & r1_partfun1(C,E) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1324 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_xboole_0) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1325 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1326 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1327 (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]. 6.36/6.31 1328 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1329 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1330 (all A all B (v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A,B) -> A = k1_xboole_0)) # label(t114_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1331 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1332 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1333 (all A all B all C (m1_subset_1(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t121_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1334 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1335 (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]. 6.36/6.31 1336 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1337 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1338 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) & k1_xboole_0 = B -> A = k1_xboole_0))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1339 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),B) & r1_tarski(k1_relat_1(C),A) -> C = k3_partfun1(C,A,B)))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1340 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> f4_s5_partfun1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (r2_hidden(B,f1_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(C,f2_s5_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1341 (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]. 6.36/6.31 1342 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(B),A) -> v1_funct_1(B) & m2_relset_1(B,k1_relat_1(B),A)))) # label(t25_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1343 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1344 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1345 (all A (m2_relset_1(k6_partfun1(A),A,A) & v1_partfun1(k6_partfun1(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1346 (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]. 6.36/6.31 1347 (all A all B all C (C = k4_partfun1(A,B) <-> (all D ((exists E (v1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & r1_tarski(k1_relat_1(E),A) & E = D & v1_funct_1(E))) <-> r2_hidden(D,C))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1348 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,k1_xboole_0) -> C = D)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1349 (all A all B all C all D all E all F (r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1350 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1351 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k1_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1352 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1353 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1354 (all A (v1_relat_1(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1355 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) & (all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1356 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1357 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1358 (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]. 6.36/6.31 1359 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(D,k4_relset_1(A,B,C)) & r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) -> E = D))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1360 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1361 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (v1_relat_1(C) & v1_funct_1(C) -> C != k2_xboole_0(A,B))) & (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1362 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C))) & r2_hidden(C,k9_relat_1(D,A))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1363 (exists A (v1_funct_1(A) & v1_xboole_0(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1364 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1365 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1366 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1367 (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]. 6.36/6.31 1368 (all A k1_tarski(k1_xboole_0) = k4_partfun1(A,k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1369 (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]. 6.36/6.31 1370 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_partfun1(A,B)))))) # label(t135_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1371 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (v1_partfun1(E,A,B) & r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1372 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1373 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1374 (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]. 6.36/6.31 1375 (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]. 6.36/6.31 1376 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1377 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> v1_partfun1(B,k1_xboole_0,A))) # label(t112_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1378 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1379 (all A all B all C (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) -> r2_hidden(C,f3_s4_partfun1))) & (all A all B all C all D (p1_s4_partfun1(A,B,C) & p1_s4_partfun1(A,B,D) & r2_hidden(B,f2_s4_partfun1) & r2_hidden(A,f1_s4_partfun1) -> C = D)) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & (all B all C (r2_hidden(C,f2_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(B,f1_s4_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & v1_funct_1(A))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1380 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1381 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1382 (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]. 6.36/6.31 1383 (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]. 6.36/6.31 1384 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1385 (all A all B all C all D (m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1386 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,B) & k1_relat_1(D) = k1_tarski(A) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1387 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> k10_relat_1(C,B) = k4_relset_1(A,B,C))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1388 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1389 (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]. 6.36/6.31 1390 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1391 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = B)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1392 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C))) <-> r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1393 (all A all B all C (m2_relset_1(C,A,B) -> (A = k4_relset_1(A,B,C) <-> v1_partfun1(C,A,B)))) # label(d4_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1394 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> r1_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1395 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,k4_relset_1(A,B,D)) -> r2_hidden(k1_funct_1(D,C),B)))) # label(t27_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1396 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1397 (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]. 6.36/6.31 1398 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1399 (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]. 6.36/6.31 1400 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1401 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k9_relat_1(C,B) = k1_xboole_0)) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1402 (all A all B exists C (v1_funct_1(C) & v1_relat_1(C) & m1_relset_1(C,A,B))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1403 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1404 (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]. 6.36/6.31 1405 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1406 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1407 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1408 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (v1_partfun1(C,A,B) & r1_partfun1(C,D) & v1_partfun1(D,A,B) -> C = D))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1409 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1410 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1411 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1412 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((k1_xboole_0 = B -> A = k1_xboole_0) & r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1413 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1414 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(C,k6_relat_1(B)) = C)) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1415 (all A all B all C (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) -> B = C)) & (all A all B (r2_hidden(A,f1_s2_partfun1) & p1_s2_partfun1(A,B) -> r2_hidden(B,f2_s2_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B ((exists C p1_s2_partfun1(B,C)) & r2_hidden(B,f1_s2_partfun1) <-> r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)))))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1416 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1417 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1418 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (D = k5_partfun1(A,B,C) <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_partfun1(F,A,B) & r1_partfun1(C,F) & E = F)) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1419 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k1_xboole_0,B) -> D = C)))) # label(t58_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1420 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1421 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> v1_funct_1(C) & m2_relset_1(C,A,B)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1422 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1423 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1424 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1425 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1426 (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]. 6.36/6.31 1427 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & r1_partfun1(A,B) -> B = A))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1428 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1429 (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]. 6.36/6.31 1430 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1431 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1432 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1433 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1434 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1435 (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]. 6.36/6.31 1436 (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]. 6.36/6.31 1437 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1438 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D)) = k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1439 (all A all B all C all D k3_mcart_1(k4_tarski(A,B),C,D) = k4_mcart_1(A,B,C,D)) # label(t32_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1440 (all A all B (k1_xboole_0 != k2_zfmisc_1(A,B) -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k1_mcart_1(C) != C & C != k2_mcart_1(C))))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1441 (all A all B all C -(B != k1_xboole_0 & (exists D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) & (exists E exists F exists G (D = k3_mcart_1(E,F,G) & -(k5_mcart_1(A,B,C,D) = E & k6_mcart_1(A,B,C,D) = F & G = k7_mcart_1(A,B,C,D)))))) & C != k1_xboole_0 & k1_xboole_0 != A)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1442 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D)) = k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1443 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D -((r2_hidden(D,A) | r2_hidden(C,A)) & k4_tarski(C,D) = B)))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1444 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1445 (all A all B all C all D all E all F all G all H (r1_tarski(C,D) & r1_tarski(G,H) & r1_tarski(E,F) & r1_tarski(A,B) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1446 (all A all B all C all D all E k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,E)) = k2_enumset1(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D),k3_mcart_1(A,C,E),k3_mcart_1(B,C,E))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1447 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1448 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1449 (all A all B all C all D all E all F all G all H (-r1_xboole_0(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) -> -r1_xboole_0(B,F) & -r1_xboole_0(D,H) & -r1_xboole_0(C,G) & -r1_xboole_0(A,E))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1450 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1451 (all A all B all C all D all E all F all G all H -(A != k1_xboole_0 & k1_xboole_0 != B & k1_xboole_0 != D & F != k1_xboole_0 & k1_xboole_0 != G & H != k1_xboole_0 & (exists I ((exists J (J = I & -(k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J) & k11_mcart_1(E,F,G,H,J) = k11_mcart_1(A,B,C,D,I) & k9_mcart_1(E,F,G,H,J) = k9_mcart_1(A,B,C,D,I) & k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I)) & m1_subset_1(J,k4_zfmisc_1(E,F,G,H)))) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != E & k1_xboole_0 != C)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1452 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B (B = k2_mcart_1(A) <-> (all C all D (k4_tarski(C,D) = A -> B = D)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1453 (all A all B all C -(B != k1_xboole_0 & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)) = D)) & k1_xboole_0 != A)) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1454 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> (C = k1_mcart_1(A) | k1_mcart_1(A) = B) & k2_mcart_1(A) = D)) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1455 (all A all B all C all D -(k1_xboole_0 != A & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k9_mcart_1(A,B,C,D,E) != E & k11_mcart_1(A,B,C,D,E) != E & k10_mcart_1(A,B,C,D,E) != E & k8_mcart_1(A,B,C,D,E) != E)) & k1_xboole_0 != D & C != k1_xboole_0 & k1_xboole_0 != B)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1456 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) -> k13_mcart_1(A,B,C,D,E,F) = k3_zfmisc_1(D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1457 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k4_mcart_1(k8_mcart_1(A,B,C,D,E),k9_mcart_1(A,B,C,D,E),k10_mcart_1(A,B,C,D,E),k11_mcart_1(A,B,C,D,E)) = E)) & D != k1_xboole_0 & B != k1_xboole_0)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1458 (all A all B all C (r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C) -> r2_hidden(A,k2_zfmisc_1(B,C)) | (all D all E k4_tarski(D,E) != A))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1459 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1460 (all A all B all C -(A != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D != k6_mcart_1(A,B,C,D) & D != k7_mcart_1(A,B,C,D) & D != k5_mcart_1(A,B,C,D))) & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1461 (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]. 6.36/6.31 1462 (all A all B all C all D all E all F all G all H (r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) <-> r2_hidden(C,G) & r2_hidden(D,H) & r2_hidden(B,F) & r2_hidden(A,E))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1463 (all A -((all B -(r2_hidden(B,A) & (all C all D all E (r2_hidden(E,B) & r2_hidden(D,E) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1464 (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]. 6.36/6.31 1465 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (all E (m1_subset_1(E,k1_zfmisc_1(B)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> (all G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) -> (r2_hidden(G,k3_zfmisc_1(D,E,F)) -> r2_hidden(k5_mcart_1(A,B,C,G),D) & r2_hidden(k6_mcart_1(A,B,C,G),E) & r2_hidden(k7_mcart_1(A,B,C,G),F)))))))))) # label(t76_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1466 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k15_mcart_1(A)) & v1_relat_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1467 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> C = F & B = E & A = D)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1468 (all A all B all C all D all E all F -(A != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != F & (exists G (m1_subset_1(G,k3_zfmisc_1(A,B,C)) & (exists H (H = G & -(k5_mcart_1(A,B,C,G) = k5_mcart_1(D,E,F,H) & k6_mcart_1(D,E,F,H) = k6_mcart_1(A,B,C,G) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H)) & m1_subset_1(H,k3_zfmisc_1(D,E,F)))))) & E != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 != B)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1469 (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]. 6.36/6.31 1470 (all A all B all C all D k3_zfmisc_1(k2_zfmisc_1(A,B),C,D) = k4_zfmisc_1(A,B,C,D)) # label(t54_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1471 (all A all B all C (k3_zfmisc_1(A,B,C) != k1_xboole_0 <-> A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1472 (all A all B all C -(C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (E = k7_mcart_1(A,B,C,D) <-> (all F all G all H (k3_mcart_1(F,G,H) = D -> H = E))))))) & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1473 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> C = k1_xboole_0 | D = k1_xboole_0 | G = C & H = D & B = F & E = A | k1_xboole_0 = B | k1_xboole_0 = A)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1474 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> D = F))))))) -> k1_xboole_0 = B | k1_xboole_0 = C | k5_mcart_1(A,B,C,E) = D | A = k1_xboole_0))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1475 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k1_mcart_1(A),B) & r2_hidden(k2_mcart_1(A),C))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1476 (all A all B (k3_zfmisc_1(B,B,B) = k3_zfmisc_1(A,A,A) -> A = B)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1477 (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]. 6.36/6.31 1478 (all A all B all C all D all E all F all G all H (m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(A)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1479 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & r1_xboole_0(B,A))))) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1480 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(A,B,C,D) = k4_zfmisc_1(E,F,G,H) -> D = H & G = C & B = F & E = A | k1_xboole_0 = k4_zfmisc_1(A,B,C,D))) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1481 (all A all B all C all D all E all F (A = k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) & B = k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1482 (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]. 6.36/6.31 1483 (all A all B -(-(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C = k4_tarski(k1_mcart_1(C),k2_mcart_1(C)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1484 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(A != k1_xboole_0 & k1_xboole_0 != C & (exists E exists F exists G (-(k5_mcart_1(A,B,C,D) = E & G = k7_mcart_1(A,B,C,D) & F = k6_mcart_1(A,B,C,D)) & D = k3_mcart_1(E,F,G))) & B != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1485 (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]. 6.36/6.31 1486 (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]. 6.36/6.31 1487 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1488 (all A all B all C all D all E all F (r1_tarski(A,B) & r1_tarski(E,F) & r1_tarski(C,D) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1489 (all A all B all C all D k4_mcart_1(A,B,C,D) = k4_tarski(k3_mcart_1(A,B,C),D)) # label(d4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1490 (all A -(A != k1_xboole_0 & (all B -((all C all D all E all F -((r2_hidden(C,A) | r2_hidden(D,A)) & B = k4_mcart_1(C,D,E,F))) & r2_hidden(B,A))))) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1491 (all A all B all C all D all E all F all G all H (m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(A)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = k4_zfmisc_1(E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1492 (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]. 6.36/6.31 1493 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1494 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> G = E))))))))) -> k1_xboole_0 = B | D = k1_xboole_0 | E = k8_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | k1_xboole_0 = A))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1495 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> H = D))))))) -> C = k1_xboole_0 | D = k7_mcart_1(A,B,C,E) | B = k1_xboole_0 | A = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1496 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k3_zfmisc_1(A,B,C) = k1_xboole_0 | D = A & E = B & C = F)) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1497 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (E = k3_mcart_1(F,G,H) -> D = G))))))) -> A = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | C = k1_xboole_0 | k1_xboole_0 = B))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1498 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> k1_mcart_1(A) = B & k2_mcart_1(A) = C)) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.31 1499 (all A all B all C all D all E all F k6_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(A,D,E),k3_mcart_1(A,C,F),k3_mcart_1(A,D,F),k3_mcart_1(B,C,E),k3_mcart_1(B,D,E),k3_mcart_1(B,C,F),k3_mcart_1(B,D,F)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k2_tarski(E,F))) # label(t46_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1500 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B))) -> k1_xboole_0 = A)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1501 (all A all B all C all D k2_tarski(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k1_tarski(D))) # label(t40_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1502 (all A -((all B -(r2_hidden(B,A) & (all C all D (r2_hidden(D,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))))) & k1_xboole_0 != A)) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1503 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(k1_xboole_0 != C & (exists F exists G exists H exists I (-(k10_mcart_1(A,B,C,D,E) = H & I = k11_mcart_1(A,B,C,D,E) & G = k9_mcart_1(A,B,C,D,E) & F = k8_mcart_1(A,B,C,D,E)) & E = k4_mcart_1(F,G,H,I))) & k1_xboole_0 != D & B != k1_xboole_0 & A != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1504 (all A all B all C all D -(C != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = H)) <-> F = k9_mcart_1(A,B,C,D,E)))))) & k1_xboole_0 != D & B != k1_xboole_0 & k1_xboole_0 != A)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1505 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1506 (all A all B -(B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) != C & C != k1_mcart_1(C))) & k1_xboole_0 != A)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1507 (all A all B all C all D all E ((all F (r2_hidden(F,A) <-> (exists G exists H exists I exists J (r2_hidden(G,B) & r2_hidden(I,D) & k4_mcart_1(G,H,I,J) = F & r2_hidden(J,E) & r2_hidden(H,C))))) -> A = k4_zfmisc_1(B,C,D,E))) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1508 (all A -(k1_xboole_0 != A & (all B -((all C all D all E -((r2_hidden(D,A) | r2_hidden(C,A)) & B = k3_mcart_1(C,D,E))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1509 (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]. 6.36/6.32 1510 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_mcart_1(k1_funct_1(A,C)))) & k1_relat_1(B) = k1_relat_1(A) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1511 (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]. 6.36/6.32 1512 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = H))))))))) -> D = k1_xboole_0 | E = k9_mcart_1(A,B,C,D,F) | C = k1_xboole_0 | B = k1_xboole_0 | A = k1_xboole_0))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1513 (all A all B all C all D all E all F (-r1_xboole_0(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) -> -r1_xboole_0(C,F) & -r1_xboole_0(B,E) & -r1_xboole_0(A,D))) # label(t52_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1514 (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]. 6.36/6.32 1515 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1516 (all A all B all C all D -(-(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (k10_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> F = I))))))) & k1_xboole_0 != D & k1_xboole_0 != C & B != k1_xboole_0 & A != k1_xboole_0)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1517 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1518 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1519 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1520 (all A ((exists B exists C k4_tarski(B,C) = A) -> k2_mcart_1(A) != A & k1_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1521 (all A all B all C all D ((all E ((exists F exists G exists H (r2_hidden(F,B) & r2_hidden(H,D) & k3_mcart_1(F,G,H) = E & r2_hidden(G,C))) <-> r2_hidden(E,A))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1522 (all A all B (k2_mcart_1(k4_tarski(A,B)) = B & k1_mcart_1(k4_tarski(A,B)) = A)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1523 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1524 (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]. 6.36/6.32 1525 (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]. 6.36/6.32 1526 (all A all B all C all D -(C != k1_xboole_0 & k1_xboole_0 != D & (exists E ((exists F exists G exists H exists I (E = k4_mcart_1(F,G,H,I) & -(G = k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = I & k10_mcart_1(A,B,C,D,E) = H & F = k8_mcart_1(A,B,C,D,E)))) & m1_subset_1(E,k4_zfmisc_1(A,B,C,D)))) & k1_xboole_0 != B & k1_xboole_0 != A)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1527 (all A all B all C all D -(k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> ((all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> F = J)) <-> k11_mcart_1(A,B,C,D,E) = F))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1528 (all A all B all C all D all E all F (m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(A)) -> m1_subset_1(k13_mcart_1(A,B,C,D,E,F),k1_zfmisc_1(k3_zfmisc_1(A,B,C))))) # label(dt_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1529 (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]. 6.36/6.32 1530 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1531 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k16_mcart_1(A)) & v1_funct_1(k16_mcart_1(A)))) # label(dt_k16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1532 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k2_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) <-> B = k16_mcart_1(A)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1533 (all A all B all C all D all E all F (k3_zfmisc_1(D,E,F) = k3_zfmisc_1(A,B,C) -> k1_xboole_0 = A | C = k1_xboole_0 | D = A & E = B & F = C | k1_xboole_0 = B)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1534 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> (k5_mcart_1(A,B,C,D) = E <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> F = E))))))) & k1_xboole_0 != C & k1_xboole_0 != A)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1535 (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]. 6.36/6.32 1536 (all A all B all C all D all E -((all F all G all H all I -(r2_hidden(H,D) & r2_hidden(I,E) & k4_mcart_1(F,G,H,I) = A & r2_hidden(G,C) & r2_hidden(F,B))) & r2_hidden(A,k4_zfmisc_1(B,C,D,E)))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1537 (all A all B all C -(k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k2_mcart_1(D) = k7_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = k1_mcart_1(k1_mcart_1(D)))))) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1538 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1539 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> I = E))))))))) -> B = k1_xboole_0 | C = k1_xboole_0 | k10_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | k1_xboole_0 = A))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1540 (all A all B (k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) -> A = B)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1541 (all A -((all B -(r2_hidden(B,A) & (all C (r2_hidden(C,B) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1542 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k2_tarski(C,D))) -> (D = k2_mcart_1(A) | C = k2_mcart_1(A)) & k1_mcart_1(A) = B)) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1543 (all A all B all C (-(-r1_tarski(A,k3_zfmisc_1(A,B,C)) & -r1_tarski(A,k3_zfmisc_1(B,C,A)) & -r1_tarski(A,k3_zfmisc_1(C,A,B))) -> A = k1_xboole_0)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1544 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> k2_zfmisc_1(C,D) = k12_mcart_1(A,B,C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1545 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E)) = k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1546 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> (k1_mcart_1(A) = C | B = k1_mcart_1(A)) & r2_hidden(k2_mcart_1(A),D))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1547 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B ((all C all D (k4_tarski(C,D) = A -> B = C)) <-> B = k1_mcart_1(A))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1548 (all A all B all C -(k1_xboole_0 != B & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> (E = k6_mcart_1(A,B,C,D) <-> (all F all G all H (D = k3_mcart_1(F,G,H) -> E = G))))))) & C != k1_xboole_0 & A != k1_xboole_0)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1549 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) = k8_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E))) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E) & k2_mcart_1(k1_mcart_1(E)) = k10_mcart_1(A,B,C,D,E))) & k1_xboole_0 != C)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1550 (all A -((all B -(r2_hidden(B,A) & (all C all D all E all F all G (r2_hidden(C,D) & r2_hidden(F,G) & r2_hidden(G,B) & r2_hidden(E,F) & r2_hidden(D,E) -> r1_xboole_0(C,A))))) & A != k1_xboole_0)) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1551 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = J))))))))) -> k1_xboole_0 = A | k11_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | k1_xboole_0 = C | k1_xboole_0 = B))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1552 (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]. 6.36/6.32 1553 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(B,k2_tarski(C,D))) -> r2_hidden(k1_mcart_1(A),B) & (k2_mcart_1(A) = C | k2_mcart_1(A) = D))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1554 (all A k1_mcart_1(k1_mcart_1(A)) = k17_mcart_1(A)) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1555 (all A all B all C all D -(r2_hidden(A,k3_zfmisc_1(B,C,D)) & (all E all F all G -(r2_hidden(F,C) & k3_mcart_1(E,F,G) = A & r2_hidden(G,D) & r2_hidden(E,B))))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1556 (all A all B all C all D all E all F all G all H (k4_mcart_1(E,F,G,H) = k4_mcart_1(A,B,C,D) -> E = A & H = D & G = C & F = B)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1557 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1558 (all A all B all C all D -(k1_xboole_0 != A & C != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> (F = k8_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (k4_mcart_1(G,H,I,J) = E -> G = F))))))) & k1_xboole_0 != B)) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1559 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (k2_mcart_1(A) = E | k2_mcart_1(A) = D) & (k1_mcart_1(A) = C | B = k1_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1560 (all A all B all C all D (k4_zfmisc_1(A,B,C,D) != k1_xboole_0 <-> B != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != C & A != k1_xboole_0)) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1561 (all A -((all B -((all C all D all E all F (r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,B) & r2_hidden(C,D) -> r1_xboole_0(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1562 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k8_mcart_1(A,B,C,D,I),E) & r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k10_mcart_1(A,B,C,D,I),G)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1563 (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]. 6.36/6.32 1564 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1565 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1566 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & (all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & (all B -(r2_hidden(B,k3_relat_1(A)) & (all C (v3_ordinal1(C) -> -r4_wellord1(k2_wellord1(A,k1_wellord1(A,B)),k1_wellord2(C))))))))) # label(t13_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1567 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1568 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1569 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1570 (all A (v3_ordinal1(A) -> (all B (r1_tarski(B,A) -> v2_wellord1(k1_wellord2(B)))))) # label(t9_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1571 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1572 (all A (-v1_xboole_0(A) -> -((all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))) & k1_relat_1(B) = A))) & (all B -(k1_xboole_0 = B & r2_hidden(B,A)))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1573 (all A all B (v1_relat_1(B) -> (B = k1_wellord2(A) <-> A = k3_relat_1(B) & (all C all D (r2_hidden(D,A) & r2_hidden(C,A) -> (r1_tarski(C,D) <-> r2_hidden(k4_tarski(C,D),B))))))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1574 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1575 (all A -((all B -(p1_s1_wellord2(A,B) & r2_hidden(B,f2_s1_wellord2))) & r2_hidden(A,f1_s1_wellord2))) -> (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_wellord2 & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & r1_tarski(k2_relat_1(A),f2_s1_wellord2) & v1_relat_1(A))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1576 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1577 (all A all B ((exists C (v1_funct_1(C) & k1_relat_1(C) = A & B = k2_relat_1(C) & v2_funct_1(C) & v1_relat_1(C))) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1578 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(C)) & r4_wellord1(A,k1_wellord2(B)) -> C = B))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1579 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) -> (r1_wellord2(A,B) <-> A = k2_wellord2(B)))))) # label(d3_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1580 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r4_wellord1(k1_wellord2(A),k1_wellord2(B)) -> A = B))))) # label(t11_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1581 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1582 (all A all B all C (r2_wellord2(B,C) & r2_wellord2(A,B) -> r2_wellord2(A,C))) # label(t22_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1583 (all A (v1_relat_1(A) -> -((all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & v2_wellord1(A)))) # label(t14_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1584 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1585 (all A -((all B all C -(r2_hidden(B,f2_s2_wellord2) & r2_hidden(C,f3_s2_wellord2) & p1_s2_wellord2(A,B,C))) & r2_hidden(A,f1_s2_wellord2))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (exists B (k1_relat_1(B) = f1_s2_wellord2 & (all C (r2_hidden(C,f1_s2_wellord2) -> p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = f1_s2_wellord2 & v1_funct_1(B) & v1_relat_1(B))))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1586 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> k1_wellord1(k1_wellord2(B),A) = A))))) # label(t10_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1587 (all A all B (r2_wellord2(A,B) <-> r2_tarski(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1588 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1589 (all A all B (v3_ordinal1(B) -> (r1_tarski(A,B) -> r1_ordinal1(k2_wellord2(k1_wellord2(A)),B)))) # label(t17_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1590 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1591 (all A exists B (r2_wellord1(B,A) & v1_relat_1(B))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1592 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> v2_wellord1(k2_wellord1(B,A)) & A = k3_relat_1(k2_wellord1(B,A))))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1593 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1594 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1595 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1596 (all A (-v1_xboole_0(A) -> -((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r1_xboole_0(B,C) | C = B)) & (all B exists C (r2_hidden(C,A) & (all D k1_tarski(D) != k3_xboole_0(B,C)))) & (all B -(r2_hidden(B,A) & B = k1_xboole_0))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1597 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B (v3_ordinal1(B) -> (B = k2_wellord2(A) <-> r4_wellord1(A,k1_wellord2(B)))))))) # label(d2_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1598 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1599 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1600 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1601 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1602 (all A all B (r1_tarski(A,B) -> k2_wellord1(k1_wellord2(B),A) = k1_wellord2(A))) # label(t8_wellord2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1603 (all A all B all C (v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k3_funct_2(k1_xboole_0,A,C,B))) # label(t60_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1604 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (A = k2_relat_1(C) & k2_relat_1(B) = A -> A = k2_relat_1(k4_funct_2(A,B,C))))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1605 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,k1_tarski(B)) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> C = D)))) # label(t66_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1606 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1607 (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]. 6.36/6.32 1608 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1609 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (exists E (r2_hidden(E,k4_relset_1(A,B,C)) & k1_funct_1(D,E) != k1_funct_1(C,E))))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1610 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1611 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (exists C (v1_funct_2(C,A,A) & r1_partfun1(B,C) & m2_relset_1(C,A,A) & v1_funct_1(C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1612 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1613 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (v2_funct_1(B) -> (all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1614 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1615 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1616 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1617 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(A != k1_xboole_0 & B != k1_xboole_0 & -((all D all E (v1_funct_1(E) & m2_relset_1(E,D,A) & v1_funct_2(E,D,A) -> (all F (v1_funct_1(F) & v1_funct_2(F,D,A) & m2_relset_1(F,D,A) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> E = F))))) <-> v2_funct_1(C))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1618 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1619 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1620 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F all G (r2_hidden(G,B) & r2_hidden(F,A) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) -> D = E))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1621 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)) & k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1622 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1623 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> (r1_partfun1(C,D) <-> (all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(C,E) = k1_funct_1(D,E))))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1624 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1625 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1626 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (v2_funct_1(B) & k2_relat_1(B) = A -> v1_funct_1(B) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1627 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1628 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k3_funct_2(A,B,C,B) = A))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1629 (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & (all B (m1_subset_1(B,f1_s4_funct_2) -> k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B))) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1630 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),k2_relat_1(D)) | B = k1_xboole_0))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1631 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1632 (exists A (f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & (all B (m1_subset_1(B,f1_s10_funct_2) -> (f3_s10_funct_2 != B -> k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,B) = f5_s10_funct_2(B)))) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_2(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1633 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) -> (r1_tarski(B,A) -> B = k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) & k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1634 (all A (m1_subset_1(A,f1_s7_funct_2) -> (all B (m1_subset_1(B,f2_s7_funct_2) -> (exists C (m1_subset_1(C,f3_s7_funct_2) & p1_s7_funct_2(A,B,C))))))) -> (exists A (v1_funct_2(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & m2_relset_1(A,k2_zfmisc_1(f1_s7_funct_2,f2_s7_funct_2),f3_s7_funct_2) & (all B (m1_subset_1(B,f1_s7_funct_2) -> (all C (m1_subset_1(C,f2_s7_funct_2) -> p1_s7_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_1(A))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1635 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) -> B = k1_xboole_0 | v2_funct_1(C) & k2_relat_1(D) = A))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1636 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1637 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> A = k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)))) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1638 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1639 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1640 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1641 (all A all B (m1_relset_1(B,A,A) -> (v1_funct_1(B) & v1_funct_2(B,A,A) & v1_relat_2(B) & v1_partfun1(B,A,A) -> v1_funct_1(B) & v2_funct_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1642 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1643 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> k2_funct_2(A,B,C,A) = k2_relat_1(C)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1644 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1645 (all A all B all C (m2_relset_1(C,A,B) -> C = k7_relset_1(A,B,B,B,C,k6_partfun1(B)) & k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C)) # label(t23_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1646 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | C = k1_xboole_0))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1647 (all A all B all C (m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k9_funct_2(A,B,C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1648 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k10_relat_1(C,D) = k3_funct_2(A,B,C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1649 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1650 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (all E k1_tarski(E) != B) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1651 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> m1_subset_1(k3_funct_2(A,B,C,D),k1_zfmisc_1(A)))) # label(dt_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1652 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B) -> k2_relat_1(C) = B))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1653 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1654 (all A (r2_hidden(A,f1_s9_funct_2) -> (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)) & (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> k1_funct_1(A,B) = f4_s9_funct_2(B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_1(A))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1655 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1656 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1657 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1658 (all A -((all B -(r2_hidden(B,f2_s1_funct_2) & p1_s1_funct_2(A,B))) & r2_hidden(A,f1_s1_funct_2))) -> (exists A ((all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2) & v1_funct_1(A))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1659 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,A) & E = k1_funct_1(D,F) & r2_hidden(F,C))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1660 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1661 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1662 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,A,B) & v1_funct_1(E) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & m1_relset_1(D,A,B) & v1_funct_1(D) -> v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1663 (all A all B k1_funct_2(A,B) = k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B))) # label(t160_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1664 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & m1_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_relat_1(B,C) = k5_funct_2(A,B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1665 (all A all B all C ((all D ((exists E (E = D & A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & v1_funct_1(E) & v1_relat_1(E))) <-> r2_hidden(D,C))) <-> C = k1_funct_2(A,B))) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1666 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1667 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1668 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1669 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> k1_xboole_0 != A & B = k1_xboole_0 | r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C)))))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1670 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1671 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) | A != k1_xboole_0 & B = k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1672 (all A all B all C (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v3_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v1_funct_2(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1673 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | B = k1_xboole_0 & k1_xboole_0 != A | k1_xboole_0 != B & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1674 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_partfun1(k3_partfun1(B,A,A),A,A))) # label(t134_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1675 (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]. 6.36/6.32 1676 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1677 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) -> m2_relset_1(B,k1_xboole_0,A) & v1_funct_2(B,k1_xboole_0,A) & v1_funct_1(B)))) # label(t55_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1678 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,B,C) & k2_relat_1(B) = A -> k6_partfun1(A) = C))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1679 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1680 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r2_hidden(C,A) -> k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) | B = k1_xboole_0))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1681 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_partfun1(B,C) -> B = C))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1682 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 = B & A != k1_xboole_0 | r2_hidden(D,k5_partfun1(A,B,C))))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1683 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1684 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_tarski(C,A) -> m2_relset_1(k2_partfun1(A,B,D,C),C,B) & v1_funct_2(k2_partfun1(A,B,D,C),C,B) & v1_funct_1(k2_partfun1(A,B,D,C)) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1685 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1686 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1687 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.32 1688 (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]. 6.36/6.32 1689 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)))) # label(t159_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1690 (all A all B (r2_hidden(A,f1_s6_funct_2) & r2_hidden(B,f2_s6_funct_2) -> r2_hidden(f4_s6_funct_2(A,B),f3_s6_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s6_funct_2) & r2_hidden(C,f2_s6_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s6_funct_2(B,C))) & m2_relset_1(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2))) # label(s6_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1691 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) <-> B = k2_relat_1(C)))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1692 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r1_tarski(k2_relat_1(D),C) -> A != k1_xboole_0 & k1_xboole_0 = B | v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C)))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1693 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B & B = k7_relset_1(A,A,A,A,B,k6_partfun1(A)))) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1694 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> k1_relat_1(C) = A & r1_tarski(k2_relat_1(C),B)))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1695 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1696 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1697 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1698 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1699 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1700 (all A all B all C (m1_relset_1(B,A,A) & v1_funct_1(C) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k4_funct_2(A,B,C) = k5_relat_1(B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1701 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_2(D,k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(D) -> k9_funct_2(A,B,C) = D)) # label(d5_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1702 (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]. 6.36/6.33 1703 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1704 (all A (v1_relat_1(A) & v1_funct_1(A) -> m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1705 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (v2_funct_1(C) & k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) & B = k2_relat_1(C) -> k1_xboole_0 = B | D = k2_funct_1(C) | A = k1_xboole_0))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1706 (all A all B (-v1_xboole_0(B) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1707 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v2_funct_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1708 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (B != k1_xboole_0 -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1709 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> ((all C all D (r2_hidden(D,A) & k1_funct_1(B,D) = k1_funct_1(B,C) & r2_hidden(C,A) -> D = C)) <-> v2_funct_1(B)))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1710 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) != f7_s11_funct_2(B) & f4_s11_funct_2 != B & f3_s11_funct_2 != B))) & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) = f6_s11_funct_2 & k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) = f5_s11_funct_2)) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1711 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> k1_xboole_0 != A & B = k1_xboole_0 | D = C))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1712 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1713 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1714 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_2(D,k1_tarski(A),B) -> (k1_xboole_0 != B -> r1_tarski(k2_funct_2(k1_tarski(A),B,D,C),k1_tarski(k1_funct_1(D,A)))))) # label(t64_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1715 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1716 (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]. 6.36/6.33 1717 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1718 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1719 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1720 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1721 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1722 (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]. 6.36/6.33 1723 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v3_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v2_funct_1(C) & v1_funct_1(C)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1724 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (k2_relat_1(C) = B <-> (all D -(r2_hidden(D,B) & k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D))))))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1725 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1726 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1727 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E -((all F -(k1_funct_1(D,F) = E & r2_hidden(F,C) & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1728 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B = k2_relat_1(C) & v2_funct_1(C) -> k1_xboole_0 = B | k5_relat_1(C,k2_funct_1(C)) = k6_partfun1(A) & k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C)))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1729 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1730 (all A all B all C (m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))) & (B = k1_xboole_0 -> A = k1_xboole_0 | (v1_funct_2(C,A,B) <-> C = k1_xboole_0)))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1731 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> -((all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C)) & B = k2_relat_1(D) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1732 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1733 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E -(r2_hidden(E,k2_funct_2(A,B,D,C)) & (all F (m1_subset_1(F,A) -> -(k1_funct_1(D,F) = E & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1734 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1735 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> ((all D all E (r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) -> D = E)) <-> v2_funct_1(C))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1736 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1737 (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & (all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1738 (all A all B all C all D all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> -((k1_xboole_0 = C -> B = k1_xboole_0) & -r1_tarski(k3_funct_2(A,B,E,D),k3_funct_2(A,C,k1_partfun1(A,B,B,C,E,F),k2_funct_2(B,C,F,D))) & (k1_xboole_0 = B -> k1_xboole_0 = A)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1739 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1740 (all A all B all C all D (-v1_xboole_0(A) & m1_relset_1(C,A,B) & m1_subset_1(D,A) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k1_funct_1(C,D) = k8_funct_2(A,B,C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1741 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) & k2_relat_1(D) = B -> k1_xboole_0 != B & C = k1_xboole_0 | v2_funct_1(E) & v2_funct_1(D)))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1742 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1743 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1744 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (r2_hidden(C,A) & r2_hidden(k1_funct_1(E,C),D) -> k1_funct_1(k9_relset_1(A,B,D,E),C) = k1_funct_1(E,C) | k1_xboole_0 = B))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1745 (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]. 6.36/6.33 1746 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k5_relat_1(D,E) = k7_funct_2(A,B,C,D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1747 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1748 (all A all B -(r2_hidden(A,f1_s5_funct_2) & r2_hidden(B,f2_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))))) -> (exists A ((all B all C (r2_hidden(C,f2_s5_funct_2) & r2_hidden(B,f1_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_1(A))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1749 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1750 (all A all B (v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v1_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v3_funct_2(k6_funct_2(A,B),A,A) & v1_funct_1(k6_funct_2(A,B)))) # label(dt_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1751 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))))) -> E = D))))) # label(t120_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1752 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C | C = k1_xboole_0 | B = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1753 (all A all B all C all D all E all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (r2_hidden(D,A) & r2_hidden(E,B) -> r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C) | C = k1_xboole_0))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1754 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1755 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1756 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (-(A != k1_xboole_0 & k1_xboole_0 != C & k1_xboole_0 = B) -> v1_funct_1(k1_partfun1(A,B,B,C,D,E)) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C)))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1757 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1758 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (B != k1_xboole_0 -> (B = k2_relat_1(C) <-> (all D (k1_xboole_0 != D -> (all E (v1_funct_1(E) & m2_relset_1(E,B,D) & v1_funct_2(E,B,D) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,F) = k1_partfun1(A,B,B,D,C,E) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1759 (all A (m1_subset_1(A,f1_s13_funct_2) -> m1_subset_1(f3_s13_funct_2(A),f2_s13_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> f3_s13_funct_2(B) = k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B))) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1760 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (B = k4_funct_2(A,C,B) & v2_funct_1(B) -> C = k6_partfun1(A)))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1761 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1762 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1763 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> k2_funct_2(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1764 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r2_hidden(C,A) & v2_funct_1(D) -> C = k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) | B = k1_xboole_0))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1765 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A (m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2) & v1_funct_1(A))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1766 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> ((all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> r1_partfun1(B,C)))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1767 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1768 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (k5_funct_2(A,B,C) = C -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1769 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1770 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1771 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> ((all E B != k1_tarski(E)) & k5_partfun1(A,B,D) = k5_partfun1(A,B,C) -> C = D))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1772 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -(r2_hidden(D,B) & (all E -(D = k1_funct_1(C,E) & r2_hidden(E,A))))) -> k2_relat_1(C) = B | k1_xboole_0 = B))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1773 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1774 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1775 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1776 (all A all B (v1_funct_1(B) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_1(B) = k6_funct_2(A,B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1777 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (B != k1_xboole_0 -> (all E (r2_hidden(E,A) & r2_hidden(k1_funct_1(D,E),C) <-> r2_hidden(E,k10_relat_1(D,C))))))) # label(t46_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1778 (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]. 6.36/6.33 1779 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,A,B) & v1_partfun1(C,A,B) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1780 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1781 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> -(-v2_funct_1(C) & (exists D (m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & v1_funct_2(D,B,A) & v1_funct_1(D))) & B != k1_xboole_0))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1782 (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]. 6.36/6.33 1783 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1784 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1785 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> k2_funct_2(A,A,B,A) = k2_relat_1(B))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1786 (all A all B (v1_funct_1(B) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_1(C) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> C = k6_funct_2(A,B)))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1787 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v2_funct_1(C) & v2_funct_2(C,A,B) <-> v3_funct_2(C,A,B)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1788 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> k1_funct_1(A,B) = f3_s2_funct_2(B))) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & v1_funct_1(A))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1789 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1790 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1791 (all A (k1_xboole_0 != A -> k1_xboole_0 = k1_funct_2(A,k1_xboole_0))) # label(t14_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1792 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> r1_partfun1(C,D) | B = k1_xboole_0 & k1_xboole_0 != A))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1793 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> ((k1_xboole_0 = B -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1794 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> -((all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> -r1_partfun1(C,D))) & (B = k1_xboole_0 -> k1_xboole_0 = A)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1795 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) -> v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1796 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1797 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1798 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1799 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> v1_partfun1(C,A,B) | k1_xboole_0 != A & B = k1_xboole_0))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1800 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | k1_xboole_0 = B))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1801 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> -(r1_partfun1(C,E) & r1_partfun1(D,E)))) & r1_partfun1(C,D)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1802 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) & k2_relat_1(C) = B -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1803 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1804 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v1_funct_2(B,A,A) -> v1_funct_1(k4_funct_2(A,B,C)) & m2_relset_1(k4_funct_2(A,B,C),A,A) & v1_funct_2(k4_funct_2(A,B,C),A,A))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1805 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1806 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1807 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r1_tarski(k2_relat_1(B),A) & A = k4_relset_1(A,A,B))) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1808 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> r1_tarski(k10_relat_1(D,C),A))) # label(t47_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1809 (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]. 6.36/6.33 1810 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1811 (all A all B exists C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & v1_relat_1(C))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1812 (all A (m1_subset_1(A,f1_s14_funct_2) -> (exists B (m1_subset_1(B,f2_s14_funct_2) & p1_s14_funct_2(A,B))))) -> (exists A (v1_funct_2(A,f1_s14_funct_2,f2_s14_funct_2) & (all B (m1_subset_1(B,f1_s14_funct_2) -> p1_s14_funct_2(B,k8_funct_2(f1_s14_funct_2,f2_s14_funct_2,A,B)))) & m2_relset_1(A,f1_s14_funct_2,f2_s14_funct_2) & v1_funct_1(A))) # label(s14_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1813 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1814 (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]. 6.36/6.33 1815 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (B = k2_relat_1(C) & (all E all F ((E = k1_funct_1(C,F) & r2_hidden(F,A) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (r2_hidden(E,B) & k1_funct_1(D,E) = F -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) -> k1_xboole_0 = A | k2_funct_1(C) = D | k1_xboole_0 = B))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1816 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1817 $T # label(t6_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1818 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> a_3_7_domain_1(A,B,C) = k7_subset_1(A,B,C))))))) # label(t64_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1819 (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]. 6.36/6.33 1820 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(F,B) & m1_subset_1(G,C) & m1_subset_1(H,D) & m1_subset_1(E,A) & -v1_xboole_0(D) & -v1_xboole_0(C) & -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]. 6.36/6.33 1821 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(E,A) & m1_subset_1(F,B) & m1_subset_1(H,D) & m1_subset_1(G,C) & -v1_xboole_0(D) -> k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H))) # label(redefinition_k5_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1822 (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_1_domain_1(B,C))))) # label(fraenkel_a_2_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1823 (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) -> k14_domain_1(A,B,C,D) = k17_mcart_1(D))) # label(redefinition_k14_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1824 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k6_domain_1(A,B) = k1_tarski(B))) # label(redefinition_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1825 (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 ((exists G ((exists H (m1_subset_1(H,D) & (exists I (m1_subset_1(I,E) & k4_mcart_1(F,G,H,I) = A)))) & m1_subset_1(G,C))) & m1_subset_1(F,B)))))))))))) # label(t31_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1826 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & -v1_xboole_0(C) -> (r2_hidden(A,a_4_2_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) & p1_s4_domain_1(F,G,H,I) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D)))))) # label(fraenkel_a_4_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1827 (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_3_domain_1(A,B,C) = k6_subset_1(A,B,C))))))) # label(t60_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1828 (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]. 6.36/6.33 1829 $T # label(t47_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1830 $T # label(t27_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1831 (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(C) = k2_mcart_1(D) -> C = D))))))))) # label(t12_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1832 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) -> (r2_hidden(A,a_3_0_domain_1(B,C,D)) <-> (exists E exists F exists G (m1_subset_1(G,D) & A = k4_domain_1(B,C,D,E,F,G) & m1_subset_1(F,C) & m1_subset_1(E,B)))))) # label(fraenkel_a_3_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1833 (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]. 6.36/6.33 1834 (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) -> F = A))))))) <-> k5_mcart_1(B,C,D,E) = A))))))))) # label(t24_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1835 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (m1_subset_1(E,B) & -(r2_hidden(E,C) <-> r2_hidden(E,D)) & E = A)) <-> r2_hidden(A,a_3_7_domain_1(B,C,D))))) # label(fraenkel_a_3_7_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1836 (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 ((exists H (m1_subset_1(H,C) & (exists I ((exists J (F = k4_mcart_1(G,H,I,J) & m1_subset_1(J,E))) & m1_subset_1(I,D))))) & m1_subset_1(G,B))) <-> r2_hidden(F,A))) <-> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t33_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1837 (all A all B (-v1_xboole_0(B) -> ((exists C (A = C & p2_s5_domain_1(C) & m1_subset_1(C,B))) <-> r2_hidden(A,a_1_4_domain_1(B))))) # label(fraenkel_a_1_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1838 (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]. 6.36/6.33 1839 (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]. 6.36/6.33 1840 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k7_domain_1(A,C,B) = k7_domain_1(A,B,C))) # label(commutativity_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1841 $T # label(t29_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1842 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(D,A) & m1_subset_1(B,A) -> k10_domain_1(A,B,C,D,E,F) = k3_enumset1(B,C,D,E,F))) # label(redefinition_k10_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1843 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (p1_s5_domain_1(B) -> p2_s5_domain_1(B)))) -> r1_tarski(a_1_3_domain_1(A),a_1_4_domain_1(A))))) # label(s5_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1844 (all A all B (-v1_xboole_0(B) -> ((exists C (C = A & -$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]. 6.36/6.33 1845 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((all E ((exists F ((exists G ((exists H (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))) -> k3_zfmisc_1(B,C,D) = A))))))))) # label(t16_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1846 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> -(r2_hidden(A,k2_zfmisc_1(B,C)) & (all D (m1_subset_1(D,B) -> (all E (m1_subset_1(E,C) -> A != k4_tarski(D,E)))))))))) # label(t9_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1847 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> k2_mcart_1(C) = k3_domain_1(A,B,C))) # label(redefinition_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1848 (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) -> J = A)))))))))))))))))))) # label(t43_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1849 $T # label(t20_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1850 (all A ((exists B (m1_subset_1(B,f1_s10_domain_1) & p1_s10_domain_1(B) & B = A)) <-> r2_hidden(A,a_0_4_domain_1))) # label(fraenkel_a_0_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1851 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & p1_s6_domain_1(C) & C = A)) <-> r2_hidden(A,a_1_5_domain_1(B))))) # label(fraenkel_a_1_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1852 $T # label(t13_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1853 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_3_6_domain_1(B,C,D)) <-> (exists E ((-r2_hidden(E,D) <-> r2_hidden(E,C)) & E = A & m1_subset_1(E,B)))))) # label(fraenkel_a_3_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1854 (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) & B = A)))) # label(fraenkel_a_0_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1855 (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) -> k16_domain_1(A,B,C,D) = k19_mcart_1(D))) # label(redefinition_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1856 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & -v1_xboole_0(D) & -v1_xboole_0(E) -> (r2_hidden(A,a_4_0_domain_1(B,C,D,E)) <-> (exists F exists G exists H exists I (m1_subset_1(I,E) & A = k5_domain_1(B,C,D,E,F,G,H,I) & m1_subset_1(H,D) & m1_subset_1(G,C) & m1_subset_1(F,B)))))) # label(fraenkel_a_4_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1857 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> ((all F (r2_hidden(F,A) <-> (exists G ((exists H (m1_subset_1(H,C) & (exists I ((exists J (m1_subset_1(J,E) & k4_mcart_1(G,H,I,J) = F)) & m1_subset_1(I,D))))) & m1_subset_1(G,B))))) -> k4_zfmisc_1(B,C,D,E) = A))))))))))) # label(t32_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1858 (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]. 6.36/6.33 1859 $T # label(t38_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1860 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> k14_mcart_1(A,B,C,D,E,F,G,H) = a_8_0_domain_1(A,B,C,D,E,F,G,H))))))))))))))))) # label(t55_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1861 (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]. 6.36/6.33 1862 (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]. 6.36/6.33 1863 (all A all B all C all D (-v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists E exists F exists G (m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D) & k4_domain_1(B,C,D,E,F,G) = A & p1_s3_domain_1(E,F,G))) <-> r2_hidden(A,a_3_8_domain_1(B,C,D))))) # label(fraenkel_a_3_8_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1864 (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) -> G = A))))))) <-> k6_mcart_1(B,C,D,E) = A))))))))) # label(t25_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1865 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k17_domain_1(A,B,C,D),C))) # label(dt_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.33 1866 (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) -> (k5_domain_1(B,C,D,E,G,H,I,J) = F -> G = A)))))))))))))))))))) # label(t40_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1867 (all A all B all C all D all E (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_4_1_domain_1(B,C,D,E)) <-> (exists F exists G (m1_subset_1(F,B) & m1_subset_1(G,C) & r2_hidden(G,E) & r2_hidden(F,D) & k1_domain_1(B,C,F,G) = A))))) # label(fraenkel_a_4_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1868 (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]. 6.36/6.34 1869 $T # label(t36_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1870 $T # label(t46_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1871 (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) | r2_hidden(E,D) & -r2_hidden(E,C)) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_4_domain_1(B,C,D))))) # label(fraenkel_a_3_4_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1872 $T # label(t7_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1873 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(C) & -v1_xboole_0(B) -> m1_subset_1(k15_domain_1(A,B,C,D),B))) # label(dt_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1874 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C & p1_s1_domain_1(C)))))) # label(fraenkel_a_1_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1875 $T # label(t3_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1876 (all A ((exists B exists C (m1_subset_1(C,f2_s9_domain_1) & p1_s9_domain_1(B,C) & A = f4_s9_domain_1(B,C) & m1_subset_1(B,f1_s9_domain_1))) <-> r2_hidden(A,a_0_2_domain_1))) # label(fraenkel_a_0_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1877 $T # label(t1_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1878 (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]. 6.36/6.34 1879 (all A all B all C all D all E all F all G all H all I (-v1_xboole_0(C) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(I,k1_zfmisc_1(E)) & m1_subset_1(F,k1_zfmisc_1(B)) & -v1_xboole_0(E) & -v1_xboole_0(D) & -v1_xboole_0(B) -> ((exists J exists K exists L exists M (m1_subset_1(K,C) & m1_subset_1(M,E) & A = k5_domain_1(B,C,D,E,J,K,L,M) & r2_hidden(J,F) & r2_hidden(M,I) & r2_hidden(L,H) & r2_hidden(K,G) & m1_subset_1(L,D) & m1_subset_1(J,B))) <-> r2_hidden(A,a_8_0_domain_1(B,C,D,E,F,G,H,I))))) # label(fraenkel_a_8_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1880 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> ((exists D exists E (k1_domain_1(B,C,D,E) = A & p1_s2_domain_1(D,E) & m1_subset_1(E,C) & m1_subset_1(D,B))) <-> r2_hidden(A,a_2_3_domain_1(B,C))))) # label(fraenkel_a_2_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1881 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> ((exists E (A = E & -r2_hidden(E,D) & r2_hidden(E,C) & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_3_domain_1(B,C,D))))) # label(fraenkel_a_3_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1882 (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]. 6.36/6.34 1883 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(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]. 6.36/6.34 1884 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k3_subset_1(A,B) = a_2_2_domain_1(A,B))))) # label(t57_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1885 $T # label(t11_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1886 $T # label(t10_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1887 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_6_domain_1(B)) <-> (exists C (m1_subset_1(C,B) & A = C & p2_s6_domain_1(C)))))) # label(fraenkel_a_1_6_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1888 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_subset_1(D,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]. 6.36/6.34 1889 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(D,B) & m1_subset_1(C,A) & -v1_xboole_0(A) -> m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)))) # label(dt_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1890 (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]. 6.36/6.34 1891 $T # label(t34_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1892 (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) -> k17_domain_1(A,B,C,D) = k20_mcart_1(D))) # label(redefinition_k17_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1893 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)))) # label(dt_k6_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1894 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> ((exists E (m1_subset_1(E,B) & (exists F ((exists G (m1_subset_1(G,D) & A = k3_mcart_1(E,F,G))) & m1_subset_1(F,C))))) <-> r2_hidden(A,k3_zfmisc_1(B,C,D))))))))) # label(t15_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1895 (all A (r2_hidden(A,a_0_0_domain_1) <-> (exists B (m1_subset_1(B,f1_s7_domain_1) & p1_s7_domain_1(B) & B = A)))) # label(fraenkel_a_0_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1896 (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]. 6.36/6.34 1897 (all A all B all C all D (m1_subset_1(C,A) & m1_subset_1(D,B) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k4_tarski(C,D) = k1_domain_1(A,B,C,D))) # label(redefinition_k1_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1898 (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 -> H = A))))))))) <-> k9_mcart_1(B,C,D,E,F) = A))))))))))) # label(t41_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1899 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) & -v1_xboole_0(C) -> 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]. 6.36/6.34 1900 (all A all B all C all D all E all F all G (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) & -v1_xboole_0(B) -> (r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G)) <-> (exists H exists I exists J (m1_subset_1(H,B) & m1_subset_1(I,C) & r2_hidden(H,E) & r2_hidden(I,F) & r2_hidden(J,G) & k4_domain_1(B,C,D,H,I,J) = A & m1_subset_1(J,D)))))) # label(fraenkel_a_6_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1901 (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_5_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_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1902 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k2_tarski(B,C) = k7_domain_1(A,B,C))) # label(redefinition_k7_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1903 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) -> m1_subset_1(k3_domain_1(A,B,C),B))) # label(dt_k3_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1904 $T # label(t35_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1905 $T # label(t2_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1906 $T # label(t18_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1907 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(B,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]. 6.36/6.34 1908 (all A all B all C all D all E all F all G all H (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(H,A) & m1_subset_1(G,A) & m1_subset_1(E,A) & m1_subset_1(D,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]. 6.36/6.34 1909 $T # label(t30_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1910 $T # label(t21_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1911 $T # label(t4_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1912 $T # label(t39_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1913 (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]. 6.36/6.34 1914 $T # label(t5_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1915 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_subset_1(C,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]. 6.36/6.34 1916 $T # label(t44_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1917 $T # label(t19_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1918 (all A all B all C all D all E all F all G (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(G,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]. 6.36/6.34 1919 (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]. 6.36/6.34 1920 (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)) -> k12_mcart_1(A,B,C,D) = a_4_1_domain_1(A,B,C,D))))))))) # label(t53_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1921 (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(H,A) & m1_subset_1(I,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) -> k6_enumset1(B,C,D,E,F,G,H,I) = k13_domain_1(A,B,C,D,E,F,G,H,I))) # label(redefinition_k13_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1922 (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]. 6.36/6.34 1923 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_subset_1(D,k2_zfmisc_1(A,k2_zfmisc_1(B,C))) & -v1_xboole_0(C) -> m1_subset_1(k16_domain_1(A,B,C,D),B))) # label(dt_k16_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1924 $T # label(t23_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1925 (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)) -> (A = k7_mcart_1(B,C,D,E) <-> (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) -> H = A)))))))))))))))) # label(t26_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1926 (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]. 6.36/6.34 1927 (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]. 6.36/6.34 1928 (all A all B all C (-v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,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]. 6.36/6.34 1929 (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]. 6.36/6.34 1930 (all A all B all C all D all E all F all G (m1_subset_1(D,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(E,A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(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]. 6.36/6.34 1931 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_3_domain_1(B)) <-> (exists C (A = C & p1_s5_domain_1(C) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_3_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1932 (all A all B all C all D all E all F all G all H (m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(E,A) & m1_subset_1(D,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]. 6.36/6.34 1933 $T # label(t37_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1934 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_0_domain_1(B,C)) <-> (exists D exists E (k1_domain_1(B,C,D,E) = A & m1_subset_1(E,C) & m1_subset_1(D,B)))))) # label(fraenkel_a_2_0_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1935 (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 (r2_hidden(E,A) <-> (exists F (m1_subset_1(F,B) & (exists G (m1_subset_1(G,C) & (exists H (m1_subset_1(H,D) & E = k3_mcart_1(F,G,H))))))))) <-> A = k3_zfmisc_1(B,C,D)))))))))) # label(t17_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1936 (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) & k9_mcart_1(A,B,C,D,F) = k9_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = k11_mcart_1(A,B,C,D,F) & k10_mcart_1(A,B,C,D,E) = k10_mcart_1(A,B,C,D,F) -> F = E))))))))))))) # label(t45_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1937 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(B) -> (r2_hidden(A,a_2_2_domain_1(B,C)) <-> (exists D (m1_subset_1(D,B) & -r2_hidden(D,C) & A = D))))) # label(fraenkel_a_2_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1938 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> (k5_mcart_1(A,B,C,D) = k5_mcart_1(A,B,C,E) & k7_mcart_1(A,B,C,E) = k7_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) = k6_mcart_1(A,B,C,E) -> E = D))))))))))) # label(t28_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1939 (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) -> k8_domain_1(A,B,C,D) = k1_enumset1(B,C,D))) # label(redefinition_k8_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1940 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(B,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]. 6.36/6.34 1941 $T # label(t22_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1942 (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) -> k18_mcart_1(D) = k15_domain_1(A,B,C,D))) # label(redefinition_k15_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1943 $T # label(t14_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1944 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & m1_subset_1(D,A) & m1_subset_1(E,B) & m1_subset_1(F,C) -> k4_domain_1(A,B,C,D,E,F) = k3_mcart_1(D,E,F))) # label(redefinition_k4_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1945 $T # label(t8_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1946 (all A (-v1_xboole_0(A) -> a_1_0_domain_1(A) = A)) # label(t48_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1947 (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)) -> k4_subset_1(A,B,C) = a_3_2_domain_1(A,B,C))))))) # label(t59_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1948 (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)) -> (A = k10_mcart_1(B,C,D,E,F) <-> (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)))))))))))))))))))) # label(t42_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1949 (all A all B all C all D (-v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) -> (r2_hidden(A,a_3_1_domain_1(B,C,D)) <-> (exists E (m1_subset_1(E,B) & A = E & r2_hidden(E,C) & r2_hidden(E,D)))))) # label(fraenkel_a_3_1_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1950 (all A (r2_hidden(A,a_0_5_domain_1) <-> (exists B (m1_subset_1(B,f1_s10_domain_1) & p2_s10_domain_1(B) & A = B)))) # label(fraenkel_a_0_5_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1951 (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(C,A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_subset_1(G,A) & m1_subset_1(H,A) & m1_subset_1(I,A) & m1_subset_1(D,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]. 6.36/6.34 1952 (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 ((r2_hidden(E,C) | r2_hidden(E,D)) & E = A & m1_subset_1(E,B))) <-> r2_hidden(A,a_3_2_domain_1(B,C,D))))) # label(fraenkel_a_3_2_domain_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1953 (all A all B all C all D (-v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1954 (all A all B all C (v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_funcop_1(A,B,C)) & v1_relat_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1955 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,E,G),F) = k8_funct_2(B,A,D,G))) -> k7_funcop_1(A,B,C,E,F) = D))))))))))))) # label(t61_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1956 (all A (k2_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k1_relat_1(k2_funcop_1(k1_xboole_0,A)) = k1_xboole_0)) # label(t16_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1957 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k4_funcop_1(A,B,C)) & v1_relat_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1958 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(B,A),D)))))))) # label(t37_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1959 (all A all B all C all D all E (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(D,B,A) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> k3_funcop_1(C,D,E) = k6_funcop_1(A,B,C,D,E))) # label(redefinition_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1960 (all A all B k10_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A) # label(t21_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1961 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,A) & m2_relset_1(E,B,A) & v1_funct_1(E) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)) = k8_funct_2(B,A,D,G))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1962 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1963 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_2(k8_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k8_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k8_funcop_1(A,B,C,D,E)))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1964 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> (all E (m1_subset_1(E,A) -> k1_funct_1(k1_funcop_1(D),E) = k4_tarski(k2_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E)),k1_mcart_1(k8_funct_2(A,k2_zfmisc_1(B,C),D,E))))))))))))) # label(t71_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1965 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> ((all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) & k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) -> k3_funcop_1(C,A,B) = D))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1966 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k8_funcop_1(B,A,C,E,k8_funcop_1(B,A,C,F,D)) = k8_funcop_1(B,A,C,k2_binop_1(B,B,B,C,E,F),D)))))))))))))) # label(t77_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1967 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) & -v1_xboole_0(A) -> D = k10_funcop_1(A,B,C,k10_funcop_1(A,B,C,D)))) # label(involutiveness_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1968 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,A) & m2_relset_1(E,B,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k6_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),k8_funct_2(B,A,E,F)))))))))))))) # label(t48_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1969 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k7_relat_1(A,B),D)))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1970 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> -((all D all E k4_tarski(D,E) != k1_funct_1(A,C)) & k1_funct_1(A,C) != k1_funct_1(B,C)) & (all D all E (k4_tarski(D,E) = k1_funct_1(A,C) -> k4_tarski(E,D) = k1_funct_1(B,C))))) <-> k1_funcop_1(A) = B))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1971 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1972 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1973 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k3_funcop_1(B,k2_funcop_1(k1_relat_1(A),C),A) = k5_funcop_1(B,C,A)))))) # label(t41_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1974 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(k3_funcop_1(D,B,C),A) = k3_funcop_1(k5_relat_1(D,A),B,C))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1975 (all A k13_funct_3(k6_partfun1(A),k6_partfun1(A)) = k12_funct_3(A)) # label(t2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1976 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k8_funcop_1(A,A,B,C,k6_partfun1(A)),C))))))) # label(t70_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1977 (all A all B (v1_xboole_0(B) -> v2_funct_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_xboole_0(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1978 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1979 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k4_funcop_1(C,B,D),A) = k4_funcop_1(k5_relat_1(C,A),B,D)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1980 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k5_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k10_relat_1(A,B),C)))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1981 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funct_2(A,B,B,D,k8_funcop_1(B,B,C,E,k6_partfun1(B))) = k8_funcop_1(B,A,C,E,D))))))))))) # label(t69_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1982 (all A all B all C (-r2_hidden(B,C) -> k10_relat_1(k2_funcop_1(A,B),C) = k1_xboole_0)) # label(t22_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1983 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v1_binop_1(C,B) -> k7_funcop_1(B,A,C,D,E) = k8_funcop_1(B,A,C,E,D)))))))))))) # label(t79_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1984 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1985 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k2_relat_1(C)),k1_relat_1(A)) -> k3_xboole_0(k1_relat_1(B),k1_relat_1(C)) = k1_relat_1(k3_funcop_1(A,B,C))))))))) # label(t84_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1986 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k5_relat_1(k13_funct_3(B,k2_funcop_1(k1_relat_1(B),C)),A) = k4_funcop_1(A,B,C)))))) # label(d4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1987 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1988 (all A all B k2_zfmisc_1(A,k1_tarski(B)) = k2_funcop_1(A,B)) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1989 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & v1_funct_1(k7_funcop_1(A,B,C,D,E)))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1990 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> v1_funct_1(k4_funcop_1(C,D,E)) & v1_funct_2(k4_funcop_1(C,D,E),A,B) & m2_relset_1(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1991 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E)) = k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E)))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1992 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> k8_funct_2(A,B,F,G) = k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)))) -> k6_funcop_1(B,A,C,D,E) = F))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1993 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1994 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (k1_tarski(B) = k2_relat_1(A) -> k2_funcop_1(k1_relat_1(A),B) = A)))) # label(t15_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1995 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) -> k2_funcop_1(B,k1_funct_1(A,C)) = k5_relat_1(k2_funcop_1(B,C),A))))) # label(t23_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1996 (all A all B (A != k1_xboole_0 -> k1_tarski(B) = k2_relat_1(k2_funcop_1(A,B)))) # label(t14_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1997 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(B,D) = k7_relat_1(A,D) -> k7_relat_1(k3_funcop_1(E,A,C),D) = k7_relat_1(k3_funcop_1(E,B,C),D)))))))))) # label(t29_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1998 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,A),D) = k7_relat_1(k3_funcop_1(E,C,B),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 1999 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_2(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2000 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) -> v1_funct_1(k10_funcop_1(A,B,C,D)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2001 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k8_funcop_1(B,A,C,E,D),F) = k8_funcop_1(B,A,C,E,k7_funcop_1(B,A,C,D,F))))))))))))))) # label(t74_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2002 (all A all B (v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)))) # label(fc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2003 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,A) & v1_funct_2(D,A,A) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),D),C) = k2_binop_1(A,A,A,B,C,k8_funct_2(A,A,D,C)))))))))) # label(t54_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2004 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_funct_1(k4_funcop_1(B,A,D),C) = k1_binop_1(B,k1_funct_1(A,C),D))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2005 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k7_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k7_relat_1(A,C),B)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2006 (all A all B (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) # label(fc7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2007 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2008 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k5_funcop_1(D,E,B),C) = k7_relat_1(k5_funcop_1(D,E,A),C))))))))) # label(t43_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2009 (all A (v1_relat_1(A) -> (all B all C (k2_zfmisc_1(B,C) = A -> B = k1_xboole_0 | B = k1_relat_1(A) & k2_relat_1(A) = C | C = k1_xboole_0)))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2010 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> k5_relat_1(C,k3_funcop_1(D,A,B)) = k3_funcop_1(D,k5_relat_1(C,A),k5_relat_1(C,B)))))))))) # label(t31_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2011 (all A all B all C (r2_hidden(B,A) -> k1_funct_1(k2_funcop_1(A,C),B) = C)) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2012 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(A) -> k2_relat_1(D) = k9_funcop_1(A,B,C,D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2013 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C) = k2_binop_1(A,A,A,B,C,C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2014 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2015 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,B) & m2_relset_1(E,B,B) -> k6_funcop_1(B,A,C,k7_funct_2(A,B,B,D,E),D) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,E,k6_partfun1(B))))))))))))) # label(t52_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2016 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,A,B) & v1_funct_2(F,A,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,D,k6_funcop_1(B,A,C,E,F)) = k6_funcop_1(B,A,C,k6_funcop_1(B,A,C,D,E),F)))))))))))))) # label(t76_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2017 (all A all B all C all D all E (m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & m1_subset_1(D,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k8_funcop_1(A,B,C,D,E) = k5_funcop_1(C,D,E))) # label(redefinition_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2018 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funcop_1(k1_funcop_1(A)) = A)) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2019 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_xboole_0 = k1_relat_1(B) & k1_relat_1(A) = k1_xboole_0 -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2020 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(A,C) = B)) -> A = k2_funcop_1(k1_relat_1(A),B))))) # label(t17_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2021 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(B) = k1_relat_1(A) -> k1_relat_1(k5_relat_1(C,A)) = k1_relat_1(k5_relat_1(C,B))))))))) # label(t3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2022 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(B,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2023 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k7_relat_1(A,B))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2024 (all A all B (-v1_xboole_0(B) -> v1_funct_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2025 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> k5_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2026 (exists A (v1_funcop_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2027 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2028 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) & m1_subset_1(E,A) & v1_funct_1(C) & -v1_xboole_0(B) -> k7_funcop_1(A,B,C,D,E) = k4_funcop_1(C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2029 (all A all B (r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) & A = k1_relat_1(k2_funcop_1(A,B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2030 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D k5_funcop_1(k5_relat_1(C,A),D,B) = k5_relat_1(k5_funcop_1(C,D,B),A)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2031 (all A (v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2032 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F) = k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2033 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> k7_funcop_1(B,A,C,D,E) = k7_funct_2(A,B,B,D,k7_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t63_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2034 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C))))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2035 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (v3_binop_1(C,B) -> k6_funcop_1(B,A,C,D,D) = D))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2036 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2037 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(k4_funcop_1(D,B,E),C) = k7_relat_1(k4_funcop_1(D,A,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.34 2038 (all A all B all C (r2_hidden(B,C) -> A = k10_relat_1(k2_funcop_1(A,B),C))) # label(t20_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2039 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k1_funcop_1(A)) & v1_relat_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2040 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k6_funcop_1(A,A,B,k6_partfun1(A),k6_partfun1(A)),C))))))) # label(t56_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2041 (all A all B all C (r2_hidden(C,B) -> v1_funct_1(k2_funcop_1(A,C)) & v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B))) # label(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2042 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k5_funcop_1(B,D,A))) -> k1_binop_1(B,D,k1_funct_1(A,C)) = k1_funct_1(k5_funcop_1(B,D,A),C))))))) # label(t42_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2043 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2044 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k7_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,E),F) = k7_funcop_1(B,A,C,D,k2_binop_1(B,B,B,C,E,F))))))))))))))) # label(t78_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2045 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (all E (m1_subset_1(E,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2046 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2047 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k1_funcop_1(D) = k10_funcop_1(A,B,C,D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2048 (all A k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A)) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2049 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B (r2_hidden(B,k1_relat_1(A)) -> v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)))) <-> v1_funcop_1(A)))) # label(d6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2050 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> m2_relset_1(k5_funcop_1(C,E,D),A,B) & v1_funct_2(k5_funcop_1(C,E,D),A,B) & v1_funct_1(k5_funcop_1(C,E,D)))))))))))) # label(t65_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2051 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)) = k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2052 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> v1_funct_1(k3_funcop_1(C,D,E)) & m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2053 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B k7_relat_1(k1_funcop_1(A),B) = k1_funcop_1(k7_relat_1(A,B))))) # label(t7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2054 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2055 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2056 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) -> k4_relat_1(k9_funcop_1(A,B,C,D)) = k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2057 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2058 (all A all B all C all D all E (v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,B,A) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & m1_relset_1(D,B,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k6_funcop_1(A,B,C,D,E)) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2059 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2060 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2061 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(C) & v1_funct_1(C) -> v1_relat_1(k5_funcop_1(A,B,C)) & v1_funct_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2062 (all A all B all C k7_relat_1(k2_funcop_1(A,B),C) = k2_funcop_1(k3_xboole_0(A,C),B)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2063 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(B != k1_xboole_0 & r2_hidden(C,k1_relat_1(A)) & k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)) = k1_xboole_0)))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2064 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,D,E) = k6_funcop_1(B,A,C,E,D)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2065 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),k6_partfun1(B))) = k6_funcop_1(B,A,C,D,D))))))))) # label(t53_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2066 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> k3_funcop_1(A,B,C) = k5_relat_1(k13_funct_3(B,C),A))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2067 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(A,k7_relat_1(B,C)) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2068 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(k3_funcop_1(C,A,B),D))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2069 (all A all B all C k1_funcop_1(k2_funcop_1(A,k4_tarski(B,C))) = k2_funcop_1(A,k4_tarski(C,B))) # label(t26_funcop_1) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2070 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_4(A,B)) & v1_relat_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2071 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2072 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & m2_relset_1(G,k2_zfmisc_1(A,B),E) -> (all H (m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_2(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & v1_funct_1(k3_funct_4(G,H)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2073 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_funct_4(A,B)) <-> r1_partfun1(A,B)))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2074 (all A all B (v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) & v1_relat_1(A) -> A = k1_funct_4(A,A))) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2075 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> B = k1_funct_4(B,A) & k1_funct_4(A,B) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2076 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2077 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_partfun1(B,C) -> k1_funct_1(k1_funct_4(B,C),A) = k1_funct_1(B,A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2078 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (C != k1_xboole_0 -> k2_funct_4(k2_funct_4(D)) = D))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2079 (all A all B (r1_tarski(A,B) <-> r1_tarski(k6_partfun1(A),k6_partfun1(B)))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2080 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(C,k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(A,C))))))) # label(t76_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2081 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> k2_zfmisc_1(B,A) = k1_relat_1(k2_funct_4(C))))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2082 (all A all B all C all D (A != B -> k1_funct_1(k4_funct_4(A,B,C,D),B) = D & k1_funct_1(k4_funct_4(A,B,C,D),A) = C)) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2083 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(B,A) = k1_funct_4(A,B)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2084 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2085 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_partfun1(A,B) -> k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2086 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2087 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2088 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(C,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2089 (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]. 6.36/6.35 2090 (all A all B all C all D all E all F all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (v1_funct_2(H,k2_zfmisc_1(D,E),F) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> -(C != k1_xboole_0 & F != k1_xboole_0 & -(v1_funct_1(k3_funct_4(G,H)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)))))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2091 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) -> v1_funct_1(k5_funct_4(A,B,C,D,E)) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2092 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2093 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2094 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B A = k1_funct_4(A,k7_relat_1(A,B))))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2095 (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]. 6.36/6.35 2096 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C))) -> k1_funct_1(C,k4_tarski(B,A)) = k1_funct_1(k2_funct_4(C),k4_tarski(A,B))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2097 (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]. 6.36/6.35 2098 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,k1_funct_4(B,C)))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2099 (all A all B all C all D (v1_funct_1(k4_funct_4(A,B,C,D)) & v1_relat_1(k4_funct_4(A,B,C,D)))) # label(fc1_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2100 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(k1_funct_4(B,C))) <-> r2_hidden(A,k1_relat_1(B)) | r2_hidden(A,k1_relat_1(C))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2101 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (v1_partfun1(D,A,B) -> k1_funct_4(C,D) = D))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2102 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_xboole_0(A,B) = k1_funct_4(A,B) <-> r1_partfun1(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2103 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(k2_funct_4(C)) = k2_relat_1(C)))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2104 (all A all B all C all D (A != C -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2105 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k7_relat_1(k1_funct_4(A,B),k1_relat_1(A)) = A))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2106 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2107 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2108 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D all E all F all G (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & r2_hidden(k4_tarski(F,G),k1_relat_1(B)) -> k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G))) = k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))))) & (all D (r2_hidden(D,k1_relat_1(C)) <-> (exists E exists F exists G exists H (k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & r2_hidden(k4_tarski(E,F),k1_relat_1(A)))))) <-> C = k3_funct_4(A,B)))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2109 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2110 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2111 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k3_funct_4(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t59_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2112 (all A all B all C all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (C != k1_xboole_0 -> v1_funct_1(k2_funct_4(D)) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C)))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2113 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> B = k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)))))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2114 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> k4_funct_4(B,C,D,E) = k5_funct_4(A,B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2115 (all A all B all C all D all E all F (k4_funct_4(A,B,E,F) = k4_funct_4(A,B,C,D) -> E = C & F = D | B = A)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2116 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(B,C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2117 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k2_funct_4(A)) & v1_funct_1(k2_funct_4(A)))) # label(dt_k2_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2118 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2119 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_funct_4(A) = B <-> (all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(A,k4_tarski(C,D)) = k1_funct_1(B,k4_tarski(D,C)))) & (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (r2_hidden(k4_tarski(D,E),k1_relat_1(A)) & k4_tarski(E,D) = C))))))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2120 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,A) = k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2121 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k1_relat_1(E) = k2_tarski(A,B) & D = k1_funct_1(E,B) & C = k1_funct_1(E,A) -> k4_funct_4(A,B,C,D) = E))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2122 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2123 (all A -((all B all C -r1_tarski(A,k2_zfmisc_1(B,C))) & (all B -((all C all D k4_tarski(C,D) != B) & r2_hidden(B,A))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2124 (all A all B all C all D all E all F all G (v1_funct_1(G) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_1(H) -> v1_funct_1(k3_funct_4(G,H)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)))))) # label(t62_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2125 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2126 (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]. 6.36/6.35 2127 (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]. 6.36/6.35 2128 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_relat_1(B) -> k1_funct_4(A,C) = k1_funct_4(k1_funct_4(A,B),C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2129 (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]. 6.36/6.35 2130 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k7_relat_1(k1_funct_4(A,B),k4_xboole_0(k1_relat_1(A),k1_relat_1(B))),A))))) # label(t25_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2131 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> B = k1_funct_4(A,B)))))) # label(t20_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2132 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2133 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k3_funct_4(A,B)) & v1_relat_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2134 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> k1_xboole_0 = A | B = D)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2135 (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]. 6.36/6.35 2136 (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]. 6.36/6.35 2137 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(C,D) & r1_tarski(k1_relat_1(B),D) -> k7_relat_1(k1_funct_4(A,B),D) = B & A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t81_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2138 (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]. 6.36/6.35 2139 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_4(A,k1_xboole_0) = A)) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2140 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_xboole_0(k1_relat_1(A),k1_relat_1(B)) -> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t36_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2141 (all A all B all C k4_funct_4(A,B,C,C) = k2_funcop_1(k2_tarski(A,B),C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2142 (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]. 6.36/6.35 2143 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_xboole_0(k1_relat_1(B),C) & r1_tarski(k1_relat_1(A),C) -> A = k7_relat_1(k1_funct_4(A,B),C))))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2144 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(k1_xboole_0,A) = A)) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2145 (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]. 6.36/6.35 2146 (all A all B k1_funct_4(k6_partfun1(A),k6_partfun1(B)) = k6_partfun1(k2_xboole_0(A,B))) # label(t23_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2147 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t9_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2148 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> k2_funct_4(k2_funct_4(D)) = D)))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2149 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k7_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C))))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2150 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2151 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> k1_funct_4(C,D) = D))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2152 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> k1_funct_4(B,C) = C)))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2153 (all A all B all C all D all E (v1_relat_1(E) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2154 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))) # label(t49_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2155 (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]. 6.36/6.35 2156 (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]. 6.36/6.35 2157 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (C = k1_funct_4(A,B) <-> k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) & (all D (r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)) & (-r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2158 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2159 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k1_funct_4(C,D),A,B) & v1_funct_1(k1_funct_4(C,D)))))) # label(t41_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2160 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_xboole_0(k1_relat_1(B),k1_relat_1(C)) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t17_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2161 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r1_tarski(k1_relat_1(A),k2_xboole_0(B,C)) -> k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = A)))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2162 (all A all B all C all D (B != A -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2163 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r2_hidden(k4_tarski(A,C),k1_relat_1(E)) & r2_hidden(k4_tarski(B,D),k1_relat_1(F)) <-> r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k1_relat_1(k3_funct_4(E,F)))))))) # label(t57_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2164 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2165 (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]. 6.36/6.35 2166 (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> p1_s1_ordinal2(B)))) -> A = k1_xboole_0 | p1_s1_ordinal2(A)))) & p1_s1_ordinal2(k1_xboole_0) -> (all A (v3_ordinal1(A) -> p1_s1_ordinal2(A))) # label(s1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.36/6.35 2167 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2168 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2169 (all A (v3_ordinal1(A) -> (all B (B = f1_s8_ordinal2(A) <-> (exists C (v1_funct_1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s8_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f4_s8_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & f2_s8_ordinal2 = k1_funct_1(C,k1_xboole_0) & B = k1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2170 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s6_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0))) <-> f2_s6_ordinal2(A) = B)))) & k1_relat_1(f1_s6_ordinal2) = f3_s6_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,A) = f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) | k1_xboole_0 = A))) & (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_xboole_0) = f4_s6_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s6_ordinal2)) -> k1_funct_1(f1_s6_ordinal2,A) = f2_s6_ordinal2(A)))) # label(s6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2171 (all A (v3_ordinal1(A) -> (all B -((all C (v3_ordinal1(C) -> -(r1_ordinal1(A,C) & r2_hidden(C,B)))) & r2_hidden(A,k7_ordinal2(B)))))) # label(t29_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2172 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,C) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2173 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k10_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & k9_ordinal2(C) = B & k1_relat_1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & v1_ordinal2(C) & v1_relat_1(C)))))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2174 (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]. 6.46/6.44 2175 (exists A (v1_relat_1(A) & v1_ordinal2(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2176 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2177 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2178 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f1_s14_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f3_s14_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f4_s14_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_funct_1(C) & v1_relat_1(C)))))))) -> f1_s14_ordinal2(k1_xboole_0) = f2_s14_ordinal2 # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2179 (exists A (v1_funct_1(A) & v1_ordinal2(A) & k1_relat_1(A) = f1_s3_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> k1_funct_1(A,B) = f2_s3_ordinal2(B)))) & v5_ordinal1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2180 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2181 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2182 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k14_ordinal2(B,D) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2183 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2184 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_ordinal2(A) <-> (exists B (r1_tarski(k2_relat_1(A),B) & v3_ordinal1(B)))))) # label(d8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2185 (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]. 6.46/6.44 2186 (all A (v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2187 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2188 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2189 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k14_ordinal2(A,B)))))) # label(t45_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2190 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2191 (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]. 6.46/6.44 2192 (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]. 6.46/6.44 2193 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2194 (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]. 6.46/6.44 2195 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.46/6.44 2196 (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]. 6.46/6.44 2197 f2_s10_ordinal2 != k1_xboole_0 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & k1_relat_1(f1_s10_ordinal2) = f2_s10_ordinal2 & v4_ordinal1(f2_s10_ordinal2) & (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s10_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s10_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C))) <-> B = f3_s10_ordinal2(A))))) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2198 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (f3_s16_ordinal2(A) = B <-> (exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & B = k1_ordinal2(C) & k1_funct_1(C,k1_xboole_0) = f4_s16_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s16_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | k1_xboole_0 = D))) & k1_ordinal1(A) = k1_relat_1(C) & v1_relat_1(C)))))))) & f2_s16_ordinal2 != k1_xboole_0 & k1_relat_1(f1_s16_ordinal2) = f2_s16_ordinal2 & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s16_ordinal2) -> k1_funct_1(f1_s16_ordinal2,A) = f3_s16_ordinal2(A)))) & v4_ordinal1(f2_s16_ordinal2) -> f3_s16_ordinal2(f2_s16_ordinal2) = f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2199 (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]. 6.50/6.45 2200 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & k1_ordinal1(B) = k1_relat_1(D) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k15_ordinal2(A,k1_funct_1(D,E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_xboole_0 = E | k12_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E)))) & k1_ordinal2(D) = C & v1_ordinal2(D) & v5_ordinal1(D))) <-> C = k16_ordinal2(A,B)))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2201 (exists A (v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s2_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> k1_funct_1(A,B) = f2_s2_ordinal2(B)))) & v1_relat_1(A))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2202 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k14_ordinal2(k15_ordinal2(A,B),B) = k15_ordinal2(k1_ordinal1(A),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2203 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k4_ordinal2) = A & k16_ordinal2(k4_ordinal2,A) = k4_ordinal2)) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2204 (all A (v3_ordinal1(A) -> (all B ((all C (v3_ordinal1(C) -> (r2_hidden(C,B) -> r1_ordinal1(A,C)))) -> r1_ordinal1(A,k6_ordinal2(B)) | k2_ordinal2(B) = k1_xboole_0)))) # label(t23_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2205 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2206 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2207 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A) & k9_ordinal2(A) = k6_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2208 (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]. 6.50/6.45 2209 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2210 (all A (A = k5_ordinal2 <-> r2_hidden(k1_xboole_0,A) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(k1_xboole_0,B) -> r1_tarski(A,B)))) & v3_ordinal1(A) & v4_ordinal1(A))) # label(d5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2211 (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]. 6.50/6.45 2212 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2213 (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]. 6.50/6.45 2214 (all A (v3_ordinal1(A) -> k1_ordinal1(A) = k7_ordinal2(k1_tarski(A)))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2215 (all A all B (v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2216 (all A all B (v3_ordinal1(A) & v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2217 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_relat_1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k8_ordinal2(C) = B & v1_funct_1(C) & v1_relat_1(C))) <-> B = k11_ordinal2(A)))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2218 (all A (v3_ordinal1(A) -> k16_ordinal2(A,k1_xboole_0) = k4_ordinal2)) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2219 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2220 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2221 (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]. 6.50/6.45 2222 (all A (v3_ordinal1(A) -> (all B (v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> v3_ordinal1(k1_funct_1(B,A))))))) # label(t34_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2223 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k16_ordinal2(B,D)))) -> k12_ordinal2(C) = k16_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2224 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) -> A = k1_xboole_0 | r2_hidden(k15_ordinal2(B,A),k15_ordinal2(C,A))))))))) # label(t57_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2225 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_relat_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_funct_1(B,A) = k1_ordinal2(B)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2226 (all A (v3_ordinal1(A) -> A = k14_ordinal2(A,k1_xboole_0))) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2227 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2228 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2229 (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]. 6.50/6.45 2230 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.50/6.45 2231 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v1_funct_1(C) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k1_relat_1(C) = A & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k3_tarski(k8_ordinal2(C)) = k15_ordinal2(A,B))))))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2232 (all A (v3_ordinal1(A) -> k1_xboole_0 = k15_ordinal2(k1_xboole_0,A))) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2233 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2234 (all A all B (v3_ordinal1(B) -> v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2235 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f4_s15_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & f1_s15_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | f3_s15_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f2_s15_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_ordinal1(A) = k1_relat_1(C) & k1_ordinal2(C) = B & v1_funct_1(C)))))))) -> (all A (v3_ordinal1(A) -> f2_s15_ordinal2(A,f4_s15_ordinal2(A)) = f4_s15_ordinal2(k1_ordinal1(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2236 (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]. 6.67/6.60 2237 (all A (v3_ordinal1(A) -> (exists B ((exists C (v3_ordinal1(C) & v4_ordinal1(B) & v4_ordinal2(C) & k14_ordinal2(B,C) = A)) & v3_ordinal1(B))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2238 (exists A (v1_relat_1(A) & v5_ordinal1(A) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & (all B (v3_ordinal1(B) -> (v4_ordinal1(B) & r2_hidden(B,f1_s11_ordinal2) -> k1_xboole_0 = B | k1_funct_1(A,B) = f4_s11_ordinal2(B,k2_ordinal1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> f3_s11_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & f1_s11_ordinal2 = k1_relat_1(A) & v1_ordinal2(A) & v1_funct_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2239 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2240 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f2_s12_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> f5_s12_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | f6_s12_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & B = k1_ordinal2(C)))))))) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_xboole_0) = f4_s12_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> A = k1_xboole_0 | f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A)) = k1_funct_1(f1_s12_ordinal2,A)))) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> f2_s12_ordinal2(A) = k1_funct_1(f1_s12_ordinal2,A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2241 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2242 (all A (v3_ordinal1(A) -> A = k15_ordinal2(k4_ordinal2,A) & k15_ordinal2(A,k4_ordinal2) = A)) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.60 2243 (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]. 6.67/6.62 2244 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2245 (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]. 6.67/6.62 2246 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_ordinal2(D) = C & A = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k1_funct_1(D,E) = k8_ordinal2(k2_ordinal1(D,E)) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_funct_1(D,k1_ordinal1(E)) = k1_ordinal1(k1_funct_1(D,E))))) & k1_ordinal1(B) = k1_relat_1(D))) <-> C = k14_ordinal2(A,B)))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2247 (all A all B (v3_ordinal1(B) -> ((all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C)))) & r1_tarski(k2_ordinal2(A),B) <-> k7_ordinal2(A) = B))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2248 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2249 (exists A (v2_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2250 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A))) # label(d10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2251 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2252 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_ordinal2(A) -> v1_ordinal2(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2253 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2254 (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]. 6.67/6.62 2255 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_relat_1(C))) & B != A & (exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = A & k1_relat_1(C) = k1_ordinal1(f1_s13_ordinal2) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s13_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_ordinal2(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.67/6.62 2256 (exists A (v3_ordinal1(A) & (exists B (v1_relat_1(B) & v5_ordinal1(B) & A = k1_ordinal2(B) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & f2_s13_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> f3_s13_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(C) -> k1_funct_1(B,C) = f4_s13_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & v1_ordinal2(B) & v1_funct_1(B))))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2257 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k16_ordinal2(A,B)))) # label(dt_k16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2258 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2259 (all A k6_ordinal2(A) = k1_setfam_1(k2_ordinal2(A))) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2260 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2261 (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]. 6.71/6.66 2262 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & B = k1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f2_s9_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f3_s9_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & k1_funct_1(C,k1_xboole_0) = f1_s9_ordinal2 & k1_relat_1(C) = k1_ordinal1(A) & v5_ordinal1(C) & v1_relat_1(C))) <-> f4_s9_ordinal2(A) = B)))) -> (all A (v3_ordinal1(A) -> f4_s9_ordinal2(k1_ordinal1(A)) = f2_s9_ordinal2(A,f4_s9_ordinal2(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2263 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v5_ordinal1(D) & v1_ordinal2(D) & k1_funct_1(D,k1_xboole_0) = k1_xboole_0 & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(A)) -> k1_funct_1(D,E) = k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) | E = k1_xboole_0))) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(A)) -> k14_ordinal2(k1_funct_1(D,E),B) = k1_funct_1(D,k1_ordinal1(E))))) & k1_relat_1(D) = k1_ordinal1(A) & C = k1_ordinal2(D) & v1_funct_1(D) & v1_relat_1(D))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2264 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2265 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2266 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2267 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2268 f1_s4_ordinal2 = k1_relat_1(f5_s4_ordinal2) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_xboole_0) = f2_s4_ordinal2) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) | k1_xboole_0 = A))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A)) = k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f1_s4_ordinal2) -> k1_xboole_0 = A | f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,A)))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) -> f6_s4_ordinal2 = f5_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2269 (all A (v3_ordinal1(A) -> k7_ordinal2(A) = A)) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2270 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2271 (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]. 6.71/6.66 2272 (all A all B -((exists C (v1_funct_1(C) & k1_ordinal2(C) = A & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D) | D = k1_xboole_0))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & f2_s7_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & v5_ordinal1(C) & v1_relat_1(C))) & A != B & (exists C (v1_funct_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> k1_funct_1(C,D) = f4_s7_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & B = k1_ordinal2(C) & v1_relat_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2273 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> f3_s7_ordinal2(C,k1_funct_1(B,C)) = k1_funct_1(B,k1_ordinal1(C))))) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C)) | k1_xboole_0 = C))) & k1_funct_1(B,k1_xboole_0) = f2_s7_ordinal2 & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(B) & k1_ordinal2(B) = A & v5_ordinal1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2274 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (k1_funct_1(A,B) = C & v4_ordinal1(B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | k1_xboole_0 = B))))) <-> v3_ordinal2(A)))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2275 (all A all B ((all C (r2_hidden(C,B) <-> r2_hidden(C,A) & (exists D (D = C & v4_ordinal1(D) & v3_ordinal1(D))))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2276 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2277 (all A (v3_ordinal1(A) -> (all B (v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) & v1_relat_1(B) -> (k1_xboole_0 != A -> ((all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -((all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r1_ordinal1(E,F) & r2_hidden(F,k1_relat_1(B)) -> r2_hidden(k1_funct_1(B,F),D) & r2_hidden(C,k1_funct_1(B,F))))) & r2_hidden(E,k1_relat_1(B))))) & r2_hidden(A,D) & r2_hidden(C,A)))))) <-> r1_ordinal2(A,B))) & (A = k1_xboole_0 -> ((exists C ((all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_xboole_0))) & r2_hidden(C,k1_relat_1(B)) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2278 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2279 (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]. 6.71/6.66 2280 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2281 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2282 (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]. 6.71/6.66 2283 (exists A (v1_relat_1(A) & v5_ordinal1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> f3_s5_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> k1_funct_1(A,B) = f4_s5_ordinal2(B,k2_ordinal1(A,B)) | B = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & v1_funct_1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2284 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k16_ordinal2(A,k1_ordinal1(B)) = k15_ordinal2(A,k16_ordinal2(A,B)))))) # label(t61_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2285 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2286 (all A all B ((all C (r2_hidden(C,A) & v3_ordinal1(C) <-> r2_hidden(C,B))) <-> B = k2_ordinal2(A))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2287 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2288 (all A all B all C (v1_finset_1(A) & v1_finset_1(C) & v1_finset_1(B) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2289 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2290 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2291 (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]. 6.71/6.66 2292 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2293 (all A -(v1_finset_1(A) & k1_xboole_0 != A & (all B -((all C (r2_hidden(C,A) -> r1_tarski(B,C))) & r2_hidden(B,A))) & v6_ordinal1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2294 (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]. 6.71/6.66 2295 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2296 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2297 (all A all B all C (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(fc15_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2298 (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]. 6.71/6.66 2299 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(t28_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2300 (all A -(v1_finset_1(A) & v6_ordinal1(A) & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2301 (all A all B (v1_finset_1(k2_zfmisc_1(A,B)) -> v1_finset_1(B) | A = k1_xboole_0)) # label(t23_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2302 (all A (v1_finset_1(k1_zfmisc_1(A)) <-> v1_finset_1(A))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2303 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2304 (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]. 6.71/6.66 2305 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) & v1_finset_1(D) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2306 (all A ((exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))) <-> v1_finset_1(A))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2307 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.66 2308 (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]. 6.71/6.66 2309 (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]. 6.71/6.67 2310 (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]. 6.71/6.67 2311 (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]. 6.71/6.67 2312 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2313 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2314 (exists A (-v1_xboole_0(A) & v1_finset_1(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2315 (all A exists B (v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v2_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v1_ordinal1(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2316 (all A all B (-v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2317 (all A all B (v1_finset_1(k2_zfmisc_1(B,A)) -> v1_finset_1(B) | A = k1_xboole_0)) # label(t22_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2318 (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]. 6.71/6.67 2319 (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]. 6.71/6.67 2320 (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]. 6.71/6.67 2321 (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]. 6.71/6.67 2322 (all A all B (v1_funct_1(A) & v1_finset_1(B) & v1_relat_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2323 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(t19_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2324 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2325 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2326 (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]. 6.71/6.67 2327 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2328 (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]. 6.71/6.67 2329 (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]. 6.71/6.67 2330 (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]. 6.71/6.67 2331 (exists A (v1_funct_1(A) & k1_relat_1(A) = f1_s1_finset_1 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (p1_s1_finset_1(B) -> k1_funct_1(A,B) = f2_s1_finset_1(B)) & (-p1_s1_finset_1(B) -> k1_funct_1(A,B) = f3_s1_finset_1(B))))) & v1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2332 p1_s2_finset_1(k1_xboole_0) & (all A all B (p1_s2_finset_1(B) & r1_tarski(B,f1_s2_finset_1) & r2_hidden(A,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & v1_finset_1(f1_s2_finset_1) -> p1_s2_finset_1(f1_s2_finset_1) # label(s2_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2333 (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]. 6.71/6.67 2334 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2335 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2336 (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]. 6.71/6.67 2337 (all A (v1_finset_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & (all C -(r2_hidden(C,B) & (all D (r1_tarski(C,D) & r2_hidden(D,B) -> D = C))))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2338 (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]. 6.71/6.67 2339 (all A (v1_finset_1(k3_tarski(A)) <-> v1_finset_1(A) & (all B (r2_hidden(B,A) -> v1_finset_1(B))))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2340 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v1_finset_1(k1_relat_1(A)) -> v1_finset_1(k2_relat_1(A))))) # label(t26_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2341 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2342 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & -v1_xboole_0(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2343 (all A (-v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2344 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2345 (all A (-v1_xboole_0(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) & v3_finsub_1(k5_finsub_1(A)) & v1_finsub_1(k5_finsub_1(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2346 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2347 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k2_xboole_0(B,C),A))) <-> v1_finsub_1(A))) # label(d1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2348 $T # label(t6_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2349 (all A (v1_finsub_1(A) & v3_finsub_1(A) <-> v4_finsub_1(A))) # label(d4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2350 $T # label(t22_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2351 $T # label(t31_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2352 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> m1_subset_1(k4_finsub_1(A,B,C),A))) # label(dt_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2353 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> r2_hidden(k1_xboole_0,A))) # label(t18_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2354 $T # label(t4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2355 $T # label(t9_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2356 (all A all B (r1_tarski(A,B) -> r1_tarski(k5_finsub_1(A),k5_finsub_1(B)))) # label(t23_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2357 $T # label(t12_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2358 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (v1_finset_1(A) -> m1_subset_1(B,k5_finsub_1(A))))) # label(t34_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2359 $T # label(t5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2360 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(A,C) & m1_subset_1(B,C) -> m1_subset_1(k5_xboole_0(A,B),C)))) # label(t14_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2361 (all A (v2_finsub_1(A) <-> (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k3_xboole_0(B,C),A))))) # label(d2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2362 (all A (v1_finset_1(A) -> k5_finsub_1(A) = k1_zfmisc_1(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2363 $T # label(t33_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2364 (all A v4_finsub_1(k1_zfmisc_1(A))) # label(t20_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2365 $T # label(t2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2366 (all A ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_xboole_0(B,C),A))) <-> v3_finsub_1(A))) # label(d3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2367 $T # label(t1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2368 $T # label(t29_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2369 (all A all B all C (v4_finsub_1(C) & -v1_xboole_0(C) -> (m1_subset_1(B,C) & m1_subset_1(A,C) -> m1_subset_1(k3_xboole_0(A,B),C)))) # label(t13_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2370 (all A all B k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B)) = k5_finsub_1(k3_xboole_0(A,B))) # label(t24_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2371 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k2_xboole_0(B,C) = k1_finsub_1(A,B,C))) # label(redefinition_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2372 $T # label(t8_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2373 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k3_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t16_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2374 $T # label(t7_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2375 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_finsub_1(A,C,B) = k4_finsub_1(A,B,C))) # label(commutativity_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2376 $T # label(t3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2377 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) -> m1_subset_1(k3_finsub_1(A,B,C),A))) # label(dt_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2378 $T # label(t11_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2379 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t15_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2380 (all A v4_finsub_1(k5_finsub_1(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2381 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k5_xboole_0(B,C) = k4_finsub_1(A,B,C))) # label(redefinition_k4_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2382 (all A (-v1_xboole_0(A) & v4_finsub_1(A) -> (all B (v4_finsub_1(B) & -v1_xboole_0(B) -> -v1_xboole_0(k3_xboole_0(A,B)) & v4_finsub_1(k3_xboole_0(A,B)))))) # label(t21_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2383 (all A all B (v4_finsub_1(B) -> (k5_finsub_1(A) = B <-> (all C (r2_hidden(C,B) <-> v1_finset_1(C) & r1_tarski(C,A)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2384 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> k3_finsub_1(A,B,B) = B)) # label(idempotence_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2385 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> m1_subset_1(B,k1_zfmisc_1(A)))) # label(t32_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2386 (all A all B all C (-v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k3_xboole_0(B,C) = k3_finsub_1(A,B,C))) # label(redefinition_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2387 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A))))) -> v4_finsub_1(A)))) # label(t17_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2388 (all A (v4_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & -v1_xboole_0(k1_zfmisc_1(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2389 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) -> k4_xboole_0(B,C) = k2_finsub_1(A,B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2390 (all A (v4_finsub_1(A) -> v1_finsub_1(A) & v3_finsub_1(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2391 (exists A (-v1_xboole_0(A) & v2_finsub_1(A) & v3_finsub_1(A) & v4_finsub_1(A) & v1_finsub_1(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2392 (all A r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A))) # label(t26_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2393 (all A all B r1_tarski(k2_xboole_0(k5_finsub_1(A),k5_finsub_1(B)),k5_finsub_1(k2_xboole_0(A,B)))) # label(t25_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2394 (all A all B (m1_subset_1(B,k5_finsub_1(A)) -> v1_finset_1(B))) # label(t30_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2395 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_finsub_1(A,B,B) = B)) # label(idempotence_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2396 $T # label(t19_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2397 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k2_finsub_1(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2398 (all A ((all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_xboole_0(B,C),A) & r2_hidden(k4_xboole_0(B,C),A))) <-> v4_finsub_1(A))) # label(t10_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2399 (all A all B all C (v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k1_finsub_1(A,C,B) = k1_finsub_1(A,B,C))) # label(commutativity_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2400 (all A all B all C (v4_finsub_1(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k3_finsub_1(A,C,B) = k3_finsub_1(A,B,C))) # label(commutativity_k3_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2401 (all A (v1_finsub_1(A) & v3_finsub_1(A) -> v4_finsub_1(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2402 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v4_finsub_1(A) & -v1_xboole_0(A) -> m1_subset_1(k1_finsub_1(A,B,C),A))) # label(dt_k1_finsub_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2403 (all A (r2_hidden(A,a_0_0_numbers) <-> (exists B (A = B & np__0 = k1_funct_1(B,k13_arytm_3) & m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)))))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2404 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2405 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2406 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2407 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2408 (all A (v1_membered(A) -> ((all B (v1_xcmplx_0(B) -> r2_hidden(B,A))) -> A = k2_numbers))) # label(t11_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2409 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_int_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2410 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2411 (all A all B (v1_membered(B) & v1_membered(A) -> v1_membered(k2_xboole_0(A,B)))) # label(fc22_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2412 (all A (-v1_xboole_0(A) & v3_membered(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2413 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2414 (all A all B (v1_xcmplx_0(A) & v1_xcmplx_0(B) -> v1_membered(k2_tarski(A,B)))) # label(fc12_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2415 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2416 (all A all B (v5_membered(A) -> v5_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc36_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2417 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_tarski(A,B) <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d10_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2418 (all A all B (v3_membered(A) & v3_membered(B) -> v1_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)))) # label(fc44_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2419 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2420 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2421 (all A all B (v4_membered(A) & v4_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2422 (all A all B (v2_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2423 (all A ((all B (r2_hidden(B,A) -> v4_membered(B))) -> v4_membered(k3_tarski(A)))) # label(t24_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2424 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2425 (all A all B (v3_membered(B) & r2_hidden(B,A) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2426 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2427 (all A (v1_xreal_0(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2428 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2429 (all A all B (r2_hidden(B,A) & v5_membered(B) -> v5_membered(k1_setfam_1(A)))) # label(t30_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2430 (all A all B (v3_membered(A) -> v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2431 (all A (v1_membered(A) & -v1_xboole_0(A) -> (exists B (v1_xcmplx_0(B) & r2_hidden(B,A))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2432 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2433 (all A (v4_membered(A) & -v1_xboole_0(A) -> (exists B (v1_int_1(B) & r2_hidden(B,A))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2434 (all A (v2_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v1_membered(B))))) # label(cc17_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2435 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2436 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2437 (all A (m1_subset_1(A,k1_zfmisc_1(k5_numbers)) -> v4_membered(A) & v5_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc9_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2438 (all A all B (v4_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2439 (all A all B (v1_membered(A) & v1_membered(B) -> v1_membered(k5_xboole_0(A,B)))) # label(fc42_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2440 (all A (v3_membered(A) -> ((all B (v1_rat_1(B) -> r2_hidden(B,A))) -> k3_numbers = A))) # label(t13_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2441 (all A all B all C (v1_int_1(C) & v1_int_1(B) & v1_int_1(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2442 (all A all B all C (v1_xreal_0(C) & v1_xreal_0(B) & v1_xreal_0(A) -> v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2443 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2444 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> A = B))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2445 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2446 (all A all B (v4_membered(B) & r2_hidden(B,A) -> v4_membered(k1_setfam_1(A)))) # label(t29_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2447 (all A all B (r2_hidden(B,A) & v1_membered(B) -> v1_membered(k1_setfam_1(A)))) # label(t26_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2448 (exists A ((all B (v1_rat_1(B) -> (p1_s3_membered(B) <-> r2_hidden(B,A)))) & v3_membered(A))) # label(s3_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2449 (all A all B (v4_membered(A) & v4_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2450 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2451 (all A ((all B (r2_hidden(B,A) -> v1_membered(B))) -> v1_membered(k3_tarski(A)))) # label(t21_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2452 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2453 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2454 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2455 (all A (v3_membered(A) <-> (all B (r2_hidden(B,A) -> v1_rat_1(B))))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2456 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2457 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2458 (all A all B (v2_membered(A) & v2_membered(B) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2459 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v1_membered(A) & v2_membered(A) & v4_membered(A) & v3_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2460 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2461 (all A all B (v3_membered(A) -> v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v1_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2462 (all A (v1_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B))))) # label(cc16_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2463 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2464 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B)))) <-> B = A))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2465 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2466 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v1_membered(A) & v2_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2467 (exists A ((all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))) & v1_membered(A))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2468 (all A all B (v4_ordinal2(A) & v4_ordinal2(B) -> v2_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2469 (all A ((all B (r2_hidden(B,A) -> v1_xcmplx_0(B))) <-> v1_membered(A))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2470 (all A all B (v1_int_1(B) & v1_int_1(A) -> v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2471 (all A all B (v3_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2472 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (B = A <-> (all C (v1_rat_1(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2473 (all A (v2_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xreal_0(B))))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2474 (all A (v5_membered(A) & -v1_xboole_0(A) -> (exists B (v4_ordinal2(B) & r2_hidden(B,A))))) # label(t10_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2475 (all A all B all C (v4_ordinal2(B) & v4_ordinal2(C) & v4_ordinal2(A) -> v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2476 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2477 (all A all B (v5_membered(B) & v5_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2478 (all A (v1_rat_1(A) -> v1_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc9_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2479 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v4_ordinal2(B) & v1_int_1(B) & v1_rat_1(B) & v1_xreal_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2480 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d12_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2481 (all A (v5_membered(A) -> (all B (v5_membered(B) -> ((all C (v4_ordinal2(C) -> -(r2_hidden(C,A) & r2_hidden(C,B)))) <-> r1_xboole_0(A,B)))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2482 (all A (v1_membered(A) -> (all B (v1_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xcmplx_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2483 (exists A (v5_membered(A) & (all B (v4_ordinal2(B) -> (p1_s5_membered(B) <-> r2_hidden(B,A)))))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2484 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2485 (all A all B (v2_membered(A) & v2_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2486 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2487 (all A all B all C (v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) -> v1_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2488 (all A (v3_membered(A) -> (all B (v3_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_rat_1(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d18_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2489 (all A (v2_membered(A) -> ((all B (v1_xreal_0(B) -> r2_hidden(B,A))) -> A = k1_numbers))) # label(t12_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2490 (all A all B (v2_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2491 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v1_membered(A) & v3_membered(A) & v2_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2492 (all A all B (v3_membered(B) & v3_membered(A) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc24_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2493 (all A ((all B (r2_hidden(B,A) -> v2_membered(B))) -> v2_membered(k3_tarski(A)))) # label(t22_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2494 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B) & v5_membered(B) & v4_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2495 (all A (v2_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_xreal_0(B))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2496 (exists A ((all B (v1_int_1(B) -> (p1_s4_membered(B) <-> r2_hidden(B,A)))) & v4_membered(A))) # label(s4_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2497 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2498 (all A all B all C (v1_xcmplx_0(C) & v1_xcmplx_0(B) & v1_xcmplx_0(A) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2499 (all A (v1_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B))))) # label(cc10_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2500 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2501 (exists A (-v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v5_membered(A) & v4_membered(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2502 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (A = B <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,A) <-> r2_hidden(C,B))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2503 (all A all B (v5_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2504 (all A all B (v4_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2505 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,A) & r2_hidden(C,B))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2506 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc30_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2507 (all A (v4_membered(A) -> ((all B (v1_int_1(B) -> r2_hidden(B,A))) -> A = k4_numbers))) # label(t14_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2508 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_rat_1(B) & v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2509 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2510 (all A (v4_ordinal2(A) -> v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2511 (all A ((all B (r2_hidden(B,A) -> v3_membered(B))) -> v3_membered(k3_tarski(A)))) # label(t23_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2512 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v3_membered(B) & v4_membered(B) & v2_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2513 (exists A (v2_membered(A) & (all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2514 (all A (v2_membered(A) -> (all B (v2_membered(B) -> ((all C (v1_xreal_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d7_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2515 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d6_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2516 (all A (v5_membered(A) -> ((all B (v4_ordinal2(B) -> r2_hidden(B,A))) -> k5_numbers = A))) # label(t15_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2517 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2518 (all A all B (r2_hidden(B,A) & v2_membered(B) -> v2_membered(k1_setfam_1(A)))) # label(t27_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2519 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2520 (all A (v1_xboole_0(A) -> v5_membered(A) & v4_membered(A) & v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2521 (all A all B (v1_rat_1(B) & v1_rat_1(A) -> v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc14_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2522 (all A ((all B (r2_hidden(B,A) -> v5_membered(B))) -> v5_membered(k3_tarski(A)))) # label(t25_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2523 (all A (v1_int_1(A) -> v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2524 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & r1_tarski(A,k1_relat_1(B)) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2525 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2526 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> -r1_tarski(B,A)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2527 (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]. 6.71/6.67 2528 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2529 (all A (v1_finset_1(A) -> v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2530 (all A (k1_xboole_0 = A <-> r2_wellord2(A,k1_xboole_0))) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2531 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2532 (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]. 6.71/6.67 2533 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> r1_xreal_0(A,B)))))) # label(t72_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2534 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2535 (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]. 6.71/6.67 2536 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2537 (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]. 6.71/6.67 2538 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2539 (all A exists B (r2_wellord2(A,B) & v3_ordinal1(B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2540 (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]. 6.71/6.67 2541 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2542 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2543 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2544 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> A = B))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2545 (all A all B all C all D (r2_wellord2(A,B) & r2_hidden(C,A) & r2_hidden(D,B) -> r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))))) # label(t61_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2546 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2547 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2548 (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]. 6.71/6.67 2549 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2550 (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]. 6.71/6.67 2551 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2552 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2553 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2554 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2555 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2556 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_finset_1(A) & v1_xcmplx_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2557 (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]. 6.71/6.67 2558 (all A all B (v1_card_1(B) -> ((all C (v1_card_1(C) -> (r2_hidden(k1_card_1(A),C) -> r1_tarski(B,C)))) & r2_hidden(k1_card_1(A),B) <-> k2_card_1(A) = B))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2559 (all A all B ((exists C (v1_funct_1(C) & r1_tarski(k2_relat_1(C),B) & A = k1_relat_1(C) & v2_funct_1(C) & v1_relat_1(C))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2560 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2561 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2562 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2563 (all A all B (r2_wellord2(A,B) <-> k1_card_1(B) = k1_card_1(A))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2564 (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]. 6.71/6.67 2565 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2566 (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]. 6.71/6.67 2567 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k3_card_1(A),k3_card_1(B)) <-> r2_hidden(A,B)))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2568 (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]. 6.71/6.67 2569 (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]. 6.71/6.67 2570 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) <-> r1_ordinal1(A,B)))))) # label(t56_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2571 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2572 (all A (v1_finset_1(A) -> k1_card_1(A) = k4_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2573 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_relat_1(C) = k1_ordinal1(A) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D)))))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D)))) = k1_funct_1(C,k1_ordinal1(D))))) & k1_funct_1(C,k1_xboole_0) = k1_card_1(k5_numbers) & B = k1_ordinal2(C) & v1_funct_1(C))) <-> B = k3_card_1(A))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2574 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2575 (all A k1_card_1(k1_tarski(A)) = k4_ordinal2) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.67 2576 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2577 (exists A (v1_ordinal1(A) & v1_card_1(A) & v1_finset_1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2578 (all A all B (v1_card_1(B) -> (k1_card_1(A) = B <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2579 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2580 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2581 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2582 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_hidden(A,B) <-> r1_tarski(A,B) & B != A))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2583 (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]. 6.71/6.68 2584 (all A (v3_ordinal1(A) -> v1_card_1(k3_card_1(A)) & v3_ordinal1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)) & v1_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2585 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> -r2_wellord2(A,B) & r2_hidden(k1_card_1(A),k1_card_1(B)))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2586 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2587 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2588 (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]. 6.71/6.68 2589 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2590 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2591 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2592 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2593 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(A) = k1_card_1(B) -> A = B))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2594 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_ordinal1(A) = k1_nat_1(A,np__1))) # label(t52_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2595 (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]. 6.71/6.68 2596 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2597 (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]. 6.71/6.68 2598 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2599 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) <-> B = k4_card_1(A)))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2600 (all A all B (r2_wellord2(A,k1_tarski(B)) <-> (exists C k1_tarski(C) = A))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2601 (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]. 6.71/6.68 2602 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2603 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2604 (all A (v1_card_1(A) -> (p1_s1_card_1(A) -> p1_s1_card_1(k2_card_1(A))))) & (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> (r2_hidden(B,A) -> p1_s1_card_1(B)))) & v2_card_1(A) -> A = k1_xboole_0 | p1_s1_card_1(A)))) & p1_s1_card_1(k1_xboole_0) -> (all A (v1_card_1(A) -> p1_s1_card_1(A))) # label(s1_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2605 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2606 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (v1_funct_1(C) & r1_tarski(A,k2_relat_1(C)) & k1_relat_1(C) = B & v1_relat_1(C))))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2607 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2608 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2609 (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]. 6.71/6.68 2610 (all A all B (k1_card_1(B) = k1_card_1(A) -> k2_card_1(A) = k2_card_1(B))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2611 (all A all B all C all D (r1_xboole_0(C,D) & r2_wellord2(B,D) & r2_wellord2(A,C) & r1_xboole_0(A,B) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2612 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2613 (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]. 6.71/6.68 2614 (all A (v1_finset_1(A) & v1_card_1(A) -> (exists B (k1_card_1(B) = A & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2615 (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]. 6.71/6.68 2616 (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]. 6.71/6.68 2617 (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]. 6.71/6.68 2618 (all A (m1_subset_1(A,k5_numbers) -> v3_ordinal1(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v1_xreal_0(A) & v4_ordinal2(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2619 (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]. 6.71/6.68 2620 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2621 (all A all B ((exists C k1_tarski(C) = A) <-> k1_card_1(k1_tarski(B)) = k1_card_1(A))) # label(t49_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2622 (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]. 6.71/6.68 2623 (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]. 6.71/6.68 2624 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2625 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2626 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2627 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k3_card_1(B) = k3_card_1(A) -> B = A))))) # label(t42_card_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2628 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> k1_funct_1(A,B) = f2_s2_finseq_1(B)))) & k3_finseq_1(A) = f1_s2_finseq_1)) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2629 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2630 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2631 (exists A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2632 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k3_finseq_1(B) = k3_finseq_1(A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) -> B = A))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2633 (all A all B (m1_finseq_1(B,A) -> v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2634 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A)) = k2_finseq_1(A)))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2635 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2636 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & A = k2_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2637 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (np__2 = k3_finseq_1(C) & k1_funct_1(C,np__2) = B & k1_funct_1(C,np__1) = A <-> k10_finseq_1(A,B) = C))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2638 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(A) = k2_finseq_1(B) -> A = B))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2639 (all A (v1_relat_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k2_finseq_1(B) = k1_relat_1(A))) <-> v1_finseq_1(A)))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2640 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,B) -> r1_xreal_0(k3_finseq_1(A),k3_finseq_1(B))))))) # label(t84_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2641 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2642 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2643 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2644 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2645 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2646 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2647 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k3_finseq_1(A) = np__0 <-> A = k1_xboole_0))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2648 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)))) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2649 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> -((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(A = D & r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B)))))) & r2_hidden(A,k4_finseq_1(B))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2650 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> A = k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1))) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2651 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & -r2_hidden(C,k4_finseq_1(A)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(C = k1_nat_1(k3_finseq_1(A),D) & r2_hidden(D,k4_finseq_1(B)))))))))))) # label(t38_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2652 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> A = k4_card_1(k1_card_1(A)) & k4_card_1(A) = A)) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2653 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2654 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k2_relat_1(A) & v2_funct_1(A) & v2_funct_1(B) -> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2655 (all A exists B (m1_finseq_1(B,A) & v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v2_funct_1(B) & v1_relat_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2656 (all A -(v1_finset_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,k2_finseq_1(B)))))) # label(t77_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2657 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k1_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2658 (all A k9_finseq_1(A) = k5_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2659 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (k3_finseq_1(A) = np__0 <-> A = k6_finseq_1(B))))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2660 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(A = k4_tarski(C,k1_funct_1(B,C)) & r2_hidden(C,k4_finseq_1(B))))) & r2_hidden(A,B)))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2661 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) -> v1_finset_1(k1_relat_1(A)))) # label(fc17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2662 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> -(r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> C != k7_finseq_1(A,E))) & k7_finseq_1(A,B) = k7_finseq_1(C,D)))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2663 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2664 (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]. 6.71/6.68 2665 (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]. 6.71/6.68 2666 (all A (v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)))) # label(dt_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2667 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k4_finseq_1(A) = k1_relat_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2668 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2669 p1_s3_finseq_1(k1_xboole_0) & (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) -> (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2670 (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]. 6.71/6.68 2671 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,B) & p1_s1_finseq_1(A,C) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B -p1_s1_finseq_1(A,B)) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1))))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))) & k4_finseq_1(A) = k2_finseq_1(f1_s1_finseq_1))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2672 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k9_finseq_1(A) <-> k1_funct_1(B,np__1) = A & k1_relat_1(B) = k2_finseq_1(np__1)))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2673 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2674 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> v1_relat_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_finseq_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2675 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k2_relat_1(A)))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2676 (all A all B (v1_relat_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_finseq_1(A) & v1_funct_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2677 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> A = k7_finseq_1(k1_xboole_0,A) & A = k7_finseq_1(A,k1_xboole_0))) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2678 (exists A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2679 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2680 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_relat_1(A) = k2_finseq_1(B) <-> B = k3_finseq_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2681 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2682 (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]. 6.71/6.68 2683 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(A,k2_finseq_1(B)) <-> r1_xreal_0(np__1,A) & r1_xreal_0(A,B)))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2684 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B)))))))))) # label(t41_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2685 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2686 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C))) & r2_hidden(B,k2_finseq_1(A)) | r1_xreal_0(B,np__0)))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2687 (all A all B (m1_finseq_1(B,A) -> v1_xboole_0(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2688 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(B)) -> k1_funct_1(B,C) = k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C))))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2689 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -((all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B))) & r2_hidden(A,k2_finseq_1(f2_s5_finseq_1))))) -> (exists A (k4_finseq_1(A) = k2_finseq_1(f2_s5_finseq_1) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f2_s5_finseq_1)) -> p1_s5_finseq_1(B,k1_funct_1(A,B))))) & m2_finseq_1(A,f1_s5_finseq_1))) # label(s5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2690 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A))))))) # label(t20_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2691 (all A (v4_ordinal2(A) -> A = np__0 | r2_hidden(A,k2_finseq_1(A)))) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2692 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> A = k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)))))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2693 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2694 (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]. 6.71/6.68 2695 (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]. 6.71/6.68 2696 (all A k1_tarski(k4_tarski(np__1,A)) = k9_finseq_1(A)) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2697 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (C = k7_finseq_1(A,B) <-> k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) = k4_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D))))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2698 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (k2_relat_1(B) = A & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(-r1_xreal_0(D,C) & r1_xreal_0(F,E) & F = k1_funct_1(B,D) & E = k1_funct_1(B,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(np__1,C)))))))))) <-> B = k14_finseq_1(A)))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2699 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> k7_finseq_1(B,C) = k8_finseq_1(A,B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2700 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2701 (all A (v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A))) # label(dt_k6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2702 (all A (v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2703 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2704 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2705 (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]. 6.71/6.68 2706 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)) & v1_finseq_1(k11_finseq_1(A,B,C)) & v1_finset_1(k11_finseq_1(A,B,C)))) # label(fc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2707 (all A all B all C (k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C) & k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) = k11_finseq_1(A,B,C))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2708 (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]. 6.71/6.68 2709 (exists A (v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & -v1_xboole_0(A))) # label(rc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2710 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2711 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))))) # label(t35_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2712 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (m2_finseq_1(k7_finseq_1(A,B),C) -> m2_finseq_1(B,C) & m2_finseq_1(A,C))))))) # label(t50_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2713 (all A (v4_ordinal2(A) -> k2_finseq_1(A) = k4_xboole_0(k2_finseq_1(k2_xcmplx_0(A,np__1)),k1_tarski(k2_xcmplx_0(A,np__1))))) # label(t12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2714 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2715 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> k15_finseq_1(A) = k5_relat_1(k14_finseq_1(k1_relat_1(A)),A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2716 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (A = k1_funct_1(B,np__1) & np__1 = k3_finseq_1(B) <-> k9_finseq_1(A) = B))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2717 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (A = k1_xboole_0 <-> k1_xboole_0 = k14_finseq_1(A)))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2718 (all A all B (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2719 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> r1_xreal_0(C,k3_finseq_1(A)) | k1_funct_1(k7_finseq_1(A,B),C) = k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A)))))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2720 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2721 (all A all B (v1_funct_1(k10_finseq_1(A,B)) & v1_relat_1(k10_finseq_1(A,B)))) # label(fc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2722 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2723 (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & C = B & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2724 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2725 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2726 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k17_finseq_1(A) <-> (all C all D (r2_hidden(C,k3_relat_1(A)) & (exists E (v1_relat_1(E) & C = k1_funct_1(E,np__1) & (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,F) -> r1_xreal_0(k3_finseq_1(E),F) | r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,k1_nat_1(F,np__1))),A)))) & k1_funct_1(E,k3_finseq_1(E)) = D & r1_xreal_0(np__1,k3_finseq_1(E)) & v1_finseq_1(E) & v1_funct_1(E))) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(C,D),B)))))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2727 (all A all B all C k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)) = k11_finseq_1(A,B,C)) # label(d10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2728 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2729 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2730 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))) & v1_finseq_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2731 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2732 (all A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k2_relat_1(k14_finseq_1(k1_relat_1(A))))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2733 (all A all B all C (v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)))) # label(fc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2734 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2735 (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]. 6.71/6.68 2736 (all A all B all C all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (B = k1_funct_1(D,np__2) & k1_funct_1(D,np__3) = C & A = k1_funct_1(D,np__1) & np__3 = k3_finseq_1(D) <-> D = k11_finseq_1(A,B,C)))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2737 (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]. 6.71/6.68 2738 (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]. 6.71/6.68 2739 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2740 (all A all B (v1_relat_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2741 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B)))) <-> v2_finseq_1(A)))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2742 (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]. 6.71/6.68 2743 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2744 (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]. 6.71/6.68 2745 (exists A (-v1_xboole_0(A) & v1_finseq_1(A) & v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2746 (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]. 6.71/6.68 2747 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2748 (all A (v4_ordinal2(A) -> k2_xboole_0(k2_finseq_1(A),k1_tarski(k2_xcmplx_0(A,np__1))) = k2_finseq_1(k2_xcmplx_0(A,np__1)))) # label(t11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2749 (all A all B (v4_ordinal2(B) -> ((exists C (r1_xreal_0(np__1,C) & r1_xreal_0(C,B) & A = C & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_0_finseq_1(B))))) # label(fraenkel_a_1_0_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2750 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2751 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2752 (all A (-v1_xboole_0(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2753 (exists A (v1_finseq_1(A) & v1_finset_1(A) & v2_funct_1(A) & v1_funct_1(A) & v1_relat_1(A) & v1_xboole_0(A))) # label(rc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2754 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2755 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k1_tarski(A) = k2_relat_1(B) & k4_finseq_1(B) = k2_finseq_1(np__1) <-> B = k9_finseq_1(A)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2756 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(C,B) = k7_finseq_1(A,B) | k7_finseq_1(B,C) = k7_finseq_1(B,A) -> A = C))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2757 (all A all B (v1_funct_1(A) & -v1_xboole_0(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_finseq_1(A) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2758 (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]. 6.71/6.68 2759 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> C = k3_finseq_1(k16_finseq_1(A,B,C))))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2760 (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]. 6.71/6.68 2761 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (m1_finseq_1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.68 2762 (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]. 6.71/6.68 2763 (all A (v1_finset_1(A) & v1_relat_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2764 (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]. 6.71/6.69 2765 (all A (v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(dt_k15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2766 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> -(k1_xboole_0 != A & (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C k7_finseq_1(B,k9_finseq_1(C)) != A)))))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2767 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2768 (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]. 6.71/6.69 2769 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> m2_finseq_1(k12_finseq_1(A,B),A))) # label(dt_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2770 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> v1_funct_1(k7_relat_1(B,A)) & v1_relat_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)) & v1_relat_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2771 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k7_finseq_1(A,B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2772 (all A all B (B = k13_finseq_1(A) <-> (all C (m2_finseq_1(C,A) <-> r2_hidden(C,B))))) # label(d11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2773 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> k3_finseq_1(A) = k1_card_1(A))) # label(redefinition_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2774 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2775 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k1_card_1(k2_finseq_1(A)) = k1_card_1(A))) # label(t76_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2776 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) & C = k7_relat_1(B,k2_finseq_1(A)) -> k2_finseq_1(A) = k4_finseq_1(C) & k3_finseq_1(C) = A))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2777 (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]. 6.71/6.69 2778 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2779 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) -> k12_finseq_1(A,B) = k5_finseq_1(B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2780 (all A (v1_relat_1(A) & v1_funct_1(A) -> -((all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> -r1_tarski(A,B))) & (exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B))))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2781 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (k7_finseq_1(A,B) = k1_xboole_0 -> A = k1_xboole_0 & B = k1_xboole_0))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2782 (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]. 6.71/6.69 2783 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k1_xboole_0 = k4_finseq_1(A)))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2784 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k4_finseq_1(B) = k4_finseq_1(A) -> B = A))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2785 (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]. 6.71/6.69 2786 (all A all B (m2_finseq_1(B,A) -> v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A))) # label(dt_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2787 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k1_tarski(A) = k2_relat_1(B) & np__1 = k3_finseq_1(B) <-> B = k9_finseq_1(A)))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2788 (all A all B all C (v4_ordinal2(C) & m1_finseq_1(B,A) -> m2_finseq_1(k16_finseq_1(A,B,C),A))) # label(dt_k16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2789 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) <-> r9_orders_1(k4_relat_1(A),B))))) # label(t166_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2790 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2791 (all A (v1_relat_1(A) -> (all B all C (r1_orders_1(A,B) & r1_tarski(C,B) -> r1_orders_1(A,C))))) # label(t128_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2792 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) -> v4_relat_2(k2_wellord1(A,B)))))) # label(t184_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2793 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) -> r1_relat_2(k4_relat_1(A),B))))) # label(t189_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2794 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2795 (all A all B (v1_relat_1(B) -> (r7_relat_2(B,A) <-> r6_relat_2(B,A) & r1_relat_2(B,A)))) # label(t92_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2796 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r7_orders_1(A,B) -> r9_orders_1(A,B))))) # label(t159_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2797 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2798 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r3_orders_1(A,B) & r2_orders_1(A,B) & r1_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2799 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2800 (all A (v1_relat_1(A) -> (v1_relat_2(A) & v8_relat_2(A) & v4_relat_2(A) <-> v2_orders_1(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2801 (all A (v1_relat_1(A) -> (v1_orders_1(A) -> v1_orders_1(k4_relat_1(A))))) # label(t104_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2802 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) -> r1_orders_1(k4_relat_1(A),B))))) # label(t136_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2803 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2804 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2805 (all A (v1_relat_1(A) -> (v3_orders_1(A) <-> v1_relat_2(A) & v8_relat_2(A) & v6_relat_2(A) & v4_relat_2(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2806 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2807 (all A (-v1_xboole_0(A) -> -r2_hidden(k1_xboole_0,k1_orders_1(A)))) # label(t4_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2808 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2809 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) & v4_relat_2(A) -> r6_orders_1(A,B))))) # label(t158_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2810 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v1_orders_1(A) & v3_orders_1(A) & v2_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2811 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2812 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2813 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A) | B = C)) <-> r9_orders_1(A,B))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2814 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2815 (all A (v1_relat_1(A) -> (v1_orders_1(A) -> r1_orders_1(A,k3_relat_1(A))))) # label(t127_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2816 (all A (v1_relat_1(A) -> (all B (r6_orders_1(A,B) <-> r7_orders_1(k4_relat_1(A),B))))) # label(t164_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2817 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2818 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2819 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2820 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2821 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> r1_orders_1(A,B))))) # label(t126_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2822 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2823 (all A (v1_relat_1(A) -> (all B all C (r2_orders_1(A,B) & r1_tarski(C,B) -> r2_orders_1(A,C))))) # label(t131_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2824 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2825 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2826 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2827 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2828 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2829 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> r2_orders_1(k4_relat_1(A),B))))) # label(t137_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2830 (all A (v1_relat_1(A) -> (all B (r6_relat_2(A,B) -> r6_relat_2(k4_relat_1(A),B))))) # label(t192_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2831 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> r5_orders_1(k4_relat_1(A),B))))) # label(t151_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2832 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) <-> r8_orders_1(k4_relat_1(A),B))))) # label(t165_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2833 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2834 (all A all B all C (v1_relat_1(C) -> (r4_relat_2(C,A) & r1_tarski(B,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2835 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2836 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2837 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) <-> r1_relat_2(A,B) & r6_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2838 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2839 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_1(B) & v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) -> (m1_orders_1(B,A) <-> (all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))))))))) # label(d1_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2840 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2841 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r7_relat_2(C,A) -> r7_relat_2(C,B)))) # label(t96_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2842 (all A (v1_relat_1(A) -> (all B all C (r2_hidden(B,C) & r9_orders_1(A,B) & v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2843 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2844 (all A (v1_relat_1(A) -> (all B (v2_orders_1(A) -> v2_orders_1(k2_wellord1(A,B)))))) # label(t114_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2845 (all A (v1_relat_1(A) -> r1_tarski(A,k2_zfmisc_1(k3_relat_1(A),k3_relat_1(A))))) # label(t180_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2846 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2847 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2848 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2849 (all A (v1_relat_1(A) -> (all B (v3_orders_1(A) -> v3_orders_1(k2_wellord1(A,B)))))) # label(t115_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2850 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2851 (all A (v1_relat_1(A) -> (all B (v6_relat_2(A) & r6_orders_1(A,B) -> r8_orders_1(A,B))))) # label(t160_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2852 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2853 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2854 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2855 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v3_orders_1(k2_wellord1(A,B)))))) # label(t135_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2856 (all A -(k1_xboole_0 != A & (all B -((all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))) & v6_ordinal1(B) & r1_tarski(B,A))) & (all B -((all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))) & r2_hidden(B,A))))) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2857 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2858 (all A (v1_relat_1(A) -> (all B (r8_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> B = C | r2_hidden(k4_tarski(C,B),A))))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2859 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2860 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2861 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2862 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2863 (all A all B (v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> A = k3_relat_1(B))) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2864 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2865 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> B = k1_xboole_0 | r2_hidden(k3_tarski(B),A))) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(B,C) & B != C & r2_hidden(C,A))))) & k1_xboole_0 != A)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2866 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B -(v1_finset_1(B) & r1_tarski(B,k2_relat_1(A)) & (all C -(v1_finset_1(C) & B = k9_relat_1(A,C) & r1_tarski(C,k1_relat_1(A)))))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2867 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C -(r2_hidden(C,k3_relat_1(A)) & r2_hidden(k4_tarski(B,C),A) & B != C)) <-> r6_orders_1(A,B))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2868 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2869 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.71/6.69 2870 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(C,k3_relat_1(A)) & B != C & r2_hidden(k4_tarski(C,B),A))) & r2_hidden(B,k3_relat_1(A)) <-> r7_orders_1(A,B))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2871 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> A = k5_relset_1(A,A,B) & A = k4_relset_1(A,A,B))) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2872 (all A (v1_relat_1(A) -> k2_wellord1(A,k1_xboole_0) = k1_xboole_0)) # label(t194_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2873 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2874 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2875 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v2_orders_1(k4_relat_1(A))))) # label(t105_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2876 (all A all B all C (v1_relat_1(C) -> (r8_relat_2(C,A) & r1_tarski(B,A) -> r8_relat_2(C,B)))) # label(t95_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2877 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2878 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2879 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2880 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v2_orders_1(k2_wellord1(A,B)))))) # label(t132_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2881 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2882 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v2_orders_1(A) & v1_orders_1(A)))) # label(t108_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2883 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2884 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2885 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2886 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2887 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> k3_relat_1(B) = A & A = k4_relset_1(A,A,B)))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2888 (all A (v1_relat_1(A) -> (v1_relat_2(A) & v8_relat_2(A) <-> v1_orders_1(A)))) # label(d3_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2889 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> v1_orders_1(B))) # label(t111_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2890 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2891 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (m1_subset_1(A,k1_zfmisc_1(B)) <-> r2_hidden(A,k1_orders_1(B))))))) # label(t6_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2892 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2893 (all A k1_orders_1(A) = k4_xboole_0(k1_zfmisc_1(A),k1_tarski(k1_xboole_0))) # label(d2_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2894 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2895 (all A all B all C all D all E (v1_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_relat_2(E) & v4_relat_2(E) -> (r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) & r2_hidden(D,A) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.72 2896 (all A -((all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(-p1_s2_orders_1(C,B) & -p1_s2_orders_1(B,C) & r2_hidden(C,A) & r2_hidden(B,A)))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (-p1_s2_orders_1(B,C) & r2_hidden(C,A) & m1_subset_1(C,f1_s2_orders_1))))) & r1_tarski(A,f1_s2_orders_1))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,C) -> p1_s2_orders_1(A,C)))))))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (p1_s2_orders_1(B,A) & p1_s2_orders_1(A,B) -> A = B))))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> p1_s2_orders_1(A,A))) -> (exists A ((all B (m1_subset_1(B,f1_s2_orders_1) -> -(p1_s2_orders_1(B,A) & B != A))) & m1_subset_1(A,f1_s2_orders_1))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2897 (all A (v1_relat_1(A) -> (all B all C (v1_relat_2(A) & r1_tarski(C,k3_relat_1(A)) & r8_orders_1(A,B) & r2_hidden(B,C) -> r4_orders_1(A,C))))) # label(t161_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2898 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2899 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2900 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r6_relat_2(A,B) -> r6_relat_2(A,C))))) # label(t186_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2901 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2902 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2903 (all A (-v1_xboole_0(A) -> (all B (m1_orders_1(B,A) -> m2_relset_1(B,A,k3_tarski(A)) & v1_funct_2(B,A,k3_tarski(A)) & v1_funct_1(B))))) # label(dt_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2904 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2905 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2906 (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,C) -> p1_s1_orders_1(A,C)))))))) & (all A -(r1_tarski(A,f1_s1_orders_1) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> -(r2_hidden(B,A) & r2_hidden(C,A) & -p1_s1_orders_1(C,B) & -p1_s1_orders_1(B,C)))))) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (-p1_s1_orders_1(C,B) & r2_hidden(C,A) & m1_subset_1(C,f1_s1_orders_1))))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,A) -> B = A))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) -> (exists A (m1_subset_1(A,f1_s1_orders_1) & (all B (m1_subset_1(B,f1_s1_orders_1) -> -(p1_s1_orders_1(A,B) & A != B))))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2907 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2908 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r3_orders_1(k4_relat_1(A),B))))) # label(t138_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2909 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2910 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2911 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2912 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2913 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r3_orders_1(A,B) -> r3_orders_1(A,C))))) # label(t134_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2914 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r1_orders_1(A,B) & r2_orders_1(A,B))))) # label(t125_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2915 (all A (v1_orders_1(k6_partfun1(A)) & v2_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2916 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2917 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.74 2918 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> (all C -(r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))) & r2_hidden(D,B))))))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2919 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2920 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) -> v1_orders_1(k2_wellord1(A,B)))))) # label(t129_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2921 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2922 (all A (r1_orders_1(k6_partfun1(A),A) & r2_orders_1(k6_partfun1(A),A))) # label(t146_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2923 (all A (v1_relat_1(A) -> (all B ((all C -(r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & (all D -(r2_hidden(D,B) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))))))) <-> r5_orders_1(A,B))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2924 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2925 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2926 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2927 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2928 (all A (-((exists B (r2_hidden(B,A) & k1_xboole_0 != B)) & k1_xboole_0 = k3_tarski(A)) & -(k3_tarski(A) != k1_xboole_0 & (all B -(r2_hidden(B,A) & k1_xboole_0 != B))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2929 (all A (v1_relat_1(A) -> (v6_relat_2(A) -> v6_relat_2(k4_relat_1(A))))) # label(t188_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2930 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2931 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(C,B) & r2_wellord1(A,B) -> r2_wellord1(A,C))))) # label(t187_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2932 (all A (v1_relat_1(A) -> (all B k4_relat_1(k2_wellord1(A,B)) = k2_wellord1(k4_relat_1(A),B)))) # label(t193_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2933 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B) & v4_relat_2(k2_wellord1(A,B)))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2934 (all A (v1_relat_1(A) -> (all B -(B = k3_relat_1(A) & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B) & r2_orders_1(A,B))))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2935 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2936 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2937 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2938 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) -> v1_relat_2(k2_wellord1(A,B)))))) # label(t182_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2939 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2940 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2941 (all A (v1_relat_1(A) -> (all B (r6_relat_2(A,B) -> v6_relat_2(k2_wellord1(A,B)))))) # label(t185_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2942 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> r2_orders_1(A,k3_relat_1(A))))) # label(t130_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2943 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & (all C -r7_orders_1(A,C)) & r5_orders_1(A,B) & B = k3_relat_1(A))))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2944 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2945 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r1_relat_2(C,A) -> r1_relat_2(C,B)))) # label(t93_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2946 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> r1_orders_1(B,A))) # label(t139_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2947 (all A -((all B -((all C -((all D (r2_hidden(D,B) -> r1_tarski(C,D))) & r2_hidden(C,A))) & v6_ordinal1(B) & r1_tarski(B,A))) & (all B -(r2_hidden(B,A) & (all C -(r2_hidden(C,A) & C != B & r1_tarski(C,B))))) & k1_xboole_0 != A)) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2948 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) <-> r6_orders_1(k4_relat_1(A),B))))) # label(t163_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2949 (all A (v1_relat_1(A) -> (all B -(r4_orders_1(A,B) & k1_xboole_0 = B)))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2950 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r1_tarski(A,B) <-> r2_hidden(A,k1_orders_1(B))))))) # label(t5_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2951 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2952 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2953 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2954 (all A (v1_relat_1(A) -> (all B (r5_orders_1(A,B) <-> r4_orders_1(k4_relat_1(A),B))))) # label(t152_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2955 (all A all B all C (v4_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v1_relat_2(C) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t12_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2956 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2957 (all A (v1_relat_1(A) -> (all B (v1_orders_1(A) -> v1_orders_1(k2_wellord1(A,B)))))) # label(t113_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2958 (all A (v1_relat_1(A) -> (all B (r1_tarski(B,k3_relat_1(A)) & v1_relat_2(A) -> B = k3_relat_1(k2_wellord1(A,B)))))) # label(t181_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2959 (all A -((all B -(r2_hidden(B,A) & (all C -(r1_tarski(C,B) & C != B & r2_hidden(C,A))))) & (all B (r1_tarski(B,A) & v6_ordinal1(B) -> r2_hidden(k1_setfam_1(B),A) | B = k1_xboole_0)) & A != k1_xboole_0)) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2960 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v3_orders_1(k4_relat_1(A))))) # label(t106_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2961 (all A all B (v4_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v1_relat_2(B) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2962 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2963 (all A all B all C all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v4_relat_2(D) & v1_relat_2(D) -> (r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(B,A) -> B = C))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2964 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2965 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) -> v8_relat_2(k2_wellord1(A,B)))))) # label(t183_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2966 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2967 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2968 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2969 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2970 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2971 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2972 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2973 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2974 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2975 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2976 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2977 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2978 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2979 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> A = k3_relat_1(B))) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2980 (all A (v1_relat_1(A) -> (all B -(k3_relat_1(A) = B & (all C (v1_relat_1(C) -> -(r1_tarski(A,C) & r3_orders_1(C,B) & k3_relat_1(C) = B))) & r2_orders_1(A,B))))) # label(t179_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2981 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2982 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r4_relat_2(A,B) & r8_relat_2(A,B) <-> r2_orders_1(A,B))))) # label(d7_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2983 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2984 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2985 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2986 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2987 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2988 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2989 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2990 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) <-> r8_relat_2(A,B) & r1_relat_2(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2991 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2992 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2993 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> r3_orders_1(A,k3_relat_1(A))))) # label(t133_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2994 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2995 (all A (v1_relat_1(A) -> (all B (r9_orders_1(A,B) & v4_relat_2(A) -> r7_orders_1(A,B))))) # label(t157_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2996 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) -> r8_relat_2(k4_relat_1(A),B))))) # label(t190_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2997 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2998 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> v1_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B))))) # label(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 2999 (all A (v1_relat_1(A) -> (all B -(B = k1_xboole_0 & r5_orders_1(A,B))))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3000 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) -> r4_relat_2(k4_relat_1(A),B))))) # label(t191_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3001 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3002 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3003 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3004 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k6_partfun1(A) = k4_eqrel_1(A,k6_partfun1(A),B))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3005 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> m2_relset_1(k3_eqrel_1(A,B,C),A,A))) # label(dt_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3006 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> ((exists C k6_eqrel_1(A,B,C) = A) -> k1_eqrel_1(A) = B))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3007 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 = A -> (B = k1_xboole_0 <-> m1_eqrel_1(B,A))) & (k1_xboole_0 != A -> (m1_eqrel_1(B,A) <-> k5_setfam_1(A,B) = A & (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> C != k1_xboole_0 & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & -r1_xboole_0(C,D) & D != C)))))))))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3008 (all A (v3_relat_2(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_2(k1_eqrel_1(A)) & v1_relat_1(k1_eqrel_1(A)))) # label(fc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3009 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> -(B = k1_xboole_0 & (exists C r2_hidden(C,A))))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3010 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_k7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3011 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & -v1_xboole_0(A) -> v1_setfam_1(k7_eqrel_1(A,B)) & -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3012 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3013 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3014 (all A all B all C (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k4_eqrel_1(A,B,B) = B)) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3015 (all A all B all C all D all E (v1_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v3_relat_2(E) -> (r2_hidden(B,k6_eqrel_1(A,E,C)) & r2_hidden(D,k6_eqrel_1(A,E,C)) -> r2_hidden(k4_tarski(B,D),E)))) # label(t30_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3016 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3017 (all A all B all C (m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(B,k6_eqrel_1(A,C,D)) <-> k6_eqrel_1(A,C,D) = k6_eqrel_1(A,C,B)))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3018 (all A (v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A,A) & v1_relat_1(k1_eqrel_1(A)))) # label(fc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3019 (all A all B all C all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v3_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) -> r2_hidden(k4_tarski(C,B),D)))) # label(t12_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3020 (all A (v3_relat_2(k6_partfun1(A)) & v8_relat_2(k6_partfun1(A)) & v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3021 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3022 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3023 (all A all B all C (v8_relat_2(B) & v1_partfun1(B,A,A) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) & v3_relat_2(B) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3024 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k2_eqrel_1(A,B,C) = k2_eqrel_1(A,C,B))) # label(commutativity_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3025 (all A all B (m1_eqrel_1(B,A) -> m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))))) # label(dt_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3026 (all A all B (m1_eqrel_1(B,A) -> (exists C (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & B = k7_eqrel_1(A,C) & v8_relat_2(C) & v3_relat_2(C))))) # label(t43_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3027 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k2_eqrel_1(A,B,B) = B)) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3028 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3029 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C) -> (all D (v8_relat_2(D) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) -> (k3_eqrel_1(A,B,C) = D -> (all E -(k6_eqrel_1(A,B,E) != k6_eqrel_1(A,D,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & r2_hidden(E,A)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3030 (all A all B (m2_relset_1(B,A,A) -> k2_eqrel_1(A,k1_eqrel_1(A),B) = B)) # label(t18_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3031 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3032 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3033 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3034 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3035 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(B) -> v3_relat_2(k4_eqrel_1(A,B,C)) & v8_relat_2(k4_eqrel_1(A,B,C)) & v1_partfun1(k4_eqrel_1(A,B,C),A,A) & m2_relset_1(k4_eqrel_1(A,B,C),A,A))) # label(dt_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3036 (all A all B all C (m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3037 (all A (v8_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v1_partfun1(k1_eqrel_1(A),A,A) & v3_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3038 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3039 (all A all B (m2_relset_1(B,A,A) -> (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) <-> v1_relat_2(B) & A = k3_relat_1(B) & v8_relat_2(B) & v3_relat_2(B)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3040 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3041 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v1_relat_2(D) -> (r2_hidden(k4_tarski(B,C),D) <-> r2_hidden(B,k6_eqrel_1(A,D,C))))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3042 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3043 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3044 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k8_eqrel_1(A,B) = k7_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3045 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)) = B)))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3046 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> -(C != k1_eqrel_1(A) & k1_eqrel_1(A) != B & k1_eqrel_1(A) = k3_eqrel_1(A,B,C)))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3047 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3048 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3049 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3050 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_eqrel_1(A,C,B) = k3_eqrel_1(A,B,C))) # label(commutativity_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3051 (all A all B all C (v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3052 (all A (r1_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3053 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3054 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,A)))) -> ((all C (r2_hidden(C,B) -> v3_relat_2(C) & v8_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A))) -> v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) | B = k1_xboole_0))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3055 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3056 (all A all B all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> (all D (r2_hidden(D,A) -> (r2_hidden(k4_tarski(D,B),C) <-> k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D)))))) # label(t44_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3057 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> B = k5_eqrel_1(A,B,B))) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3058 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> (all C -(r2_hidden(C,A) & (all D -r2_hidden(C,k6_eqrel_1(A,B,D))))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3059 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (k5_eqrel_1(A,B,C) = D <-> r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v3_relat_2(E) -> (r1_tarski(k3_eqrel_1(A,B,C),E) -> r1_tarski(D,E))))))))))) # label(d3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3060 (all A all B (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3061 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3062 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> v3_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & m2_relset_1(k5_eqrel_1(A,B,C),A,A) & v8_relat_2(k5_eqrel_1(A,B,C)))) # label(dt_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3063 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> k4_eqrel_1(A,C,B) = k4_eqrel_1(A,B,C))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3064 (all A all B (r2_hidden(B,A) -> k1_tarski(B) = k6_eqrel_1(A,k6_partfun1(A),B))) # label(t33_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3065 (all A all B all C (v3_relat_2(C) & v1_partfun1(C,B,B) & m2_relset_1(C,B,B) & v8_relat_2(C) -> -(r2_hidden(A,k7_eqrel_1(B,C)) & (all D (m1_subset_1(D,B) -> k6_eqrel_1(B,C,D) != A))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3066 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C all D -(r2_hidden(C,A) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & k6_eqrel_1(A,B,D) != k6_eqrel_1(A,B,C) & r2_hidden(D,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3067 (all A all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_eqrel_1(A,B) = C <-> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (r2_hidden(E,A) & k6_eqrel_1(A,B,E) = D)))))))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3068 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,B,k4_eqrel_1(A,B,C)) = B)))) # label(t25_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3069 (all A all B all C (v1_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t11_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3070 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3071 (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) & (all A all B all C (p1_s1_eqrel_1(B,C) & p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(A,C))) & (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) -> (exists A ((all B all C (r2_hidden(B,f1_s1_eqrel_1) & p1_s1_eqrel_1(B,C) & r2_hidden(C,f1_s1_eqrel_1) <-> r2_hidden(k4_tarski(B,C),A))) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A) & v3_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3072 (all A all B (v1_relat_2(B) & v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C k10_relset_1(A,A,B,k1_tarski(C)) = k6_eqrel_1(A,B,C)))) # label(d4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3073 (all A all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (A = k1_xboole_0 -> k7_eqrel_1(A,B) = k1_xboole_0))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3074 (all A all B (r2_hidden(B,A) -> k6_eqrel_1(A,k1_eqrel_1(A),B) = A)) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3075 (all A all B (m2_relset_1(B,A,A) -> (exists C ((all D (v3_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3076 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,B) = B)) # label(idempotence_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3077 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,C,B) = k5_eqrel_1(A,B,C))))) # label(t23_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3078 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3079 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3080 (all A all B all C all D (v3_relat_2(D) & m2_relset_1(D,B,B) & v1_partfun1(D,B,B) & v8_relat_2(D) -> (all E (v8_relat_2(E) & m2_relset_1(E,B,B) & v1_partfun1(E,B,B) & v3_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (v1_relat_1(F) & v1_funct_1(F) & r1_xreal_0(np__1,k3_finseq_1(F)) & k1_funct_1(F,np__1) = A & k1_funct_1(F,k3_finseq_1(F)) = C & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E)) | r1_xreal_0(k3_finseq_1(F),G)))) & v1_finseq_1(F))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3081 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> m2_relset_1(k2_eqrel_1(A,B,C),A,A))) # label(dt_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3082 (all A all B all C all D all E (v8_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) -> (r2_hidden(k4_tarski(B,C),E) & r2_hidden(k4_tarski(C,D),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3083 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),np__1))) # label(t19_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3084 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3085 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> m2_finseq_2(k10_finseq_1(B,C),A,k4_finseq_2(np__2,A)))))))) # label(t121_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3086 (all A (v4_ordinal2(A) -> v1_relat_1(k1_finseq_2(A)) & v1_finseq_1(k1_finseq_2(A)) & v1_funct_1(k1_finseq_2(A)))) # label(dt_k1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3087 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k3_finseq_1(C) = A)))))) # label(t109_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3088 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k4_funcop_1(D,B,A) = C & r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) -> k3_finseq_1(C) = k3_finseq_1(B)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3089 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_funct_1(k5_funcop_1(C,A,B)) & v1_finseq_1(k5_funcop_1(C,A,B)) & v1_relat_1(k5_funcop_1(C,A,B))))))) # label(t80_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3090 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(B)) -> A = k1_funct_1(k1_finseq_2(B),A)))))) # label(t56_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3091 (all A all B (m2_finseq_1(B,A) -> m1_subset_1(B,k4_finseq_2(k3_finseq_1(B),A)))) # label(t110_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3092 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_finseq_1(k2_finseq_2(A,C),B))))))) # label(t77_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3093 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> k3_funcop_1(D,E,k6_finseq_1(B)) = k6_finseq_1(C) & k6_finseq_1(C) = k3_funcop_1(D,k6_finseq_1(A),F))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3094 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_1_finseq_2(B)) <-> (exists C exists D (m1_subset_1(C,B) & m1_subset_1(D,B) & A = k10_finseq_1(C,D)))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3095 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k2_square_1(np__0,k6_xcmplx_0(A,B)) = np__0))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3096 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (k3_finseq_1(B) = k3_finseq_1(A) & r1_tarski(B,C) & r1_tarski(A,C) -> B = A))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3097 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_relat_1(D) & v1_finseq_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_square_1(k3_finseq_1(F),k3_finseq_1(G))))))))))))))))) # label(t85_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3098 (all A (v4_ordinal2(A) -> (all B k2_funcop_1(k2_finseq_1(A),B) = k2_finseq_2(A,B)))) # label(d2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3099 (all A (v4_ordinal2(A) -> k4_finseq_1(k1_finseq_2(A)) = k2_finseq_1(A))) # label(t54_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3100 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k5_funcop_1(E,D,F),C))))))))))))) # label(t91_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3101 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m1_subset_1(D,B) -> D = k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,np__1)))))))))) # label(t136_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3102 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_2_finseq_2(B)) <-> (exists C exists D exists E (m1_subset_1(D,B) & A = k11_finseq_1(C,D,E) & m1_subset_1(E,B) & m1_subset_1(C,B)))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3103 (all A all B k2_tarski(A,B) = k2_relat_1(k10_finseq_1(A,B))) # label(t147_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3104 (all A (v4_ordinal2(A) -> (all B k2_finseq_1(A) = k4_finseq_1(k2_finseq_2(A,B))))) # label(t68_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3105 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> k1_partfun1(k5_numbers,A,A,B,k6_finseq_1(A),C) = k6_finseq_1(B))))) # label(t38_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3106 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,A) -> (H = k10_finseq_1(D,E) -> k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F)) = k4_funcop_1(G,H,F)))))))))))))))))) # label(t101_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3107 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (all J (m2_finseq_1(J,B) -> (J = k10_finseq_1(F,G) & I = k10_finseq_1(D,E) -> k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) = k3_funcop_1(H,I,J)))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3108 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(E) -> (r1_xreal_0(B,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C) | np__0 = B & A != np__0))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3109 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,C) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & v1_funct_1(F) -> (all G (m2_finseq_2(G,B,k4_finseq_2(A,B)) -> m2_finseq_2(k4_funcop_1(F,G,E),D,k4_finseq_2(A,D)))))))))))))))) # label(t142_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3110 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k3_square_1(B,C) = A -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(C))))))))) # label(t2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3111 (all A all B (v4_ordinal2(A) -> v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3112 (all A (v4_ordinal2(A) -> (all B k3_finseq_1(k2_finseq_2(A,B)) = A))) # label(t69_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3113 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A))) & r2_hidden(A,k2_relat_1(B))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3114 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_2(H,k2_zfmisc_1(A,B),C) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_1(H) -> (all I (m2_finseq_1(I,B) -> (k11_finseq_1(E,F,G) = I -> k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G))))))))))))))))))))) # label(t96_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3115 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3116 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (r2_hidden(A,k4_finseq_1(B)) -> r2_hidden(A,k4_finseq_1(k7_finseq_1(B,C)))))))))) # label(t18_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3117 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3118 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C ((exists D (m1_subset_1(D,A) & (exists E (m1_subset_1(E,A) & B = k11_finseq_1(C,D,E))))) & m1_subset_1(C,A))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3119 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_finseq_1(E,C) -> (all F (v1_funct_2(F,C,D) & m2_relset_1(F,C,D) & v1_funct_1(F) -> (E = k10_finseq_1(A,B) -> k1_partfun1(k5_numbers,C,C,D,E,F) = k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B))))))))))) # label(t40_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3120 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k2_relat_1(D) = k2_finseq_1(A) & C = k5_relat_1(D,B) & r1_xreal_0(A,k3_finseq_1(B)) -> A = k3_finseq_1(C)))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3121 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(k1_nat_1(A,np__1),B)) -> (exists D ((exists E (k8_finseq_1(B,D,k12_finseq_1(B,E)) = C & m1_subset_1(E,B))) & m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.75 3122 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> a_3_0_finseq_2(A,B,C) = k4_finseq_2(k1_nat_1(A,B),C))))))) # label(t125_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3123 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,A) -> (E = k4_funcop_1(F,G,D) -> k3_finseq_1(E) = k3_finseq_1(G)))))))))))))))) # label(t98_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3124 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (A != np__0 -> (all D (m1_subset_1(D,k2_finseq_1(A)) -> C = k1_funct_1(k2_finseq_2(A,C),D)))))))))) # label(t71_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3125 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (m2_finseq_1(E,A) -> (all F (m2_finseq_1(F,B) -> m2_finseq_1(k3_funcop_1(D,E,F),C))))))))))))) # label(t84_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3126 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(np__0,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> k8_finseq_1(B,D,C) = D & D = k8_finseq_1(B,C,D))))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3127 (all A (v4_ordinal2(A) -> v1_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(k1_finseq_2(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3128 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> v1_funct_1(B) & v1_funct_2(B,k4_finseq_1(B),A) & m2_relset_1(B,k4_finseq_1(B),A))))) # label(t30_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3129 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_2(E,k2_zfmisc_1(B,C),D) & v1_funct_1(E) -> (all F (m2_finseq_2(F,B,k4_finseq_2(A,B)) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t140_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3130 (all A all B all C (v4_ordinal2(B) -> ((exists D (m2_finseq_2(D,C,k3_finseq_2(C)) & A = D & B = k3_finseq_1(D))) <-> r2_hidden(A,a_2_0_finseq_2(B,C))))) # label(fraenkel_a_2_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3131 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3132 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C k7_finseq_1(k2_finseq_2(A,C),k2_finseq_2(B,C)) = k2_finseq_2(k1_nat_1(A,B),C)))))) # label(t143_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3133 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> m2_finseq_2(D,B,k4_finseq_2(A,B)))))))))) # label(t129_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3134 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D (r2_hidden(D,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) -> k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)) = k5_relat_1(k11_finseq_1(B,C,D),A))))) # label(t146_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3135 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C ((exists D (B = k10_finseq_1(C,D) & m1_subset_1(D,A))) & m1_subset_1(C,A))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3136 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3137 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(A,k2_finseq_1(B)) -> r2_hidden(A,k2_finseq_1(k1_nat_1(B,C)))))))))) # label(t9_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3138 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (m2_finseq_1(C,B) -> (r2_hidden(A,k4_finseq_1(C)) -> r2_hidden(k1_funct_1(C,A),B)))))) # label(t13_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3139 (all A all B all C all D (m2_subset_1(C,k1_numbers,k5_numbers) & -v1_xboole_0(D) & m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(A,a_3_0_finseq_2(B,C,D)) <-> (exists E exists F (m2_finseq_2(E,D,k4_finseq_2(B,D)) & m2_finseq_2(F,D,k4_finseq_2(C,D)) & A = k8_finseq_1(D,E,F)))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3140 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> -(k3_finseq_1(C) = k1_nat_1(A,B) & (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> -(C = k7_finseq_1(D,E) & B = k3_finseq_1(E) & A = k3_finseq_1(D))))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3141 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3142 (all A (v4_ordinal2(A) -> (all B all C (r2_hidden(B,k2_finseq_1(A)) -> C = k1_funct_1(k2_finseq_2(A,C),B))))) # label(t70_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3143 (all A (v4_ordinal2(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k1_finseq_2(A),B) = k7_relat_1(B,k2_finseq_1(A)))))) # label(t63_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3144 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k2_square_1(np__0,k6_xcmplx_0(A,B)),k1_numbers,k5_numbers))))) # label(t5_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3145 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (v1_funct_1(H) & m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) -> (all I (m2_finseq_1(I,A) -> (k11_finseq_1(D,E,F) = I -> k4_funcop_1(H,I,G) = k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G))))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3146 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3147 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_funct_2(B,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(B,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(B) -> v1_funct_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3148 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (B = k12_finseq_1(A,C) & m1_subset_1(C,A))))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3149 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k5_numbers,k1_nat_1(A,np__1))) = k1_finseq_2(k1_nat_1(A,np__1)))) # label(t60_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3150 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> m2_finseq_2(k1_finseq_2(A),k5_numbers,k4_finseq_2(A,k5_numbers)))) # label(t131_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3151 (all A (v4_ordinal2(A) -> (all B a_2_0_finseq_2(A,B) = k4_finseq_2(A,B)))) # label(d4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3152 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3153 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (A != np__0 -> (all B (m1_subset_1(B,k2_finseq_1(A)) -> B = k1_funct_1(k1_finseq_2(A),B)))))) # label(t57_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3154 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> -((all E (m2_finseq_1(E,C) -> (all F (m2_finseq_1(F,C) -> -(D = k8_finseq_1(C,E,F) & k3_finseq_1(F) = B & k3_finseq_1(E) = A))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3155 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D)) & C = k3_funcop_1(D,A,B) -> k3_finseq_1(C) = k3_square_1(k3_finseq_1(A),k3_finseq_1(B))))))))))) # label(t79_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3156 (all A all B (m1_finseq_2(B,A) <-> (all C (r2_hidden(C,B) -> m2_finseq_1(C,A))))) # label(d3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3157 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3158 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(C) -> (r1_xreal_0(A,k3_finseq_1(B)) -> v1_relat_1(k5_relat_1(C,B)) & v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B))))))))) # label(t43_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3159 (all A all B (-v1_xboole_0(B) -> ((exists C (m1_subset_1(C,B) & k12_finseq_1(B,C) = A)) <-> r2_hidden(A,a_1_0_finseq_2(B))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3160 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_finseq_1(E) & v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,B) -> (k5_funcop_1(F,D,G) = E -> k3_finseq_1(G) = k3_finseq_1(E)))))))))))))))) # label(t92_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3161 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (v1_funct_2(C,k4_finseq_1(B),k4_finseq_1(B)) & m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_1(C) -> m2_finseq_1(k1_partfun1(k4_finseq_1(B),k4_finseq_1(B),k5_numbers,A,C,B),A))))))) # label(t51_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3162 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> r2_hidden(k1_funct_1(A,C),B)))) -> m2_finseq_1(A,B))))) # label(t14_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3163 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3164 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> k1_funct_2(k2_finseq_1(A),B) = k4_finseq_2(A,B))))) # label(t111_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3165 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_xreal_0(k3_finseq_1(B),A) -> B = k5_relat_1(k1_finseq_2(A),B)))))) # label(t64_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3166 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k5_numbers,B) & v1_funct_2(C,k5_numbers,B) & v1_funct_1(C) -> m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B))))))) # label(t31_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3167 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3168 (all A (-v1_xboole_0(A) -> a_1_2_finseq_2(A) = k4_finseq_2(np__3,A))) # label(t122_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.78/6.76 3169 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k2_finseq_1(A)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) -> D = C))))))))) # label(t139_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3170 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v3_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) -> (k5_relat_1(C,A) = B -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t48_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3171 (all A (m1_finseq_2(k3_finseq_2(A),A) & -v1_xboole_0(k3_finseq_2(A)))) # label(dt_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3172 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> (all J (v1_funct_2(J,k2_zfmisc_1(A,B),C) & m2_relset_1(J,k2_zfmisc_1(A,B),C) & v1_funct_1(J) -> (all K (m2_finseq_1(K,A) -> (all L (m2_finseq_1(L,B) -> (K = k11_finseq_1(D,E,F) & L = k11_finseq_1(G,H,I) -> k3_funcop_1(J,K,L) = k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I))))))))))))))))))))))))))) # label(t90_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3173 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3174 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k3_square_1(np__0,A) = np__0 & k4_square_1(A,np__0) = A & k4_square_1(np__0,A) = A & np__0 = k3_square_1(A,np__0))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3175 (all A (v4_ordinal2(A) -> k6_partfun1(k2_finseq_1(A)) = k1_finseq_2(A))) # label(d1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3176 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> m2_finseq_2(k1_partfun1(k5_numbers,B,B,C,D,E),C,k4_finseq_2(A,C)))))))))))) # label(t133_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3177 (all A all B (v4_ordinal2(A) & -v1_xboole_0(B) -> -v1_xboole_0(k4_finseq_2(A,B)))) # label(fc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3178 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> m2_finseq_1(k11_finseq_1(B,C,D),A))))))))) # label(t16_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3179 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(C)) -> v1_funct_1(k4_funcop_1(C,B,A)) & v1_finseq_1(k4_funcop_1(C,B,A)) & v1_relat_1(k4_funcop_1(C,B,A))))))) # label(t82_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3180 (exists A (m2_finseq_1(A,f2_s1_finseq_2) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_2)) -> k1_funct_1(A,B) = f3_s1_finseq_2(B)))) & f1_s1_finseq_2 = k3_finseq_1(A))) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3181 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -(-r2_hidden(A,k2_finseq_1(B)) & k1_nat_1(B,np__1) != A & r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__1)))))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3182 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_finseq_2(C,B) -> -v1_xboole_0(C) & m1_finseq_2(C,A))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3183 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C)) -> (exists E ((exists F (k8_finseq_1(C,E,F) = D & m2_finseq_2(F,C,k4_finseq_2(B,C)))) & m2_finseq_2(E,C,k4_finseq_2(A,C)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3184 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k7_relat_1(C,k2_finseq_1(A)) = B & r1_xreal_0(k3_finseq_1(C),A) -> B = C))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3185 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (k2_finseq_1(A) = B -> (all D (m2_finseq_1(D,C) -> (all E (m2_finseq_1(E,B) -> (r1_xreal_0(A,k3_finseq_1(D)) -> m2_finseq_1(k1_partfun1(k5_numbers,B,k5_numbers,C,E,D),C))))))))))))) # label(t35_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3186 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_funct_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)))))) # label(t66_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3187 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> (all C (m2_finseq_2(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3188 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) = k2_finseq_2(k1_nat_1(A,np__1),B)))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3189 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (k4_finseq_2(B,C) = k4_finseq_2(A,C) -> A = B))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3190 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_relat_1(k3_funcop_1(C,A,B)) & v1_funct_1(k3_funcop_1(C,A,B)) & v1_finseq_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3191 (all A (-v1_xboole_0(A) -> a_1_1_finseq_2(A) = k4_finseq_2(np__2,A))) # label(t119_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3192 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,B) -> (all D (m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (r1_xreal_0(A,k3_finseq_1(C)) -> m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B)))))))))) # label(t50_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3193 (all A (-v1_xboole_0(A) -> a_1_0_finseq_2(A) = k4_finseq_2(np__1,A))) # label(t116_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3194 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & m2_relset_1(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,B) -> (H = k10_finseq_1(E,F) -> k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F)) = k5_funcop_1(G,D,H)))))))))))))))))) # label(t95_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3195 (all A exists B (-v1_xboole_0(B) & m1_finseq_2(B,A))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3196 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> k6_finseq_1(C) = k4_funcop_1(E,k6_finseq_1(A),D))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3197 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (A = k3_finseq_1(B) & A = k3_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k2_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))) -> C = B))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3198 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> m2_finseq_2(k2_finseq_2(A,C),B,k4_finseq_2(A,B)))))))) # label(t132_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3199 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (r1_xreal_0(A,k3_finseq_1(B)) & k5_relat_1(D,B) = C -> k3_finseq_1(C) = A))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3200 (all A m1_subset_1(k6_finseq_1(A),k4_finseq_2(np__0,A))) # label(t114_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3201 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> m2_subset_1(k3_square_1(A,B),k1_numbers,k5_numbers) & m2_subset_1(k4_square_1(A,B),k1_numbers,k5_numbers))))) # label(t1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3202 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(A,C)) -> (all E (m2_finseq_2(E,C,k4_finseq_2(B,C)) -> m2_finseq_2(k8_finseq_1(C,D,E),C,k4_finseq_2(k1_nat_1(A,B),C)))))))))))) # label(t127_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3203 (all A all B (v4_ordinal2(A) -> m1_finseq_2(k4_finseq_2(A,B),B))) # label(dt_k4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3204 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_finseq_1(A),B) & v1_funct_2(C,k2_finseq_1(A),B) & v1_funct_1(C) -> m2_finseq_1(C,B))))))) # label(t28_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3205 (all A k4_finseq_2(np__0,A) = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A))) # label(t112_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3206 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) -> k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)) = k5_relat_1(k10_finseq_1(B,C),A))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3207 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> (all C (m2_finseq_2(C,A,B) -> m2_finseq_1(C,A))))) # label(dt_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3208 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> -((all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D k7_finseq_1(C,k9_finseq_1(D)) != B))) & k1_nat_1(A,np__1) = k3_finseq_1(B)))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3209 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(np__0 != k3_finseq_1(B) & (all C (m2_finseq_1(C,A) -> (all D (m1_subset_1(D,A) -> B != k8_finseq_1(A,C,k12_finseq_1(A,D))))))))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3210 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> (k2_finseq_1(A) = k2_relat_1(D) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B))))))))))) # label(t134_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3211 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3212 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,B) -> (k12_finseq_1(B,E) = G -> k5_funcop_1(F,D,G) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3213 (all A all B all C k1_enumset1(A,B,C) = k2_relat_1(k11_finseq_1(A,B,C))) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3214 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_finseq_1(B) = k3_square_1(A,k3_finseq_1(C))))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3215 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)))))))))) # label(t135_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3216 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) -> (k7_finseq_1(C,k9_finseq_1(A)) = k7_finseq_1(D,k9_finseq_1(B)) -> A = B & D = C))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3217 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k4_finseq_1(C) = k2_finseq_1(A))))))) # label(t144_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3218 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> B = k6_finseq_1(A))) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3219 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) -> k6_xcmplx_0(B,A) = k2_square_1(np__0,k6_xcmplx_0(B,A))))))) # label(t4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3220 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,A) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (k1_partfun1(k5_numbers,A,A,B,D,E) = C -> k3_finseq_1(C) = k3_finseq_1(D)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3221 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m2_finseq_1(C,B) -> m2_finseq_1(C,A))))))) # label(t27_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3222 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (C = k5_funcop_1(D,A,B) & r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3223 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_2(F,k2_zfmisc_1(B,C),D) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k5_funcop_1(F,E,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t141_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3224 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,B) -> (all E (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (D = k9_finseq_1(A) -> k9_finseq_1(k1_funct_1(E,A)) = k1_partfun1(k5_numbers,B,B,C,D,E)))))))))) # label(t39_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3225 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (k2_finseq_1(A) = B -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3226 (all A k3_finseq_2(A) = k13_finseq_1(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3227 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> m2_finseq_1(k4_funcop_1(E,F,D),C))))))))))))) # label(t97_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3228 (all A (v4_ordinal2(A) -> k3_finseq_1(k1_finseq_2(A)) = A)) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3229 (all A all B (-v1_xboole_0(B) -> ((exists C (A = k4_finseq_2(C,B) & m2_subset_1(C,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_1_3_finseq_2(B))))) # label(fraenkel_a_1_3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3230 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> r1_tarski(B,k3_finseq_2(A)))) # label(t105_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3231 (all A k2_finseq_2(np__3,A) = k11_finseq_1(A,A,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3232 (all A (-v1_xboole_0(A) -> k3_tarski(a_1_3_finseq_2(A)) = k3_finseq_2(A))) # label(t128_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3233 (all A (m1_finseq_2(k13_finseq_1(A),A) & -v1_xboole_0(k13_finseq_1(A)))) # label(t104_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3234 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & v1_funct_1(C) -> (k5_relat_1(C,A) = B & k4_finseq_1(A) = k2_relat_1(C) -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3235 (all A all B all C all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (m2_finseq_1(F,D) -> (all G (v1_funct_2(G,D,E) & m2_relset_1(G,D,E) & v1_funct_1(G) -> (k11_finseq_1(A,B,C) = F -> k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C)) = k1_partfun1(k5_numbers,D,D,E,F,G)))))))))) # label(t41_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3236 (all A all B all C (m2_finseq_1(C,A) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_finseq_1(k1_partfun1(k5_numbers,A,A,B,C,D),B))))) # label(t36_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3237 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_finseq_1(F) = k3_finseq_1(G) & k3_funcop_1(E,F,G) = D -> k3_finseq_1(D) = k3_finseq_1(G) & k3_finseq_1(D) = k3_finseq_1(F)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3238 p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2)) & (all A (m2_finseq_1(A,f1_s2_finseq_2) -> (all B (m1_subset_1(B,f1_s2_finseq_2) -> (p1_s2_finseq_2(A) -> p1_s2_finseq_2(k8_finseq_1(f1_s2_finseq_2,A,k12_finseq_1(f1_s2_finseq_2,B)))))))) -> (all A (m2_finseq_1(A,f1_s2_finseq_2) -> p1_s2_finseq_2(A))) # label(s2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3239 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,A) -> (all H (m2_finseq_1(H,B) -> (k12_finseq_1(B,E) = H & k12_finseq_1(A,D) = G -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k3_funcop_1(F,G,H)))))))))))))))))) # label(t88_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3240 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m2_finseq_2(k12_finseq_1(A,B),A,k4_finseq_2(np__1,A)))))) # label(t118_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3241 (all A all B (m1_finseq_2(B,A) & -v1_xboole_0(B) -> (exists C m2_finseq_2(C,A,B)))) # label(existence_m2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3242 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k5_relat_1(k1_finseq_2(A),C) = C)))))) # label(t138_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3243 (all A k2_finseq_2(np__2,A) = k10_finseq_1(A,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3244 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_1(D) -> (r1_xreal_0(B,k3_finseq_1(C)) -> v1_finseq_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)) | np__0 != A & B = np__0))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3245 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> m2_finseq_1(k10_finseq_1(B,C),A))))))) # label(t15_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3246 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> k5_funcop_1(E,D,k6_finseq_1(B)) = k6_finseq_1(C))))))))))) # label(t93_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3247 (all A (v4_ordinal2(A) -> m2_finseq_1(k6_partfun1(k2_finseq_1(A)),k5_numbers))) # label(t52_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3248 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_2(D,k5_numbers,B) & m2_relset_1(D,k5_numbers,B) & v1_funct_1(D) -> (C = k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) -> k3_finseq_1(C) = A))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3249 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,A) -> (G = k12_finseq_1(A,D) -> k4_funcop_1(F,G,E) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E))))))))))))))))) # label(t100_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3250 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(A),k1_relat_1(C)) & k5_relat_1(A,C) = B -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3251 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> m2_finseq_2(k11_finseq_1(B,C,D),A,k4_finseq_2(np__3,A)))))))))) # label(t124_finseq_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3252 (all A all B (m1_pboole(B,A) -> m1_pboole(k6_pboole(A,B),k3_finseq_2(A)))) # label(dt_k6_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3253 (all A all B all C all D (v1_funct_1(C) & m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> k5_relat_1(C,D) = k8_pboole(A,B,C,D))) # label(redefinition_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3254 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k12_pboole(A,B,C),A))) # label(dt_k12_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3255 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k11_pboole(A,B,C),A))) # label(dt_k11_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3256 (all A (v1_funct_1(k1_pboole(A)) & v3_relat_1(k1_pboole(A)) & v1_relat_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3257 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,B,k1_pboole(A)),B))) # label(t65_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3258 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3259 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) & v2_relat_1(B) -> r2_pboole(A,B,C)))))) # label(t144_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3260 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r7_pboole(A,B,C) & r7_pboole(A,C,D) -> r7_pboole(A,B,D)))))))) # label(t132_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3261 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) & r1_pboole(A,B,D) -> r4_pboole(A,C,D)))))))) # label(t10_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3262 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k3_pboole(A,C,D)) -> r4_pboole(A,B,D) & r4_pboole(A,B,C)))))))) # label(t111_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3263 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,B)),k1_pboole(A)) & r6_pboole(A,k4_pboole(A,B,k2_pboole(A,B,C)),k1_pboole(A)))))) # label(t67_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3264 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> v1_xboole_0(k1_funct_1(B,C)))) <-> v3_relat_1(B)))) # label(d15_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3265 (all A all B (m1_pboole(B,A) -> (r6_pboole(A,B,k1_pboole(A)) <-> v3_relat_1(B)))) # label(t141_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3266 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k4_pboole(A,C,D)) -> r4_pboole(A,B,C)))))))) # label(t113_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3267 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,B,C))))))) # label(t101_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3268 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,C)))))) # label(t89_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3269 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,B,C) -> v1_funcop_1(D))))) # label(cc3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3270 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3271 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d5_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3272 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) = k5_pboole(A,B,C))))) # label(d12_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3273 (exists A (v3_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3274 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (C = B <-> r6_pboole(A,B,C)))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3275 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),B) -> r5_pboole(A,B,C)))))) # label(t128_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3276 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k4_pboole(A,B,C),B))))) # label(t62_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3277 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),B),B) & r6_pboole(A,k3_pboole(A,k2_pboole(A,C,B),B),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,B)),B) & r6_pboole(A,k3_pboole(A,B,k2_pboole(A,B,C)),B))))) # label(t36_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3278 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,B,D) -> r4_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t112_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3279 (all A all B (m1_pboole(B,A) -> (r2_pboole(A,B,k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))) # label(t50_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3280 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) & r2_pboole(A,C,D) -> r1_pboole(A,B,D)))))))) # label(t9_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3281 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)) & r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,B)),k4_pboole(A,B,C)))))) # label(t76_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3282 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) & r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))))))))) # label(t45_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3283 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t57_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3284 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3285 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3286 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_funct_1(B,C) = k1_xboole_0)) -> B = k1_pboole(A)))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3287 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k3_pboole(A,C,D)) -> r2_pboole(A,B,C) & r2_pboole(A,B,D)))))))) # label(t44_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3288 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r4_pboole(A,B,D) & r2_pboole(A,B,C) -> r4_pboole(A,C,E)))))))))) # label(t110_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3289 (all A all B all C (m1_pboole(B,A) & m1_subset_1(C,A) & v2_relat_1(B) & -v1_xboole_0(A) -> -v1_xboole_0(k1_funct_1(B,C)))) # label(fc2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3290 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,D,C)),k3_pboole(A,k2_pboole(A,B,D),C))))))))) # label(t27_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3291 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))) # label(t121_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3292 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3293 (all A all B (m2_relset_1(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_2(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> k8_funct_2(k5_numbers,k3_finseq_2(k1_tarski(A)),B,C) = k2_finseq_2(C,A))) <-> B = k9_pboole(A)))) # label(d20_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3294 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) | r4_pboole(A,B,D) -> r4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t106_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3295 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,C,k2_pboole(A,k4_pboole(A,C,B),B)) & r6_pboole(A,C,k2_pboole(A,B,k4_pboole(A,C,B)))))))) # label(t72_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3296 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3297 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3298 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,B,B),k1_pboole(A)))) # label(t92_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3299 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3300 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k2_pboole(A,B,B) = B)) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3301 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (A = k1_relat_1(B) <-> m1_pboole(B,A)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3302 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r7_pboole(A,B,B))) # label(reflexivity_r7_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3303 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,D,C),k4_pboole(A,D,B))))))))) # label(t60_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3304 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,k4_pboole(A,C,D)) -> r1_pboole(A,B,C)))))))) # label(t12_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3305 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> ((all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k1_funct_1(C,D) = k4_card_3(k5_relat_1(D,B)))) <-> C = k6_pboole(A,B)))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3306 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) & r2_pboole(A,C,B) <-> r6_pboole(A,B,C)))))) # label(d13_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3307 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3308 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,D,C) & r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3309 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t94_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3310 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -r3_pboole(A,B,k1_pboole(A)))))) # label(t136_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3311 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r2_pboole(A,k3_pboole(A,B,C),k2_pboole(A,B,D)))))))) # label(t26_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3312 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t34_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3313 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r4_pboole(A,B,C) -> r4_pboole(A,C,B)))) # label(symmetry_r4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3314 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,C,B),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3315 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v3_relat_1(B) -> -v2_relat_1(B)))))) # label(cc2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3316 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k5_pboole(A,k5_pboole(A,B,C),D),k5_pboole(A,B,k5_pboole(A,C,D))))))))) # label(t98_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3317 (all A -(k1_xboole_0 = f2_s1_pboole(A) & r2_hidden(A,f1_s1_pboole))) -> (exists A (m1_pboole(A,f1_s1_pboole) & (all B (r2_hidden(B,f1_s1_pboole) -> r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)))))) # label(s1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3318 (all A all B (m1_pboole(B,A) -> (all C (m2_pboole(C,A,B) -> m1_pboole(C,A))))) # label(dt_m2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.76 3319 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k2_pboole(A,B,C),D) -> r2_pboole(A,C,D) & r2_pboole(A,B,D)))))))) # label(t43_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3320 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k2_pboole(A,C,D)),k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t38_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3321 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,k4_pboole(A,C,B)) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t63_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3322 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) & -v1_xboole_0(B) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3323 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> v1_funct_1(k6_pboole(A,B)) & -v3_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & v1_relat_1(k6_pboole(A,B)))) # label(fc1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3324 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,C)),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)),B))))) # label(t71_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3325 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & r5_pboole(A,B,C)))))))) # label(t135_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3326 (all A all B (m1_pboole(B,A) -> (all C (r2_hidden(C,A) -> m1_subset_1(k1_funct_1(B,C),k2_relat_1(B)))))) # label(t151_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3327 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> -r2_hidden(k1_xboole_0,k2_relat_1(B)))) # label(t149_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3328 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k5_pboole(A,B,C),k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t95_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3329 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,k4_pboole(A,C,D)) -> r4_pboole(A,C,k4_pboole(A,B,D))))))))) # label(t115_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3330 (exists A (m1_pboole(A,f1_s4_pboole) & (all B (r2_hidden(B,f1_s4_pboole) -> k1_funct_1(A,B) = f2_s4_pboole(B))))) # label(s4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3331 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k3_pboole(A,C,B) = k3_pboole(A,B,C))) # label(commutativity_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3332 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3333 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t79_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3334 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,B,D) & (all E (m1_pboole(E,A) -> (r2_pboole(A,E,C) & r2_pboole(A,E,D) -> r2_pboole(A,E,B)))) <-> r6_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3335 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r1_pboole(A,D,C)))) <-> r7_pboole(A,B,C)))))) # label(d14_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3336 (all A all B (m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & v1_funct_1(k10_pboole(A,B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3337 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),B)))))) # label(t127_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3338 (all A (m2_relset_1(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_2(k9_pboole(A),k5_numbers,k3_finseq_2(k1_tarski(A))) & v1_funct_1(k9_pboole(A)))) # label(dt_k9_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3339 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k3_pboole(A,B,C),A))) # label(dt_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3340 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) -> v1_setfam_1(k2_relat_1(A))))) # label(t1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3341 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,B,D) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3342 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> k1_funct_1(C,D) = k1_funct_1(B,D))) -> C = B))))) # label(t3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3343 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r6_pboole(A,B,B))) # label(reflexivity_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3344 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(r4_pboole(A,B,B) & k1_pboole(A) = B))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3345 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k4_pboole(A,B,C),A))) # label(dt_k4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3346 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,C,B) <-> m4_pboole(C,A,B)))))) # label(d23_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3347 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3348 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B) & r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3349 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,k3_pboole(A,B,C)),k3_pboole(A,B,C)) & r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),C),k3_pboole(A,B,C)))))) # label(t48_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3350 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3351 (all A all B all C (-v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) -> (r3_pboole(A,B,C) -> -r3_pboole(A,C,B)))) # label(antisymmetry_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3352 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D)),B) -> r2_pboole(A,k3_pboole(A,C,D),B)))))))) # label(t41_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3353 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)))))) # label(t129_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3354 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k5_pboole(A,B,C),A))) # label(dt_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3355 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k2_pboole(A,B,C),k1_pboole(A)) -> r6_pboole(A,C,k1_pboole(A)) & r6_pboole(A,B,k1_pboole(A))))))) # label(t54_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3356 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))))))))) # label(t75_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3357 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3358 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3359 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,k3_pboole(A,B,C),C) & r2_pboole(A,k3_pboole(A,B,C),B))))) # label(t17_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3360 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t78_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3361 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3362 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r2_pboole(A,B,C) -> v2_relat_1(C)))))) # label(t143_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3363 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k2_pboole(A,B,C))))))) # label(t105_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3364 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k3_pboole(A,k1_pboole(A),B),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,B,k1_pboole(A)),k1_pboole(A)))) # label(t55_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3365 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B))) # label(t91_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3366 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))))))) # label(t83_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3367 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,B,C) -> r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,E))))))))))) # label(t23_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3368 (all A all B (m1_pboole(B,A) -> (exists C m2_pboole(C,A,B)))) # label(existence_m2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3369 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> (exists C (m1_pboole(C,A) & r1_pboole(A,C,B))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3370 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k3_pboole(A,B,C),k5_pboole(A,B,C)))))) # label(t120_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3371 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> m1_pboole(k2_pboole(A,B,C),A))) # label(dt_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3372 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,B,D) -> r4_pboole(A,D,C)))))))) # label(t109_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3373 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (m4_pboole(C,A,B) & v1_funct_1(C) & v2_relat_1(C) & v1_relat_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3374 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C)) = k2_finseq_2(A,C)))) # label(t152_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3375 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(-r4_pboole(A,B,C) & r4_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C))))))))) # label(t114_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3376 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,C,D) & r2_pboole(A,B,C) -> r2_pboole(A,B,D)))))))) # label(t15_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3377 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,B,k4_pboole(A,C,B)))))) # label(t118_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3378 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k5_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),D))))))))) # label(t97_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3379 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) & v2_relat_1(D) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,C) & r1_pboole(A,E,B) <-> r1_pboole(A,E,D)))) -> r6_pboole(A,D,k3_pboole(A,B,C))))))))) # label(t148_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3380 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k2_pboole(A,C,B) = k2_pboole(A,B,C))) # label(commutativity_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3381 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3382 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> (r3_pboole(A,B,C) <-> r1_pboole(A,B,C)))) # label(redefinition_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3383 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> r2_pboole(A,B,B))) # label(reflexivity_r2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3384 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3385 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_subset_1(C,k2_relat_1(B)) -> (exists D (C = k1_funct_1(B,D) & r2_hidden(D,A))))))))) # label(t150_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3386 (all A all B (m1_pboole(B,A) -> ((all C -(v1_xboole_0(k1_funct_1(B,C)) & r2_hidden(C,A))) <-> v2_relat_1(B)))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3387 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))))))))) # label(t85_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3388 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A))))))))) # label(t139_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3389 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k3_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3390 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r2_pboole(A,B,D) -> r2_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t19_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3391 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))) & r6_pboole(A,k3_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t46_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3392 (all A all B (m1_pboole(B,A) -> (v2_pboole(B,A) <-> v2_relat_1(B)))) # label(redefinition_v2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3393 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> B = k3_pboole(A,B,B))) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3394 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) & r2_hidden(D,A)))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3395 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funcop_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(C,D) = k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)))) & k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) = k1_relat_1(C) <-> C = k13_pboole(A,B)))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3396 (all A all B (v1_relat_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3397 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k5_pboole(A,B,C) = k5_pboole(A,C,B))) # label(commutativity_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3398 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) -> r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A))))))))) # label(t52_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3399 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t35_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3400 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (all D (m3_pboole(D,A,B,C) -> m1_pboole(D,A))))) # label(dt_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3401 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3402 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))))))) # label(t104_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3403 (all A exists B (v1_funct_1(B) & v1_funcop_1(B) & v1_relat_1(B) & m1_pboole(B,A))) # label(rc4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3404 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k2_pboole(A,C,D)) <-> (all E (m1_pboole(E,A) -> (r2_pboole(A,D,E) & r2_pboole(A,C,E) -> r2_pboole(A,B,E)))) & r2_pboole(A,D,B) & r2_pboole(A,C,B)))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3405 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r5_pboole(A,E,C) & r5_pboole(A,D,B) & r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) -> r6_pboole(A,D,C) & r6_pboole(A,E,B)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3406 (all A all B (m1_pboole(B,A) -> (v1_pboole(B,A) <-> v3_relat_1(B)))) # label(redefinition_v1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3407 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) <-> r6_pboole(A,k4_pboole(A,B,C),k1_pboole(A))))))) # label(t58_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3408 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r5_pboole(A,B,C) -> r5_pboole(A,C,B)))) # label(symmetry_r5_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3409 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -r4_pboole(A,k1_pboole(A),B) & -r4_pboole(A,B,k1_pboole(A)))))) # label(t138_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3410 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C all D (m1_pboole(D,k1_tarski(C)) -> (k2_funcop_1(k1_tarski(C),A) = D -> k1_funct_2(k2_finseq_1(B),A) = k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B)))))))) # label(t153_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3411 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,k1_pboole(A),B),k1_pboole(A)))) # label(t66_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3412 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r7_pboole(A,B,C)))))) # label(t130_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3413 (all A all B (m1_pboole(B,A) -> (all C (m4_pboole(C,A,B) -> m1_pboole(C,A))))) # label(dt_m4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3414 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r6_pboole(A,B,C) -> r6_pboole(A,C,B)))) # label(symmetry_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3415 (all A all B k1_xboole_0 = k1_funct_1(k1_pboole(B),A)) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3416 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t88_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3417 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),C),k2_pboole(A,B,C)) & r6_pboole(A,k2_pboole(A,B,k2_pboole(A,B,C)),k2_pboole(A,B,C)))))) # label(t47_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3418 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r5_pboole(A,C,D) & r2_pboole(A,B,D) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t123_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3419 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D)),B) -> r2_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t40_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3420 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,B,C),B),B) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,B),B),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,B)),B) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,B,C)),B))))) # label(t37_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3421 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r5_pboole(A,k3_pboole(A,B,C),k4_pboole(A,B,C)))))) # label(t119_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3422 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t80_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3423 (all A k2_funcop_1(A,k1_xboole_0) = k1_pboole(A)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3424 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))))))))) # label(t59_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3425 (all A all B (m1_pboole(B,A) -> (exists C m4_pboole(C,A,B)))) # label(existence_m4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3426 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (r2_hidden(D,A) -> k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) = k1_funct_1(k5_pboole(A,B,C),D))))))) # label(t4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3427 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_relat_1(A) <-> k1_xboole_0 = A | k2_relat_1(A) = k1_tarski(k1_xboole_0)))) # label(t2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3428 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) = k1_funct_1(D,E))) <-> k14_pboole(A,B,C) = D))))))) # label(d25_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3429 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,C,k2_pboole(A,C,B))))))) # label(t103_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3430 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -(r4_pboole(A,B,C) & (all D (m1_pboole(D,A) -> -(r1_pboole(A,D,C) & r1_pboole(A,D,B))))))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3431 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,C,B),C) & r6_pboole(A,k2_pboole(A,B,C),C)))))) # label(t24_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3432 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B))) # label(rc3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3433 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,B,C)),k3_pboole(A,B,C)))))) # label(t74_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3434 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,C,k2_pboole(A,B,C)) & r2_pboole(A,B,k2_pboole(A,B,C)))))) # label(t16_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3435 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,E) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,E))))))))))) # label(t22_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3436 (all A all B (m1_pboole(B,A) -> v1_relat_1(B) & v1_funct_1(B))) # label(dt_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3437 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)) -> r6_pboole(A,B,C)))))) # label(t86_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3438 (all A exists B (v1_relat_1(B) & v1_funct_1(B) & v3_relat_1(B) & m1_pboole(B,A))) # label(rc2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3439 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,C),k5_pboole(A,B,k4_pboole(A,C,B))))))) # label(t100_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3440 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k4_pboole(A,B,B),k1_pboole(A)))) # label(t64_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3441 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),k4_pboole(A,B,C)))))) # label(t81_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3442 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,k3_pboole(A,C,D)) <-> r1_pboole(A,B,C) & r1_pboole(A,B,D)))))))) # label(t8_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3443 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v3_relat_1(B) & r2_pboole(A,C,B) -> v3_relat_1(C)))))) # label(t142_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3444 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (m2_pboole(C,A,B) <-> (all D (r2_hidden(D,A) -> m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D))))))))) # label(d17_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3445 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> v1_funct_1(k1_funct_1(D,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)))) <-> m3_pboole(D,A,B,C)))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3446 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,C) | r1_pboole(A,B,D) -> r1_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t7_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3447 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k2_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d7_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3448 (all A all B all C (m1_pboole(C,A) & v1_funcop_1(C) & m1_pboole(B,A) -> m1_pboole(k14_pboole(A,B,C),A))) # label(dt_k14_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3449 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (v2_relat_1(B) & r7_pboole(A,B,C) -> v2_relat_1(C)))))) # label(t145_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3450 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k12_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d22_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3451 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k11_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3452 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (v2_relat_1(B) -> -v3_relat_1(B)))))) # label(cc1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3453 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),C),k4_pboole(A,B,C)))))) # label(t84_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3454 (all A -((all B -p1_s3_pboole(A,B)) & r2_hidden(A,f1_s3_pboole))) -> (exists A ((all B (r2_hidden(B,f1_s3_pboole) -> p1_s3_pboole(B,k1_funct_1(A,B)))) & m1_pboole(A,f1_s3_pboole))) # label(s3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3455 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (exists D m3_pboole(D,A,B,C)))) # label(existence_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3456 (exists A (m1_pboole(A,f1_s2_pboole) & (all B (r2_hidden(B,f1_s2_pboole) -> (all C (p1_s2_pboole(B,C) & r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) <-> r2_hidden(C,k1_funct_1(A,B)))))))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3457 (exists A ((all B (m1_subset_1(B,f1_s5_pboole) -> k1_funct_1(A,B) = f2_s5_pboole(B))) & m1_pboole(A,f1_s5_pboole))) # label(s5_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3458 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r6_pboole(A,k4_pboole(A,B,C),B)))))) # label(t126_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3459 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k2_pboole(A,C,D)) & r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3460 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C)) & r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)))))) # label(t73_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3461 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) <-> r6_pboole(A,k4_pboole(A,B,C),B)))))) # label(t77_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3462 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v2_relat_1(D) & v1_funct_1(C) & -v1_xboole_0(B) -> v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A))) # label(dt_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3463 (all A all B (m1_pboole(B,A) -> (all C (v2_relat_1(C) & m1_pboole(C,A) -> ((all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) <-> r1_pboole(A,D,C)))) -> r6_pboole(A,C,B)))))) # label(t147_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3464 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k4_pboole(A,B,C),k5_pboole(A,B,k3_pboole(A,B,C))))))) # label(t102_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3465 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)))) <-> r5_pboole(A,B,C)))))) # label(d11_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3466 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k2_pboole(A,k3_pboole(A,B,C),k3_pboole(A,C,D)),k3_pboole(A,D,B)),k3_pboole(A,k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,C,D)),k2_pboole(A,D,B))))))))) # label(t42_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3467 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3468 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(-r5_pboole(A,B,C) & r2_pboole(A,C,D) & r5_pboole(A,B,D)))))))) # label(t116_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3469 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),D)))))))) # label(t68_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3470 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) -> k5_relat_1(C,D) = k7_pboole(A,B,C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3471 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,k5_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k4_pboole(A,C,k2_pboole(A,B,D)))))))))) # label(t96_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3472 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C)) & r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D))))))))) # label(t20_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3473 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r2_pboole(A,B,C) & r2_pboole(A,D,E) -> r2_pboole(A,k4_pboole(A,B,E),k4_pboole(A,C,D))))))))))) # label(t61_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3474 (all A all B (m1_pboole(B,A) -> -(r5_pboole(A,B,B) & B != k1_pboole(A)))) # label(t122_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3475 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k3_pboole(A,C,B),B) & r6_pboole(A,k3_pboole(A,B,C),B)))))) # label(t25_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3476 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,B,D),C)))))))) # label(t82_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3477 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k4_pboole(A,C,D)),k4_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t87_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3478 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r3_pboole(A,B,D) & k3_pboole(A,C,D) = k1_pboole(A) & r3_pboole(A,B,C)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3479 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k4_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d9_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3480 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C)) & r2_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))))))))) # label(t21_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3481 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3482 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))) & r6_pboole(A,k2_pboole(A,k3_pboole(A,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))))))))) # label(t39_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3483 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,C) & r2_pboole(A,C,D) -> r4_pboole(A,B,D)))))))) # label(t108_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3484 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r1_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d4_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3485 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k4_pboole(A,B,k4_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k3_pboole(A,B,D))))))))) # label(t70_pboole) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3486 (all A all B (-v3_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_struct_0(A) -> (all C (m1_struct_0(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3487 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_struct_0(C,A,B) -> m1_subset_1(C,u1_struct_0(A)))))) # label(dt_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3488 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3489 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> C = A & B = D)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3490 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3491 (all A all B (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3492 (all A (v1_struct_0(g1_struct_0(A)) & l1_struct_0(g1_struct_0(A)))) # label(dt_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3493 (all A all B (g1_struct_0(B) = g1_struct_0(A) -> A = B)) # label(free_g1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3494 (all A (l1_struct_0(A) & -v3_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3495 (all A (l2_struct_0(A) -> m1_subset_1(u2_struct_0(A),u1_struct_0(A)))) # label(dt_u2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3496 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3497 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3498 (all A all B (m1_subset_1(B,A) -> v2_struct_0(g2_struct_0(A,B)) & l2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3499 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3500 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3501 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_struct_0(A) -> m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3502 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_tarski(B,C) = k2_struct_0(A,B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3503 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3504 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k2_struct_0(A,C,B) = k2_struct_0(A,B,C))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3505 (all A all B (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) -> k1_tarski(B) = k1_struct_0(A,B))) # label(redefinition_k1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3506 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3507 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3508 (exists A (v2_struct_0(A) & l2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3509 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> g1_struct_0(u1_struct_0(A)) = A))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3510 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3511 (all A (l2_struct_0(A) -> (v2_struct_0(A) -> A = g2_struct_0(u1_struct_0(A),u2_struct_0(A))))) # label(abstractness_v2_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3512 (all A (l1_struct_0(A) -> (v3_struct_0(A) <-> v1_xboole_0(u1_struct_0(A))))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3513 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)) = k4_lattices(A,B,k3_lattices(A,C,D)))))))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)) = k3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t19_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3514 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3515 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3516 (all A (l3_lattices(A) -> (v3_lattices(A) -> A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A))))) # label(abstractness_v3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3517 (exists A (v2_lattices(A) & l2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3518 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3519 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_lattices(A) & v6_lattices(A) -> k4_lattices(A,B,C) = k4_lattices(A,C,B))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3520 (all A all B all C (v4_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) & -v3_struct_0(A) -> k1_lattices(A,B,C) = k3_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3521 (all A (-v3_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k6_lattices(A),B) = B)))) # label(t43_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3522 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3523 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_lattices(A) = k3_lattices(A,k7_lattices(A,B),B))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3524 (all A (l2_lattices(A) -> (v2_lattices(A) -> g2_lattices(u1_struct_0(A),u2_lattices(A)) = A))) # label(abstractness_v2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3525 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k7_lattices(A,B),B) = k5_lattices(A))))) # label(t47_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3526 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)) = k7_lattices(A,k3_lattices(A,B,C)))))))) # label(t51_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3527 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v1_lattices(g1_lattices(A,B)) & l1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3528 (all A all B all C (-v3_struct_0(A) & l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k2_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3529 (all A all B all C (l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v6_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3530 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) & v13_lattices(A) <-> v15_lattices(A)))) # label(d15_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.77 3531 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v13_lattices(A) & v14_lattices(A) -> -v3_struct_0(A) & v15_lattices(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3532 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v3_lattices(g3_lattices(A,B,C)) & l3_lattices(g3_lattices(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3533 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3534 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3535 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v5_lattices(A) & v8_lattices(A) & v7_lattices(A) & v9_lattices(A) & v6_lattices(A) & v4_lattices(A) <-> v10_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3536 (all A (l2_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k6_lattices(A),u1_struct_0(A)))) # label(dt_k6_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3537 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) = k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)))))))) -> v11_lattices(A)))) # label(t29_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3538 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3539 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k7_lattices(A,k4_lattices(A,B,C)) = k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))))))) # label(t50_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3540 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3541 (exists A (v3_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3542 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3543 (all A all B (-v1_xboole_0(A) & v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> -v3_struct_0(g1_lattices(A,B)) & v1_lattices(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3544 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)))))))) <-> v11_lattices(A)))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3545 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> v3_lattices(g3_lattices(A,B,C)) & -v3_struct_0(g3_lattices(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3546 (all A (-v3_struct_0(A) & l2_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> C = k1_lattices(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3547 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3548 (exists A (v3_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v15_lattices(A) & v13_lattices(A) & v7_lattices(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3549 (all A (-v3_struct_0(A) & l3_lattices(A) & v8_lattices(A) & v6_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3550 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3551 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v16_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & r2_lattices(A,C,B)))))))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3552 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v9_lattices(A) & v8_lattices(A) & v5_lattices(A) -> v10_lattices(A) & -v3_struct_0(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3553 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k3_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3554 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3555 (all A (v8_lattices(A) & l3_lattices(A) & v9_lattices(A) & v6_lattices(A) & v5_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,B,k1_lattices(A,B,C)))))))) # label(t22_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3556 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A) -> -v3_struct_0(A) & v17_lattices(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3557 (all A all B all C (v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> (r1_lattices(A,B,C) <-> r3_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3558 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3559 (all A (l1_lattices(A) & -v3_struct_0(A) -> (v6_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,C,B) = k2_lattices(A,B,C)))))))) # label(d6_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3560 (all A all B (-v1_xboole_0(A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_struct_0(g2_lattices(A,B)) & v2_lattices(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3561 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v16_lattices(A) & l3_lattices(A) & v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k7_lattices(A,B) <-> r2_lattices(A,C,B))))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3562 (all A (-v3_struct_0(A) & l1_lattices(A) -> (v13_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,C) & B = k2_lattices(A,C,B))))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3563 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k6_lattices(A),B) = k6_lattices(A))))) # label(t44_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3564 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3565 (exists A (l1_lattices(A) & -v3_struct_0(A) & v1_lattices(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3566 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3567 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3568 (all A (l3_lattices(A) -> (v15_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v14_lattices(A) & v13_lattices(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3569 (exists A (l3_lattices(A) & -v3_struct_0(A) & v5_lattices(A) & v6_lattices(A) & v11_lattices(A) & v13_lattices(A) & v15_lattices(A) & v17_lattices(A) & v16_lattices(A) & v14_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v4_lattices(A) & v3_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3570 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C all D (g2_lattices(C,D) = g2_lattices(A,B) -> D = B & C = A)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3571 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B))))))))) # label(t53_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3572 (all A (-v3_struct_0(A) & v8_lattices(A) & l3_lattices(A) & v9_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> k2_lattices(A,B,C) = B))))))) # label(t21_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3573 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3574 (all A (l3_lattices(A) -> (v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v12_lattices(A) & v10_lattices(A) & v9_lattices(A) & v6_lattices(A) & -v3_struct_0(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3575 (all A (-v3_struct_0(A) & l1_lattices(A) -> m1_subset_1(k5_lattices(A),u1_struct_0(A)))) # label(dt_k5_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3576 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k4_lattices(A,B,C) = k5_lattices(A) <-> r3_lattices(A,B,k7_lattices(A,C))))))))) # label(t52_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3577 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3578 (all A all B all C (v6_lattices(A) & l3_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v9_lattices(A) & v8_lattices(A) & -v3_struct_0(A) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3579 (exists A (v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v8_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3580 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,k5_lattices(A),B))))) # label(t41_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3581 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,B,k1_lattices(A,B,C)))))) <-> v9_lattices(A)))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3582 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3583 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3584 (all A (l2_lattices(A) & -v3_struct_0(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k6_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B)))))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3585 (all A (l1_lattices(A) -> (v1_lattices(A) -> A = g1_lattices(u1_struct_0(A),u1_lattices(A))))) # label(abstractness_v1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3586 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3587 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> k3_lattices(A,C,B) = k3_lattices(A,B,C))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3588 (exists A (l3_lattices(A) & v5_lattices(A) & v7_lattices(A) & v9_lattices(A) & v11_lattices(A) & v14_lattices(A) & v13_lattices(A) & v12_lattices(A) & v10_lattices(A) & v8_lattices(A) & v6_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3589 (all A (v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)) = k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3590 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v5_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_lattices(A,k1_lattices(A,B,C),D) = k1_lattices(A,B,k1_lattices(A,C,D))))))))))) # label(d5_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3591 (all A (l1_lattices(A) -> v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_lattices(A)))) # label(dt_u1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3592 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v17_lattices(A) <-> v11_lattices(A) & v16_lattices(A) & v15_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3593 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v17_lattices(A) -> -v3_struct_0(A) & v11_lattices(A) & v16_lattices(A) & v15_lattices(A) & v14_lattices(A) & v13_lattices(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3594 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3595 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3596 (all A (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,C,B) & r1_lattices(A,B,C) -> C = B))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3597 (all A (l3_lattices(A) -> l1_lattices(A) & l2_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3598 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k7_lattices(A,k7_lattices(A,B)))))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3599 (all A (l3_lattices(A) -> (v10_lattices(A) & -v3_struct_0(A) -> v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3600 (all A (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k5_lattices(A),B) = B)))) # label(t39_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3601 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3602 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3603 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3604 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3605 (all A all B all C (-v3_struct_0(A) & l2_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k1_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3606 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3607 (exists A (v3_lattices(A) & l3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3608 (all A (v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,C) -> r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D))))))))))) # label(t27_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3609 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v2_lattices(g2_lattices(A,B)) & l2_lattices(g2_lattices(A,B)))) # label(dt_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3610 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3611 (all A (-v3_struct_0(A) & l2_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3612 (exists A (l1_lattices(A) & -v3_struct_0(A) & v7_lattices(A) & v6_lattices(A) & v1_lattices(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3613 (all A all B all C (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> k2_lattices(A,B,C) = k4_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3614 (all A (-v3_struct_0(A) & v6_lattices(A) & v9_lattices(A) & l3_lattices(A) & v8_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,B,B))))) # label(t18_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3615 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,D) -> k2_lattices(A,k1_lattices(A,B,C),D) = k1_lattices(A,B,k2_lattices(A,C,D))))))))) <-> v12_lattices(A)))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3616 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3617 (all A (l2_lattices(A) -> m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3618 (all A (l1_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) = k2_lattices(A,B,C))))))) # label(d2_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3619 (all A (-v3_struct_0(A) & v11_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k4_lattices(A,B,C) = k4_lattices(A,B,D) & k3_lattices(A,B,D) = k3_lattices(A,B,C) -> C = D))))))))) # label(t32_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3620 (exists A (-v3_struct_0(A) & v2_lattices(A) & v5_lattices(A) & v4_lattices(A) & l2_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3621 (all A (-v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_lattices(A,B,B))))) # label(t17_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3622 (exists A (l1_lattices(A) & v1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3623 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all D all E all F (g3_lattices(A,B,C) = g3_lattices(D,E,F) -> A = D & E = B & F = C)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3624 (all A all B (l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k7_lattices(A,B),u1_struct_0(A)))) # label(dt_k7_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3625 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C all D (g1_lattices(C,D) = g1_lattices(A,B) -> B = D & A = C)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3626 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v8_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,k2_lattices(A,B,C),C) = C))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3627 (all A (-v3_struct_0(A) & l2_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,C,B) = k1_lattices(A,B,C))))) <-> v4_lattices(A)))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3628 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,B,k6_lattices(A)))))) # label(t45_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3629 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3630 (all A (-v3_struct_0(A) & l1_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,k2_lattices(A,B,C),D) = k2_lattices(A,B,k2_lattices(A,C,D)))))))) <-> v7_lattices(A)))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3631 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v14_lattices(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B))))))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3632 (all A (v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_lattices(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,B,D)))))))))) # label(t31_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3633 (all A (-v3_struct_0(A) & l2_lattices(A) & v5_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,C,D) & r1_lattices(A,B,C) -> r1_lattices(A,B,D)))))))))) # label(t25_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3634 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3635 (all A (-v3_struct_0(A) & l1_lattices(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,C,B) = B & B = k2_lattices(A,B,C))))) <-> v13_lattices(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3636 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3637 (exists A (l3_lattices(A) & -v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3638 (all A (l3_lattices(A) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k5_lattices(A),B) = k5_lattices(A))))) # label(t40_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3639 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattices(A,B,C) <-> k1_lattices(A,C,B) = k6_lattices(A) & k5_lattices(A) = k2_lattices(A,B,C) & k5_lattices(A) = k2_lattices(A,C,B) & k1_lattices(A,B,C) = k6_lattices(A)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3640 (all A (l1_struct_0(A) -> m1_subset_1(k1_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3641 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3642 (all A (l1_pre_topc(A) -> (v1_pre_topc(A) -> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = A))) # label(abstractness_v1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3643 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3644 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3645 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)))))))) # label(t50_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3646 (exists A (v2_pre_topc(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3647 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3648 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_pre_topc(A,B) <-> k2_pre_topc(A) = k5_setfam_1(u1_struct_0(A),B)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3649 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B))) & (k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k6_pre_topc(A,k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & v2_pre_topc(A) -> v3_pre_topc(B,A)))))) # label(t53_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3650 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_hidden(C,B))) & B != k1_pre_topc(A)))))) # label(t41_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3651 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> l1_pre_topc(B))))) # label(dt_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3652 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> v2_pre_topc(B))))) # label(cc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3653 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B)) = k6_pre_topc(B,D)))))))))) # label(t47_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3654 (all A (l1_struct_0(A) -> k1_xboole_0 = k1_pre_topc(A))) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3655 (all A (l1_struct_0(A) -> (all B (r1_tarski(B,k2_pre_topc(A)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(t16_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3656 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & l1_struct_0(A) -> k9_relat_1(C,D) = k4_pre_topc(A,B,C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3657 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))))) # label(t39_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3658 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(t42_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3659 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)))) # label(fc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3660 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3661 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> k6_pre_topc(A,B) = B) & (k6_pre_topc(A,B) = B & v2_pre_topc(A) -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3662 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C all D (g1_pre_topc(A,B) = g1_pre_topc(C,D) -> B = D & C = A)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3663 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3664 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3665 (all A (l1_struct_0(A) -> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3666 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3667 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3668 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k6_pre_topc(A,B)))))) # label(t48_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3669 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3670 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3671 (all A all B all C all D (l1_struct_0(A) & l1_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3672 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k3_subset_1(u1_struct_0(A),B))))) # label(t17_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3673 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (r2_hidden(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,D) & v4_pre_topc(D,A) -> r2_hidden(C,D))))))))))) # label(t45_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3674 (all A all B all C all D (l1_struct_0(A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) -> m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3675 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3676 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v5_pre_topc(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) -> v4_pre_topc(k5_pre_topc(A,B,C,D),A))))))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3677 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3678 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3679 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3680 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) = B)))) # label(t22_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3681 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v4_pre_topc(C,A)))) -> v4_pre_topc(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t44_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3682 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = C -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3683 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)))) # label(dt_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3684 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3685 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3686 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> r2_hidden(B,u1_pre_topc(A))))))) # label(d5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3687 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3688 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3689 (all A all B all C all D (l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3690 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3691 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3692 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3693 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3694 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3695 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,u1_pre_topc(A)) & r2_hidden(C,u1_pre_topc(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),u1_pre_topc(A))))))) & r2_hidden(u1_struct_0(A),u1_pre_topc(A))))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3696 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3697 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B) & -v3_struct_0(B))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3698 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3699 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3700 (all A (l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3701 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t51_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3702 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3703 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (m1_pre_topc(B,A) <-> r1_tarski(k2_pre_topc(B),k2_pre_topc(A)) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(C,u1_pre_topc(B)) <-> (exists D (C = k3_xboole_0(D,k2_pre_topc(B)) & r2_hidden(D,u1_pre_topc(A)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))))))))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3704 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_pre_topc(k3_pre_topc(A,B),A) & v1_pre_topc(k3_pre_topc(A,B)))) # label(dt_k3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3705 (all A (l1_pre_topc(A) -> m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_u1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3706 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3707 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3708 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (r2_hidden(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(E,A) & r1_xboole_0(B,E) & r2_hidden(D,E)))) <-> r2_hidden(D,C)))) <-> C = k6_pre_topc(A,B)))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3709 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3710 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3711 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3712 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & k6_setfam_1(u1_struct_0(A),C) = k6_pre_topc(A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(D,C) <-> v4_pre_topc(D,A) & r1_tarski(B,D)))))))))) # label(t46_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3713 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3714 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A)))) & -v3_struct_0(A) <-> r2_hidden(C,k6_pre_topc(A,B))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3715 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> r2_hidden(k1_xboole_0,u1_pre_topc(A)))) # label(t5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3716 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3717 (all A (l1_struct_0(A) -> v1_xboole_0(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3718 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3719 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B),A) <-> v4_pre_topc(B,A)))))) # label(d6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3720 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k2_pre_topc(A)))))) # label(t14_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3721 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> B = k5_subset_1(u1_struct_0(A),B,k2_pre_topc(A)))))) # label(t15_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3722 (all A (l1_struct_0(A) -> k3_subset_1(u1_struct_0(A),k1_pre_topc(A)) = k2_pre_topc(A))) # label(t27_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.78 3723 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3724 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A))) # label(fc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3725 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_pre_topc(k3_pre_topc(A,B)) & -v3_struct_0(k3_pre_topc(A,B)))) # label(fc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3726 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3727 (exists A (v1_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3728 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t49_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3729 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3730 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k2_pre_topc(A)))))) # label(t13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3731 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k2_pre_topc(A) != B & k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)) & -(k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) != k1_xboole_0 & B = k2_pre_topc(A)))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3732 (all A (l1_struct_0(A) -> u1_struct_0(A) = k2_pre_topc(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3733 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3734 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_pre_topc(C,A) & v1_pre_topc(C) -> (B = k2_pre_topc(C) <-> C = k3_pre_topc(A,B)))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3735 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (v4_pre_topc(D,A) & C = k3_xboole_0(D,k2_pre_topc(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3736 $T # label(t150_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3737 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & l1_orders_2(A) -> (all C (m2_orders_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(C,A))))) # label(dt_m2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3738 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_wellord1(u1_orders_2(A),C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_orders_2(A,D,E) & r2_hidden(E,B) -> r2_hidden(D,B)))))) & -m1_orders_2(B,A,C) & C != B & r1_tarski(B,C)))))))) # label(t72_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3739 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r8_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C != B -> r2_orders_2(A,C,B))))))))) # label(t160_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3740 $T # label(t22_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3741 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r6_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,B,C)))))))) # label(t159_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3742 (all A (l1_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A))))) # label(rc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3743 $T # label(t13_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3744 $T # label(t33_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3745 $T # label(t156_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3746 $T # label(t58_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3747 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v2_orders_2(A) -> (r3_orders_2(A,B,C) <-> r1_orders_2(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3748 (all A all B all C (-v3_struct_0(A) & v2_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) -> r3_orders_2(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3749 $T # label(t17_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3750 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (v5_orders_2(D,A) & r2_hidden(B,D) & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> (r2_orders_2(A,B,C) <-> -r1_orders_2(A,C,B))))))))) # label(t39_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3751 $T # label(t92_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3752 $T # label(t145_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3753 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & r2_wellord1(u1_orders_2(A),C) & -m1_orders_2(B,A,C) & C != B & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(E,B) & r2_orders_2(A,D,E) & r2_hidden(D,C) -> r2_hidden(D,B))))))))))))) # label(t73_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3754 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_orders_2(B,A,B) & B != k1_xboole_0) & -(k1_xboole_0 = B & -m1_orders_2(B,A,B)))))) # label(t68_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3755 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,C,B))) <-> r7_orders_1(u1_orders_2(A),B)))))) # label(t158_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3756 $T # label(t94_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3757 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r3_orders_1(u1_orders_2(A),B) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A)))))) # label(t135_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3758 $T # label(t19_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3759 (exists A (v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3760 $T # label(t124_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3761 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k1_orders_2(A,k1_struct_0(A,B))) <-> r2_orders_2(A,B,C)))))))) # label(t51_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3762 $T # label(t129_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3763 $T # label(t102_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3764 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> m2_orders_2(k3_tarski(k4_orders_2(A,B)),A,B))))) # label(t89_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3765 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_orders_2(A,B,C) <-> C != B & r1_orders_2(A,B,C)))))))) # label(d10_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3766 $T # label(t137_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3767 $T # label(t155_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3768 $T # label(t134_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3769 $T # label(t126_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3770 $T # label(dt_k4_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3771 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,E) & m1_orders_2(E,A,D) & r2_hidden(B,D) & r2_orders_2(A,B,C) -> r2_hidden(B,E)))))))))))) # label(t70_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3772 $T # label(t93_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3773 (all A (v2_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((r1_orders_2(A,C,B) | r1_orders_2(A,B,C)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(D,A) -> -(r2_hidden(B,D) & r2_hidden(C,D))))) & -((exists D (r2_hidden(B,D) & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(D,A))) & -r1_orders_2(A,B,C) & -r1_orders_2(A,C,B)))))))) # label(t38_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3774 (all A all B (m1_relset_1(B,A,A) -> l1_orders_2(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)))) # label(dt_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3775 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> -((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_orders_2(A,C,B) & m1_subset_1(C,u1_struct_0(A)))))) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r3_orders_2(A,C,D))))))))))) # label(t163_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3776 $T # label(t42_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3777 $T # label(t76_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3778 (all A (l1_orders_2(A) -> (r1_relat_2(u1_orders_2(A),u1_struct_0(A)) <-> v2_orders_2(A)))) # label(d4_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3779 $T # label(t31_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3780 $T # label(t53_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3781 $T # label(d7_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3782 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> v1_orders_2(g1_orders_2(A,B)) & v3_orders_2(g1_orders_2(A,B)) & v4_orders_2(g1_orders_2(A,B)) & v2_orders_2(g1_orders_2(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3783 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_orders_2(C,A,B) -> r1_tarski(C,B))))))) # label(t67_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3784 (exists A l1_orders_2(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3785 $T # label(t97_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3786 $T # label(t54_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3787 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_orders_2(A,C,B) & r2_orders_2(A,B,C)))))))) # label(t28_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3788 $T # label(t105_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3789 $T # label(t117_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3790 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> k2_orders_2(A,k2_pre_topc(A)) = k1_xboole_0)) # label(t46_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3791 $T # label(t101_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3792 (all A (v2_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v5_orders_2(k2_struct_0(A,B,C),A) & m1_subset_1(k2_struct_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))) <-> r3_orders_2(A,C,B) | r3_orders_2(A,B,C)))))))) # label(t36_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3793 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,k1_orders_2(A,C)) & r2_hidden(B,C)))))))) # label(t47_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3794 $T # label(t14_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3795 $T # label(t12_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3796 $T # label(t114_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3797 $T # label(t113_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3798 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,D) & r2_orders_2(A,B,C) <-> r2_hidden(B,k3_orders_2(A,D,C))))))))))) # label(t57_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3799 $T # label(t120_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3800 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A) -> v3_orders_1(k2_wellord1(u1_orders_2(A),B)))))) # label(t109_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3801 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> r2_hidden(k1_funct_1(B,u1_struct_0(A)),C))))))) # label(t79_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3802 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_orders_2(C,A,B) & m1_orders_2(B,A,C) & -(C = k1_xboole_0 & k1_xboole_0 = B)))))))) # label(t69_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3803 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> k2_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A))) # label(t45_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3804 $T # label(t100_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3805 $T # label(t153_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3806 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_orders_1(C,k1_orders_1(u1_struct_0(A))) -> (all D (m2_orders_2(D,A,C) -> (k1_funct_1(C,u1_struct_0(A)) = B -> k1_xboole_0 = k3_orders_2(A,D,B)))))))))) # label(t81_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3807 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A) -> r3_orders_1(u1_orders_2(A),B))))) # label(t136_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3808 $T # label(t98_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3809 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k3_orders_2(A,C,B),C))))))) # label(t61_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3810 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_orders_1(C,k1_orders_1(u1_struct_0(A))) -> (all D (m2_orders_2(D,A,C) -> (B = k3_tarski(k4_orders_2(A,C)) -> D = k3_tarski(k4_orders_2(A,C)) | m1_orders_2(D,A,B)))))))))) # label(t88_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3811 $T # label(t112_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3812 $T # label(t9_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3813 $T # label(t6_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3814 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k2_orders_2(A,k1_struct_0(A,C))) <-> r2_orders_2(A,B,C)))))))) # label(t52_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3815 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> a_2_1_orders_2(A,B) = k2_orders_2(A,B))))) # label(d13_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3816 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_orders_2(A,C,D) & r2_orders_2(A,B,C) -> r2_orders_2(A,B,D)))))))))) # label(t29_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3817 $T # label(t128_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3818 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> -((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r3_orders_2(A,D,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_orders_2(A,B,C) & m1_subset_1(C,u1_struct_0(A))))))))) # label(t162_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3819 (all A all B (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_orders_2(A) -> (all C (m1_orders_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3820 $T # label(t18_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3821 $T # label(t21_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3822 $T # label(t20_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3823 $T # label(t118_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3824 (all A all B (m1_relset_1(B,A,A) -> (all C all D (g1_orders_2(C,D) = g1_orders_2(A,B) -> C = A & D = B)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3825 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_xboole_0 = k3_orders_2(A,k1_pre_topc(A),B))))) # label(t60_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3826 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (v5_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (m2_orders_2(C,A,B) <-> C != k1_xboole_0 & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> D = k1_funct_1(B,k1_orders_2(A,k3_orders_2(A,C,D)))))) & r2_wellord1(u1_orders_2(A),C)))))))) # label(d16_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3827 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> (r2_xboole_0(C,D) <-> m1_orders_2(C,A,D)))))))))) # label(t84_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3828 $T # label(t104_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3829 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_orders_2(A,C,B) & r1_orders_2(A,B,C)))))))) # label(t30_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3830 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,D) -> r1_tarski(k3_orders_2(A,C,B),k3_orders_2(A,D,B))))))))))) # label(t65_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3831 $T # label(t7_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3832 (all A (l1_orders_2(A) -> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3833 (all A all B all C (v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v4_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_0_orders_2(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,E,D))))))))) # label(fraenkel_a_2_0_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3834 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> k1_orders_2(A,k2_pre_topc(A)) = k1_xboole_0)) # label(t44_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3835 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> (D != C -> (-m1_orders_2(D,A,C) <-> m1_orders_2(C,A,D))))))))))) # label(t83_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3836 (all A all B (-v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,k3_orders_2(B,D,C)) <-> r2_hidden(A,D) & r2_hidden(A,k2_orders_2(B,k1_struct_0(B,C)))))))))) # label(t56_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3837 $T # label(t11_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3838 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (B != k1_xboole_0 -> ((exists D (k3_orders_2(A,B,D) = C & r2_hidden(D,B) & m1_subset_1(D,u1_struct_0(A)))) <-> m1_orders_2(C,A,B))) & (k1_xboole_0 = B -> (C = k1_xboole_0 <-> m1_orders_2(C,A,B))))))))) # label(d15_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3839 $T # label(t139_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3840 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r9_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B != C -> r2_orders_2(A,B,C))))))))) # label(t161_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3841 $T # label(t133_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3842 $T # label(t15_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3843 $T # label(t125_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3844 (all A (l1_orders_2(A) -> v1_xboole_0(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A),A) & v5_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)))) # label(fc4_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3845 $T # label(t141_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3846 $T # label(t16_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3847 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) <-> r2_hidden(k4_tarski(B,C),u1_orders_2(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3848 $T # label(t2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3849 $T # label(t123_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3850 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) -> -r2_orders_2(A,B,B))) # label(irreflexivity_r2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3851 (exists A (l1_orders_2(A) & v1_orders_2(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3852 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,C) & m1_orders_2(C,A,D) -> k3_orders_2(A,D,B) = k3_orders_2(A,C,B)))))))))) # label(t71_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3853 $T # label(t90_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3854 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_orders_2(A,C,D) & r1_orders_2(A,B,C) | r2_orders_2(A,B,C) & r1_orders_2(A,C,D) -> r2_orders_2(A,B,D)))))))))) # label(t32_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3855 $T # label(t34_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3856 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_subset_1(u1_struct_0(A),k2_orders_2(A,k1_struct_0(A,C)),B) = k3_orders_2(A,B,C))))))) # label(d14_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3857 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m2_orders_2(C,A,B) -> (all D (m2_orders_2(D,A,B) -> -r1_xboole_0(C,D))))))))) # label(t82_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3858 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r2_hidden(B,k2_orders_2(A,k1_struct_0(A,B))))))) # label(t50_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3859 $T # label(t111_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3860 $T # label(t143_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3861 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_orders_2(A,B,C) -> r1_tarski(k3_orders_2(A,D,B),k3_orders_2(A,D,C))))))))))) # label(t64_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3862 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,C,B) & r1_orders_2(A,B,C) -> C = B))))))) # label(t25_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3863 $T # label(d8_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3864 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,B,B))))) # label(t24_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3865 (all A (l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(k1_struct_0(A,B),A))))) # label(t35_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3866 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r2_hidden(B,k1_orders_2(A,k1_struct_0(A,B))))))) # label(t48_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3867 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v1_relat_1(u1_orders_2(A)) & v4_relat_2(u1_orders_2(A)) & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(u1_orders_2(A)) & v1_relat_2(u1_orders_2(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3868 $T # label(t142_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3869 $T # label(t121_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3870 $T # label(t1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3871 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3872 $T # label(t116_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3873 $T # label(t130_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3874 $T # label(t152_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3875 (all A all B (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> m1_subset_1(k1_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3876 $T # label(t5_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3877 $T # label(t86_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3878 $T # label(t151_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3879 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_wellord1(u1_orders_2(A),B) -> v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(t40_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3880 (all A (v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r1_orders_2(A,B,C) -> r1_orders_2(A,B,D)))))))))) # label(t26_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3881 $T # label(t95_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3882 $T # label(t66_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3883 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (k4_orders_2(A,B) = C <-> (all D (r2_hidden(D,C) <-> m2_orders_2(D,A,B))))))))) # label(d17_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3884 $T # label(t77_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3885 $T # label(t122_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3886 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_orders_1(D,k1_orders_1(u1_struct_0(A))) -> (all E (m2_orders_2(E,A,D) -> (r2_hidden(B,E) & C = k1_funct_1(D,u1_struct_0(A)) -> r3_orders_2(A,C,B)))))))))))) # label(t80_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3887 (all A all B (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & v3_orders_2(A) & -v3_struct_0(A) -> (exists C m2_orders_2(C,A,B)))) # label(existence_m2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3888 $T # label(t96_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3889 (all A all B (-v3_struct_0(A) & v3_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (exists C m1_orders_2(C,A,B)))) # label(existence_m1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3890 $T # label(t99_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3891 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_orders_2(A,B) = a_2_0_orders_2(A,B))))) # label(d12_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3892 $T # label(t41_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3893 $T # label(t131_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3894 $T # label(t106_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3895 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -r2_hidden(B,k3_orders_2(A,C,B)))))))) # label(t62_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3896 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_orders_2(B,A) <-> r7_relat_2(u1_orders_2(A),B)))))) # label(d11_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3897 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_orders_1(k2_wellord1(u1_orders_2(A),B)) -> v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))))))) # label(t108_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3898 $T # label(t115_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3899 (all A all B (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_orders_2(A) -> m1_subset_1(k2_orders_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3900 $T # label(t55_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3901 $T # label(t127_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3902 $T # label(t146_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3903 $T # label(t103_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3904 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,k2_orders_2(A,C)) & r2_hidden(B,C)))))))) # label(t49_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3905 $T # label(t74_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3906 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(C,A)))))))) # label(t37_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3907 $T # label(t23_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3908 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> u1_struct_0(A) = k1_orders_2(A,k1_pre_topc(A)))) # label(t43_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3909 $T # label(t10_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3910 $T # label(t132_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3911 $T # label(t8_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3912 (all A all B all C (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) & v4_orders_2(B) -> (r2_hidden(A,a_2_1_orders_2(B,C)) <-> (exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,D,E)))) & A = D & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3913 $T # label(t119_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3914 $T # label(t59_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3915 (all A (l1_orders_2(A) -> (v1_orders_2(A) -> A = g1_orders_2(u1_struct_0(A),u1_orders_2(A))))) # label(abstractness_v1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3916 (all A all B (-v1_xboole_0(A) & m1_relset_1(B,A,A) -> -v3_struct_0(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)))) # label(fc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3917 $T # label(t75_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3918 $T # label(t140_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3919 (all A (l1_orders_2(A) -> (v3_orders_2(A) <-> r8_relat_2(u1_orders_2(A),u1_struct_0(A))))) # label(d5_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3920 $T # label(t85_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3921 $T # label(t138_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3922 $T # label(t91_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3923 $T # label(t154_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3924 $T # label(t144_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3925 $T # label(d1_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3926 (all A all B (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & -v3_struct_0(A) -> -v1_xboole_0(k4_orders_2(A,B)))) # label(fc5_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3927 $T # label(t149_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3928 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> k3_tarski(k4_orders_2(A,B)) != k1_xboole_0)))) # label(t87_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3929 $T # label(t63_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3930 $T # label(t157_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3931 $T # label(t3_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3932 $T # label(t4_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3933 (all A all B all C (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & -v3_struct_0(A) -> m1_subset_1(k3_orders_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k3_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3934 $T # label(d2_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3935 $T # label(t27_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3936 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k3_relat_1(k2_wellord1(u1_orders_2(A),B)) = B)))) # label(t107_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3937 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_orders_1(B,k1_orders_1(u1_struct_0(A))) -> m2_orders_2(k1_tarski(k1_funct_1(B,u1_struct_0(A))),A,B))))) # label(t78_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3938 $T # label(d3_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3939 (all A (l1_orders_2(A) -> (r4_relat_2(u1_orders_2(A),u1_struct_0(A)) <-> v4_orders_2(A)))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3940 $T # label(t148_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3941 $T # label(t147_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3942 $T # label(t110_orders_2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3943 $T # label(t16_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.79 3944 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> r8_relat_2(k10_filter_0(A,B),u1_struct_0(A))))))) # label(t83_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3945 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> k3_filter_0(A,B) = B)))) # label(t26_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3946 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,D,C) -> r3_lattices(A,k3_lattices(A,B,D),C)))))))))) # label(t6_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3947 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> k1_filter_0(A) = u1_struct_0(A))) # label(d2_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3948 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k2_filter_0(A,k5_lattices(A)) = k1_filter_0(A)))) # label(t20_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3949 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> v1_partfun1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k10_filter_0(A,B)) & v3_relat_2(k10_filter_0(A,B))))))) # label(t84_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3950 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_filter_0(E,A) -> (r2_hidden(k4_filter_0(A,B,C),E) & r2_hidden(k4_filter_0(A,C,D),E) -> r2_hidden(k4_filter_0(A,B,D),E)))))))))))) # label(t54_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3951 (all A (-v3_struct_0(A) & v3_lattices(A) & l3_lattices(A) & v10_lattices(A) -> A = k8_filter_0(A,k1_filter_0(A)))) # label(t62_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3952 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> v3_filter_0(k8_filter_0(A,B))))))) # label(t69_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3953 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v12_lattices(A) -> v12_lattices(k8_filter_0(A,B))))))) # label(t67_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3954 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m1_filter_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) <-> r2_hidden(k4_lattices(A,C,D),B))))))))))) # label(d1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3955 (all A all B (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) -> k12_filter_0(A,B) = k10_filter_0(A,B))) # label(redefinition_k12_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3956 $T # label(t25_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3957 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> m1_filter_0(k1_filter_0(A),A))) # label(dt_k1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3958 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,D,E) & r3_lattices(A,B,C) -> r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,E)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,E,C))))))))))))) # label(t4_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3959 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> m1_filter_0(u1_struct_0(A),A))) # label(t15_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3960 (all A all B (m1_filter_0(B,A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> k11_filter_0(A,B) = k10_filter_0(A,B))) # label(redefinition_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3961 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v1_filter_0(B,A) <-> (all C (m1_filter_0(C,A) -> (r1_tarski(B,C) -> C = u1_struct_0(A) | C = B))) & B != u1_struct_0(A)))))) # label(d4_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3962 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) <-> k5_lattices(A) = k4_lattices(A,B,k7_lattices(A,C))))))))) # label(t56_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3963 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k4_lattices(A,D,B),C) & r3_lattices(A,k4_lattices(A,B,D),C)))))))))) # label(t2_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3964 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) & v10_lattices(A) & r2_hidden(k5_lattices(A),B) & l3_lattices(A) & v13_lattices(A) -> k3_filter_0(A,B) = u1_struct_0(A) & k1_filter_0(A) = k3_filter_0(A,B)))))) # label(t31_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3965 (all A all B (v10_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> v1_partfun1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k12_filter_0(A,B)) & v3_relat_2(k12_filter_0(A,B)))) # label(dt_k12_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3966 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_filter_0(A,B) = a_2_0_filter_0(A,B))))) # label(d3_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3967 (all A all B (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) -> v1_partfun1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k11_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k11_filter_0(A,B)) & v3_relat_2(k11_filter_0(A,B)))) # label(dt_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3968 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = a_3_1_filter_0(A,B,C))))))) # label(t48_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3969 (all A all B (v10_lattices(A) & l3_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> m1_filter_0(k3_filter_0(A,B),A))) # label(dt_k3_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3970 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(k4_filter_0(A,B,C),D) & r2_hidden(B,D) -> r2_hidden(C,D)))))))))) # label(t41_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3971 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k6_filter_0(A,B,C) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t51_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3972 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v14_lattices(A) -> v14_lattices(k8_filter_0(A,B))))))) # label(t66_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3973 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,D,E) & r3_lattices(A,B,C) -> r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,C,E)) & r3_lattices(A,k4_lattices(A,B,D),k4_lattices(A,E,C))))))))))))) # label(t5_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3974 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v14_lattices(A) -> k6_lattices(k8_filter_0(A,k2_filter_0(A,B))) = k6_lattices(A)))))) # label(t72_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3975 (all A all B (-v3_struct_0(A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) -> -v3_struct_0(k8_filter_0(A,B)) & v10_lattices(k8_filter_0(A,B)) & l3_lattices(k8_filter_0(A,B)))) # label(dt_k8_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3976 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v13_lattices(k8_filter_0(A,k2_filter_0(A,B))))))) # label(t70_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3977 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(B != C & (all D (m1_filter_0(D,A) -> -(v1_filter_0(D,A) & (-r2_hidden(B,D) & r2_hidden(C,D) | -r2_hidden(C,D) & r2_hidden(B,D)))))))))))) # label(t60_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3978 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> k5_filter_0(A,C,B) = k5_filter_0(A,B,C))))))) # label(t46_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3979 $T # label(t8_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3980 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (v1_relat_1(C) -> (k10_filter_0(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E),C) <-> r2_hidden(k9_filter_0(A,D,E),B)))))) & r1_tarski(k3_relat_1(C),u1_struct_0(A))))))))) # label(d12_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3981 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v11_lattices(A))) # label(t39_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3982 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (exists B m1_filter_0(B,A)))) # label(existence_m1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3983 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (v13_lattices(A) -> (all B (m1_filter_0(B,A) -> -(B != u1_struct_0(A) & (all C (m1_filter_0(C,A) -> -(v1_filter_0(C,A) & r1_tarski(B,C)))))))))) # label(t22_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3984 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -(B = k4_lattices(A,E,F) & r2_hidden(E,C) & r2_hidden(F,D)))))) & r2_hidden(B,k5_filter_0(A,C,D))))))))) # label(t45_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3985 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k5_filter_0(A,B,C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t50_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3986 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (v3_filter_0(C) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (all F (m1_subset_1(F,u1_struct_0(C)) -> (all G (m1_filter_0(G,C) -> (all H (m1_subset_1(H,u1_struct_0(A)) -> (all I (m1_subset_1(I,u1_struct_0(A)) -> (all J (m1_subset_1(J,u1_struct_0(A)) -> (r1_filter_0(A,B,I,J) & r1_filter_0(A,B,H,I) -> r1_filter_0(A,B,H,J)) & (r1_filter_0(C,G,E,F) & r1_filter_0(C,G,D,E) -> r1_filter_0(C,G,D,F)))))))))))))))))))))) # label(t90_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3987 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v11_lattices(A) -> v11_lattices(k8_filter_0(A,B))))))) # label(t68_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3988 $T # label(t36_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3989 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(dt_m1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3990 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_filter_0(C,A) -> ((all D (m1_filter_0(D,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) <-> C = k3_filter_0(A,B)))))))) # label(d5_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3991 (all A (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> v14_lattices(A))) # label(t37_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3992 $T # label(t79_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3993 (all A (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,k3_filter_0(A,k4_subset_1(u1_struct_0(A),D,k6_domain_1(u1_struct_0(A),C)))) -> r2_hidden(k4_filter_0(A,C,B),k3_filter_0(A,D))))))))))) # label(t53_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3994 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(B,k2_filter_0(A,B)) & r2_hidden(k3_lattices(A,C,B),k2_filter_0(A,B)) & r2_hidden(k3_lattices(A,B,C),k2_filter_0(A,B)))))))) # label(t19_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3995 (all A all B all C all D (-v3_struct_0(B) & m1_filter_0(C,B) & m1_filter_0(D,B) & l3_lattices(B) & v10_lattices(B) -> ((exists E ((exists F ((exists G (m1_subset_1(G,u1_struct_0(B)) & r2_hidden(G,D) & r2_hidden(F,C) & r3_lattices(B,k4_lattices(B,F,G),E))) & m1_subset_1(F,u1_struct_0(B)))) & A = E & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_1_filter_0(B,C,D))))) # label(fraenkel_a_3_1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3996 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> r3_relat_2(k10_filter_0(A,B),u1_struct_0(A)))))) # label(t82_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3997 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k5_lattices(k8_filter_0(A,k2_filter_0(A,B))))))) # label(t71_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3998 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (u1_struct_0(A) != B & (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(k7_lattices(A,C),B) | r2_hidden(C,B))) <-> v1_filter_0(B,A)))))) # label(t57_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 3999 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k10_filter_0(A,D)) <-> r1_filter_0(A,D,B,C)))))))))) # label(t87_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4000 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> m2_relset_1(k10_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)))))) # label(t80_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4001 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k7_lattices(A,B),C) = k4_filter_0(A,B,C))))))) # label(t55_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4002 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,D) & r2_hidden(C,E) -> r2_hidden(k4_lattices(A,C,B),k5_filter_0(A,D,E)) & r2_hidden(k4_lattices(A,B,C),k5_filter_0(A,D,E))))))))))))) # label(t44_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4003 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> k1_realset1(u1_lattices(A),B) = u1_lattices(k8_filter_0(A,B)) & k1_realset1(u2_lattices(A),B) = u2_lattices(k8_filter_0(A,B)) & B = u1_struct_0(k8_filter_0(A,B)))))) # label(t63_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4004 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,C,B)) = k9_filter_0(A,B,C))))))) # label(d11_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4005 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (r1_lattices(A,k2_lattices(A,B,D),C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_lattices(A,k2_lattices(A,B,E),C) -> r1_lattices(A,E,D)))) & m1_subset_1(D,u1_struct_0(A)))))))) <-> v3_filter_0(A)))) # label(d7_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4006 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v14_lattices(A) -> m1_filter_0(k6_domain_1(u1_struct_0(A),k6_lattices(A)),A)))) # label(t13_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4007 $T # label(t43_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4008 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r2_hidden(k7_lattices(A,C),B) <-> r2_hidden(C,B))))))))) # label(t59_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4009 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> r1_tarski(B,k5_filter_0(A,B,C)) & r1_tarski(C,k5_filter_0(A,B,C)))))))) # label(t49_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4010 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (l3_lattices(A) & v14_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v15_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t73_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4011 $T # label(t61_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4012 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (exists C (r2_hidden(C,B) & m1_subset_1(C,u1_struct_0(A)))))))) # label(t11_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4013 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(B,D) -> r2_hidden(k4_filter_0(A,C,B),D)))))))))) # label(t42_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4014 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k9_filter_0(A,B,C),u1_struct_0(A)))) # label(dt_k9_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4015 $T # label(t17_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4016 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),k3_filter_0(A,B),C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) & k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,k3_filter_0(A,C))) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t47_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4017 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l3_lattices(A) -> m1_subset_1(k5_filter_0(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4018 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (l3_lattices(C) & v3_filter_0(C) & v10_lattices(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_filter_0(E,C) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> r1_filter_0(A,B,F,F) & r1_filter_0(C,E,D,D))))))))))))) # label(t88_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4019 $T # label(t35_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4020 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (all E (m1_subset_1(E,u1_struct_0(k8_filter_0(A,D))) -> (all F (m1_subset_1(F,u1_struct_0(k8_filter_0(A,D))) -> (F = C & E = B -> k3_lattices(A,B,C) = k3_lattices(k8_filter_0(A,D),E,F) & k4_lattices(A,B,C) = k4_lattices(k8_filter_0(A,D),E,F)))))))))))))) # label(t64_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4021 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (all E (m1_subset_1(E,u1_struct_0(k8_filter_0(A,D))) -> (all F (m1_subset_1(F,u1_struct_0(k8_filter_0(A,D))) -> (C = F & E = B -> (r3_lattices(k8_filter_0(A,D),E,F) <-> r3_lattices(A,B,C))))))))))))))) # label(t65_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4022 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,E),C) -> r3_lattices(A,E,D)))) & r3_lattices(A,k4_lattices(A,B,D),C) <-> k4_filter_0(A,B,C) = D)))))))))) # label(d8_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4023 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,B,k3_lattices(A,D,C)) & r3_lattices(A,B,k3_lattices(A,C,D))))))))))) # label(t3_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4024 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_filter_0(A,B,C,D) <-> r2_hidden(k9_filter_0(A,C,D),B)))))))))) # label(d13_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4025 $T # label(t86_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4026 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_lattices(A) = k4_filter_0(A,B,B))))) # label(t38_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4027 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (r2_hidden(B,C) -> r1_tarski(k2_filter_0(A,B),k3_filter_0(A,C))))))))) # label(t29_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4028 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k5_filter_0(A,B,C) = a_3_0_filter_0(A,B,C))))))) # label(d9_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4029 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k3_relat_1(k10_filter_0(A,B)) = u1_struct_0(A)))))) # label(t85_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4030 (all A all B all C (-v3_struct_0(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) & v11_lattices(A) & v10_lattices(A) -> k5_filter_0(A,B,C) = k6_filter_0(A,B,C))) # label(redefinition_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4031 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) | r2_hidden(C,B) <-> r2_hidden(k3_lattices(A,C,D),B)))))) <-> v2_filter_0(B,A)))))) # label(d6_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4032 (all A all B all C (l3_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k6_filter_0(A,B,C),A))) # label(dt_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4033 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> ((exists D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & (exists E (v1_funct_1(E) & E = k1_realset1(u1_lattices(A),B) & C = g3_lattices(B,D,E) & k1_realset1(u2_lattices(A),B) = D & m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B))) & m2_relset_1(D,k2_zfmisc_1(B,B),B))) <-> C = k8_filter_0(A,B)))))))) # label(d10_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4034 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (m1_filter_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_lattices(A,C,D),B)))))) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r3_lattices(A,C,D) -> r2_hidden(D,B))))))))))) # label(t9_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4035 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & -v1_xboole_0(D) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v1_xboole_0(C) & l3_lattices(B) & v10_lattices(B) -> ((exists E exists F (m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & r2_hidden(E,C) & r2_hidden(F,D) & k4_lattices(B,E,F) = A)) <-> r2_hidden(A,a_3_0_filter_0(B,C,D))))) # label(fraenkel_a_3_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4036 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (v2_filter_0(B,A) & k1_filter_0(A) != B <-> v1_filter_0(B,A)))))) # label(t58_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4037 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) -> (r2_hidden(A,a_2_0_filter_0(B,C)) <-> (exists D (A = D & r3_lattices(B,C,D) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4038 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(B,k2_filter_0(A,C)) <-> r3_lattices(A,C,B)))))))) # label(t18_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4039 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)) = k7_filter_0(A,B,C))))))) # label(t52_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4040 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_filter_0(A,C,B) = k9_filter_0(A,B,C))))))) # label(t77_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4041 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_filter_0(A,B,C),u1_struct_0(A)))) # label(dt_k4_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4042 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,D) & r3_lattices(A,B,C) -> r3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t7_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4043 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) -> v6_lattices(A) & v10_lattices(A) & v11_lattices(A) & v12_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4044 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) -> -v3_struct_0(k8_filter_0(A,B)) & v3_lattices(k8_filter_0(A,B)) & v7_lattices(k8_filter_0(A,B)) & v8_lattices(k8_filter_0(A,B)) & v10_lattices(k8_filter_0(A,B)) & v9_lattices(k8_filter_0(A,B)) & v6_lattices(k8_filter_0(A,B)) & v5_lattices(k8_filter_0(A,B)) & v4_lattices(k8_filter_0(A,B)))) # label(fc2_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4045 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (C = k6_domain_1(u1_struct_0(A),B) -> k2_filter_0(A,B) = k3_filter_0(A,C)))))))) # label(t30_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4046 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(k2_filter_0(A,B) = u1_struct_0(A) & -(all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = B))))))) # label(t23_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4047 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,D,C)) & r3_lattices(A,k3_lattices(A,D,B),k3_lattices(A,C,D)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,D,C)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,D))))))))))) # label(t1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4048 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (m1_filter_0(k6_domain_1(u1_struct_0(A),B),A) -> v14_lattices(A)))))) # label(t14_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4049 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B))) & v10_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v17_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t75_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.80 4050 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r2_hidden(B,D) -> r2_hidden(k3_lattices(A,B,C),D) & r2_hidden(k3_lattices(A,C,B),D)))))))))) # label(t10_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4051 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> v3_filter_0(A))) # label(t40_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4052 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,B,k3_lattices(A,k7_lattices(A,B),C)),C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,D),C) -> r3_lattices(A,D,k3_lattices(A,k7_lattices(A,B),C)))))))))))) # label(t34_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4053 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k3_filter_0(A,B),k3_filter_0(A,C))))))))) # label(t27_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4054 (exists A (v3_lattices(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v3_filter_0(A) & v10_lattices(A) & v5_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4055 $T # label(t21_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4056 $T # label(t28_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4057 (all A all B all C (v10_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) & l3_lattices(A) & -v3_struct_0(A) -> -v1_xboole_0(k5_filter_0(A,B,C)))) # label(fc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4058 (all A all B all C (-v3_struct_0(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> k5_filter_0(A,B,C) = k7_filter_0(A,B,C))) # label(redefinition_k7_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4059 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) -> v1_relat_1(k10_filter_0(A,B)))) # label(dt_k10_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4060 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v14_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r2_hidden(k6_lattices(A),B)))))) # label(t12_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4061 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & v10_lattices(A) -> m1_filter_0(k2_filter_0(A,B),A))) # label(dt_k2_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4062 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_filter_0(E,A) -> (r2_hidden(k9_filter_0(A,B,C),E) & r2_hidden(k9_filter_0(A,C,D),E) -> r2_hidden(k9_filter_0(A,B,D),E)))))))))))) # label(t78_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4063 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(-v3_struct_0(A) & B != k5_lattices(A) & (all C (m1_filter_0(C,A) -> -(r2_hidden(B,C) & v1_filter_0(C,A)))) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A)))))) # label(t24_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4064 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> r1_relat_2(k10_filter_0(A,B),u1_struct_0(A))))))) # label(t81_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4065 $T # label(t76_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4066 (all A all B all C (v10_lattices(A) & v17_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k7_filter_0(A,B,C),A))) # label(dt_k7_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4067 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_filter_0(D,A) -> (r1_filter_0(A,D,B,C) -> r1_filter_0(A,D,C,B)))))))))) # label(t89_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4068 $T # label(t33_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4069 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & r2_hidden(k5_lattices(A),B) & l3_lattices(A) -> B = k1_filter_0(A) & u1_struct_0(A) = B))))) # label(t32_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4070 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v15_lattices(A) & -v3_struct_0(A) & l3_lattices(A) & v12_lattices(A) & v10_lattices(A) & l3_lattices(A) & v16_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B))) & v15_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v16_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v10_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t74_filter_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4071 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> D = k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,D,E)))))) <-> r1_lattice2(A,B,C)))))))) # label(d1_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4072 (all A (-v1_xboole_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (m2_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,u1_struct_0(k1_lattice2(B))) & v1_funct_2(E,A,u1_struct_0(k1_lattice2(B))) & v1_funct_1(E) -> (D = E -> k2_lattice2(A,B,C,D) = k3_lattice2(A,k1_lattice2(B),C,E) & k2_lattice2(A,k1_lattice2(B),C,E) = k3_lattice2(A,B,C,D)))))))))))) # label(t51_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4073 (all A (-v3_struct_0(A) & l3_lattices(A) -> u2_lattices(A) = u1_lattices(k1_lattice2(A)) & u1_lattices(A) = u2_lattices(k1_lattice2(A)) & u1_struct_0(A) = u1_struct_0(k1_lattice2(A)))) # label(t18_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4074 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) -> (r3_lattices(A,B,k3_lattice2(C,A,D,E)) -> (all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)))))))))))))))) # label(t59_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4075 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v10_lattices(A) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A))))) # label(t37_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4076 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k5_finsub_1(A)) -> D = k1_relat_1(k2_partfun1(A,B,C,D)))))))) # label(t13_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4077 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & v14_lattices(C) & l3_lattices(C) & v10_lattices(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,E,k8_funct_2(A,u1_struct_0(C),D,F))))) -> r3_lattices(C,E,k3_lattice2(A,C,B,D))))))))))))) # label(t76_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4078 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(A) -> v1_setwiseo(u1_lattices(A),u1_struct_0(A)))) # label(t73_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4079 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) -> (r3_lattices(A,k2_lattice2(C,A,D,E),B) -> (all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B))))))))))))))) # label(t46_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4080 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> v11_lattices(A)))) # label(t36_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4081 (all A (l3_lattices(A) -> k1_lattice2(A) = g3_lattices(u1_struct_0(A),u1_lattices(A),u2_lattices(A)))) # label(d2_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4082 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v6_group_1(A) & v10_lattices(A) -> v4_lattices(A) & v7_lattices(A) & v10_lattices(A) & v13_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & -v3_struct_0(A)))) # label(cc3_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4083 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> D = k1_funct_4(D,k2_partfun1(A,B,D,C)))))))) # label(t9_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4084 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v1_lattice2(A) & v10_lattices(A) -> v6_lattices(A) & v3_filter_0(A) & v13_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc1_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4085 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) = C)) -> k5_lattices(A) = B))))) # label(t22_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4086 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = C)) -> B = k6_lattices(A)))))) # label(t24_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4087 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v1_binop_1(u2_lattices(A),u1_struct_0(A)) & v1_binop_1(u1_lattices(A),u1_struct_0(A)) & r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) & r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) & v2_binop_1(u1_lattices(A),u1_struct_0(A)) & v2_binop_1(u2_lattices(A),u1_struct_0(A)) -> v10_lattices(A)))) # label(t17_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4088 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v3_binop_1(u2_lattices(A),u1_struct_0(A)))) # label(t26_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4089 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v10_lattices(C) & l3_lattices(C) & v13_lattices(C) & v11_lattices(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> k2_binop_1(u1_struct_0(C),u1_struct_0(C),u1_struct_0(C),u1_lattices(C),E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)))))))))))) # label(t81_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4090 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> (k2_partfun1(A,B,C,E) = k2_partfun1(A,B,D,E) -> k2_funct_2(A,B,D,E) = k2_funct_2(A,B,C,E)))))))))) # label(t16_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4091 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> r6_binop_1(u1_struct_0(A),u1_lattices(A),u1_lattices(A)))) # label(t39_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4092 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,C) = C)) -> k6_lattices(A) = B))))) # label(t25_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4093 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(k1_funct_4(C,k2_partfun1(A,B,D,E))) & v1_funct_2(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B) & m2_relset_1(k1_funct_4(C,k2_partfun1(A,B,D,E)),A,B))))))))) # label(t6_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4094 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (k2_partfun1(A,B,D,C) = k2_partfun1(A,B,E,C) <-> (all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> k1_funct_1(D,F) = k1_funct_1(E,F))))))))))))) # label(t5_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4095 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> (C = E & D = B & r3_lattices(k1_lattice2(A),D,E) -> r3_lattices(A,C,B)))))))))))) # label(t54_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4096 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v6_group_1(A) & v10_lattices(A) & v11_lattices(A) -> v4_lattices(A) & v5_lattices(A) & v8_lattices(A) & v9_lattices(A) & v13_lattices(A) & v3_filter_0(A) & v1_lattice2(A) & v10_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A)))) # label(cc6_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4097 (all A (-v3_struct_0(A) & v3_lattices(A) & l3_lattices(A) -> A = k1_lattice2(k1_lattice2(A)))) # label(t19_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4098 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(B,A) -> k1_funct_4(A,B) = A))))) # label(t8_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4099 (all A (-v3_struct_0(A) & l1_lattices(A) & v6_lattices(A) -> v1_binop_1(u1_lattices(A),u1_struct_0(A)))) # label(t31_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4100 (all A (-v3_struct_0(A) & v6_lattices(A) & l1_lattices(A) -> v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_binop_1(u1_lattices(A),u1_struct_0(A)) & v1_funct_1(u1_lattices(A)) & v1_relat_1(u1_lattices(A)))) # label(fc4_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4101 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_1(E) -> ((exists F (r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F)) & r2_hidden(F,D) & m1_subset_1(F,C))) -> r3_lattices(A,B,k2_lattice2(C,A,D,E))))))))))))) # label(t44_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4102 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> v3_binop_1(u1_lattices(A),u1_struct_0(A)))) # label(t30_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4103 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (l3_lattices(C) & v13_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,u1_struct_0(C)) & m2_relset_1(E,A,u1_struct_0(C)) & v1_funct_1(E) -> (k2_partfun1(A,u1_struct_0(C),E,B) = k2_partfun1(A,u1_struct_0(C),D,B) -> k2_lattice2(A,C,B,D) = k2_lattice2(A,C,B,E)))))))))))) # label(t69_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4104 (all A (-v1_xboole_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_2(D,A,u1_struct_0(B)) & m2_relset_1(D,A,u1_struct_0(B)) & v1_funct_1(D) -> k7_setwiseo(A,u1_struct_0(B),u1_lattices(B),C,D) = k3_lattice2(A,B,C,D))))))))) # label(d4_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4105 (all A (l3_lattices(A) -> v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) # label(dt_k1_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4106 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)))) # label(t41_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4107 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) & v6_group_1(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v6_lattices(A)))) # label(cc4_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4108 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) & v1_funct_1(E) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,B,k8_funct_2(C,u1_struct_0(A),E,F))))) -> k1_xboole_0 = D | r3_lattices(A,B,k3_lattice2(C,A,D,E))))))))))))) # label(t61_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4109 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> B = k8_funct_2(C,u1_struct_0(A),E,F)))) -> k1_xboole_0 = D | k2_lattice2(C,A,D,E) = B))))))))))) # label(t45_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4110 (all A (l3_lattices(A) -> (v10_lattices(A) & v3_filter_0(A) & v13_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v1_lattice2(A) & v8_lattices(A) & v6_lattices(A)))) # label(cc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4111 $T # label(t1_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4112 (all A (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) -> k3_binop_1(u1_struct_0(A),u1_lattices(A)) = k6_lattices(A))) # label(t74_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4113 (all A (-v3_struct_0(A) & v4_lattices(A) & l2_lattices(A) -> v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_binop_1(u2_lattices(A),u1_struct_0(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)) & v1_relat_1(u2_lattices(A)))) # label(fc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4114 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,u1_struct_0(A)) & m2_relset_1(E,B,u1_struct_0(A)) -> (r2_hidden(C,D) -> r3_lattices(A,k3_lattice2(B,A,D,E),k8_funct_2(B,u1_struct_0(A),E,C))))))))))))) # label(t55_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4115 (all A (l2_lattices(A) & v4_lattices(A) & -v3_struct_0(A) -> v1_binop_1(u2_lattices(A),u1_struct_0(A)))) # label(t27_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4116 $T # label(t4_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4117 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v10_lattices(C) & l3_lattices(C) & v13_lattices(C) & v11_lattices(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> k4_lattices(C,E,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,k8_funcop_1(u1_struct_0(C),A,u1_lattices(C),E,D)))))))))))) # label(t83_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4118 (all A (v7_lattices(A) & l1_lattices(A) & -v3_struct_0(A) -> v2_binop_1(u1_lattices(A),u1_struct_0(A)) & v1_partfun1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_lattices(A)) & v1_relat_1(u1_lattices(A)))) # label(fc5_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4119 (all A (v11_lattices(A) & v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)))) # label(t80_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4120 (all A (-v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) -> k5_lattices(A) = k3_binop_1(u1_struct_0(A),u2_lattices(A)))) # label(t68_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4121 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (v1_setwiseo(u2_lattices(A),u1_struct_0(A)) -> k3_binop_1(u1_struct_0(A),u2_lattices(A)) = k5_lattices(A)))) # label(t28_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4122 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v3_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & -v3_struct_0(k1_lattice2(A)))) # label(fc6_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4123 $T # label(t11_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4124 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v3_filter_0(A) & v13_lattices(A) <-> v1_lattice2(A)))) # label(d6_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4125 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)))) # label(t40_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4126 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> k1_funct_4(k2_partfun1(A,B,C,E),D) = D)))))))) # label(t12_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4127 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,k4_lattices(A,B,E),C) -> r3_lattices(A,E,D)))) & r3_lattices(A,k4_lattices(A,B,D),C))))))) <-> -v3_struct_0(A) & v10_lattices(A) & v1_lattice2(A) & l3_lattices(A)))) # label(t84_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4128 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) -> (all E (v1_funct_2(E,B,u1_struct_0(A)) & m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_1(E) -> (k2_partfun1(B,u1_struct_0(A),D,C) = k2_partfun1(B,u1_struct_0(A),E,C) -> C = k1_xboole_0 | k3_lattice2(B,A,C,D) = k3_lattice2(B,A,C,E)))))))))))) # label(t60_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4129 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v14_lattices(A) -> r3_binop_1(u1_struct_0(A),k6_lattices(A),u1_lattices(A)))) # label(t72_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4130 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> (E = C & D = B -> r3_lattices(k1_lattice2(A),E,D))))))))))))) # label(t53_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4131 (exists A (l3_lattices(A) & -v3_struct_0(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v1_lattice2(A) & v10_lattices(A) & v7_lattices(A) & v4_lattices(A))) # label(rc1_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4132 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (v6_group_1(A) <-> v6_group_1(k1_lattice2(A))))) # label(t85_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4133 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v14_lattices(C) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,u1_struct_0(C)) & m2_relset_1(E,A,u1_struct_0(C)) -> (k2_partfun1(A,u1_struct_0(C),E,B) = k2_partfun1(A,u1_struct_0(C),D,B) -> k3_lattice2(A,C,B,E) = k3_lattice2(A,C,B,D)))))))))))) # label(t75_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4134 $T # label(t20_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4135 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & -v3_struct_0(k1_lattice2(A)) <-> v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & -v3_struct_0(A)))) # label(t65_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4136 (all A (v14_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k6_lattices(A) = k5_lattices(k1_lattice2(A)))) # label(t79_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4137 (all A all B all C all D (-v1_xboole_0(A) & v10_lattices(B) & l3_lattices(B) & v1_funct_1(D) & m1_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) & m1_subset_1(C,k5_finsub_1(A)) & -v3_struct_0(B) -> m1_subset_1(k2_lattice2(A,B,C,D),u1_struct_0(B)))) # label(dt_k2_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4138 $T # label(d5_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4139 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & v14_lattices(C) & l3_lattices(C) & v10_lattices(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) -> (all E (m2_relset_1(E,A,u1_struct_0(C)) & v1_funct_2(E,A,u1_struct_0(C)) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F))))) -> r3_lattices(C,k3_lattice2(A,C,B,D),k3_lattice2(A,C,B,E))))))))))))) # label(t77_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4140 (all A all B all C all D (m1_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) & v1_funct_1(D) & m1_subset_1(C,k5_finsub_1(A)) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & -v1_xboole_0(A) -> m1_subset_1(k3_lattice2(A,B,C,D),u1_struct_0(B)))) # label(dt_k3_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4141 (all A (-v3_struct_0(A) & v7_lattices(A) & l1_lattices(A) -> v2_binop_1(u1_lattices(A),u1_struct_0(A)))) # label(t32_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4142 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v10_lattices(A) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> r6_binop_1(u1_struct_0(A),u2_lattices(A),u1_lattices(A))))) # label(t35_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4143 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r3_binop_1(u1_struct_0(A),k5_lattices(A),u2_lattices(A)))) # label(t66_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4144 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B)))) -> r3_lattices(A,k2_lattice2(C,A,D,E),B) | k1_xboole_0 = D))))))))))) # label(t47_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4145 $T # label(t23_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4146 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(k1_lattice2(A))) -> (all E (m1_subset_1(E,u1_struct_0(k1_lattice2(A))) -> (C = E & D = B -> k3_lattices(A,B,C) = k4_lattices(k1_lattice2(A),D,E) & k3_lattices(k1_lattice2(A),D,E) = k4_lattices(A,B,C)))))))))))) # label(t52_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4147 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v14_lattices(A) <-> v13_lattices(k1_lattice2(A))))) # label(t64_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4148 (all A (-v3_struct_0(A) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A) -> k5_lattices(A) = k6_lattices(k1_lattice2(A)))) # label(t78_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4149 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> k1_relat_1(k2_partfun1(A,B,D,C)) = C)))))) # label(t2_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4150 (all A (-v1_xboole_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,u1_struct_0(B)) & m2_relset_1(D,A,u1_struct_0(B)) -> k2_lattice2(A,B,C,D) = k7_setwiseo(A,u1_struct_0(B),u2_lattices(B),C,D))))))))) # label(d3_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4151 (all A (-v3_struct_0(A) & l2_lattices(A) & v5_lattices(A) -> v2_binop_1(u2_lattices(A),u1_struct_0(A)))) # label(t29_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4152 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (v14_lattices(k1_lattice2(A)) <-> v13_lattices(A)))) # label(t63_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4153 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_2(E,B,u1_struct_0(A)) -> ((all F (m1_subset_1(F,B) -> (r2_hidden(F,C) -> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F))))) -> r3_lattices(A,k2_lattice2(B,A,C,D),k2_lattice2(B,A,C,E)) | C = k1_xboole_0))))))))))) # label(t48_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4154 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v1_setwiseo(u1_lattices(A),u1_struct_0(A)) -> k3_binop_1(u1_struct_0(A),u1_lattices(A)) = k6_lattices(A)))) # label(t33_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4155 (all A (-v3_struct_0(A) & l3_lattices(A) -> v3_lattices(k1_lattice2(A)) & -v3_struct_0(k1_lattice2(A)))) # label(fc1_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4156 (all A (l2_lattices(A) & v5_lattices(A) & -v3_struct_0(A) -> v2_binop_1(u2_lattices(A),u1_struct_0(A)) & v1_partfun1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u2_lattices(A)) & v1_relat_1(u2_lattices(A)))) # label(fc3_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4157 (all A (l3_lattices(A) -> (v6_group_1(A) & v10_lattices(A) & -v3_struct_0(A) -> v5_lattices(A) & v10_lattices(A) & v13_lattices(A) & v15_lattices(A) & v14_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc5_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4158 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (-v3_struct_0(C) & v11_lattices(C) & l3_lattices(C) & v13_lattices(C) & v10_lattices(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_2(D,A,u1_struct_0(C)) -> (all E (v1_funct_2(E,A,u1_struct_0(C)) & m2_relset_1(E,A,u1_struct_0(C)) & v1_funct_1(E) -> (all F (m1_subset_1(F,u1_struct_0(C)) -> ((all G (m1_subset_1(G,A) -> (r2_hidden(G,B) -> k4_lattices(C,F,k8_funct_2(A,u1_struct_0(C),E,G)) = k8_funct_2(A,u1_struct_0(C),D,G)))) -> k2_lattice2(A,C,B,D) = k4_lattices(C,F,k2_lattice2(A,C,B,E))))))))))))))) # label(t82_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4159 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) -> ((all F (m1_subset_1(F,C) -> (r2_hidden(F,D) -> k8_funct_2(C,u1_struct_0(A),E,F) = B))) -> B = k3_lattice2(C,A,D,E) | D = k1_xboole_0))))))))))) # label(t57_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4160 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_2(E,B,u1_struct_0(A)) -> ((all F (m1_subset_1(F,B) -> (r2_hidden(F,C) -> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),D,F),k8_funct_2(B,u1_struct_0(A),E,F))))) -> C = k1_xboole_0 | r3_lattices(A,k3_lattice2(B,A,C,D),k3_lattice2(B,A,C,E))))))))))))) # label(t62_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4161 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> r6_binop_1(u1_struct_0(A),u2_lattices(A),u2_lattices(A)))) # label(t34_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4162 (all A (l3_lattices(A) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v1_setwiseo(u2_lattices(A),u1_struct_0(A)))) # label(t67_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4163 (exists A (v3_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v13_lattices(A) & v3_filter_0(A) & v1_lattice2(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc2_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4164 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v10_lattices(C) & l3_lattices(C) & v13_lattices(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),E)))) -> r3_lattices(C,k2_lattice2(A,C,B,D),E)))))))))))) # label(t70_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4165 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,C) -> k1_funct_1(D,F) = k1_funct_1(E,F)))) -> k1_funct_4(E,k2_partfun1(A,B,D,C)) = E))))))))) # label(t10_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4166 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(A)) -> (all C (v13_lattices(C) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,A,u1_struct_0(C)) & m2_relset_1(D,A,u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,u1_struct_0(C)) & v1_funct_2(E,A,u1_struct_0(C)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,B) -> r3_lattices(C,k8_funct_2(A,u1_struct_0(C),D,F),k8_funct_2(A,u1_struct_0(C),E,F))))) -> r3_lattices(C,k2_lattice2(A,C,B,D),k2_lattice2(A,C,B,E))))))))))))) # label(t71_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4167 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (r6_binop_1(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) -> v11_lattices(A)))) # label(t38_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4168 $T # label(t3_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4169 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (m1_subset_1(D,k5_finsub_1(B)) -> (all E (m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_2(E,B,u1_struct_0(A)) & v1_funct_1(E) -> (r2_hidden(C,D) -> r3_lattices(A,k8_funct_2(B,u1_struct_0(A),E,C),k2_lattice2(B,A,D,E))))))))))))) # label(t43_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4170 $T # label(t42_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4171 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_1(E) -> ((exists F (m1_subset_1(F,C) & r2_hidden(F,D) & r3_lattices(A,k8_funct_2(C,u1_struct_0(A),E,F),B))) -> r3_lattices(A,k3_lattice2(C,A,D,E),B)))))))))))) # label(t56_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4172 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_1(E) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_2(E,C,u1_struct_0(A)) -> (k1_xboole_0 != D -> k2_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u2_lattices(A),B,E)) = k3_lattices(A,B,k2_lattice2(C,A,D,E))))))))))))) # label(t50_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4173 $T # label(t15_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4174 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> k1_funct_4(k2_partfun1(A,B,D,C),E) = E)))))))) # label(t7_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4175 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k3_lattices(A,B,C))) -> B = k5_lattices(A)))))) # label(t21_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4176 (all A all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,k5_finsub_1(A)) -> ((all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k1_funct_1(D,F) = k1_funct_1(C,F)))) -> k1_funct_4(D,k2_partfun1(A,B,C,E)) = D))))))))) # label(t14_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4177 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k5_finsub_1(B)) -> (all D (m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,u1_struct_0(A)) & v1_funct_2(E,B,u1_struct_0(A)) & v1_funct_1(E) -> (k2_partfun1(B,u1_struct_0(A),E,C) = k2_partfun1(B,u1_struct_0(A),D,C) -> C = k1_xboole_0 | k2_lattice2(B,A,C,E) = k2_lattice2(B,A,C,D)))))))))))) # label(t49_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.81 4178 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,k5_finsub_1(C)) -> (all E (v1_funct_2(E,C,u1_struct_0(A)) & m2_relset_1(E,C,u1_struct_0(A)) & v1_funct_1(E) -> (k1_xboole_0 != D -> k3_lattice2(C,A,D,k8_funcop_1(u1_struct_0(A),C,u1_lattices(A),B,E)) = k4_lattices(A,B,k3_lattice2(C,A,D,E))))))))))))) # label(t58_lattice2) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4179 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r2_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) <-> r2_binop_1(B,D,F) & r2_binop_1(A,C,E)))))))))))))) # label(t26_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4180 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) -> v10_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) & l3_lattices(A) & -v3_struct_0(A)))))) # label(t35_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4181 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) = k10_filter_1(A,B,k3_lattices(A,C,D),k3_lattices(B,E,F)) & k4_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) = k10_filter_1(A,B,k4_lattices(A,C,D),k4_lattices(B,E,F)))))))))))))) # label(t36_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4182 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r5_binop_1(A,C,D) -> r5_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t10_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4183 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> m2_filter_1(u2_lattices(A),u1_struct_0(A),k11_filter_0(A,B)))))) # label(t13_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4184 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & l3_lattices(B) & l3_lattices(A) -> v3_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)))) # label(dt_k8_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4185 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (exists C m1_filter_1(C,A,B)))) # label(existence_m1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4186 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v10_lattices(B) & v15_lattices(B) & l3_lattices(B) & v16_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v16_lattices(A) <-> -v3_struct_0(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v16_lattices(k8_filter_1(A,B)) & v15_lattices(k8_filter_1(A,B))))))) # label(t46_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4187 (all A all B (v10_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) & l3_lattices(A) & -v3_struct_0(A) -> (r1_filter_1(A,B) -> r1_filter_1(B,A)))) # label(symmetry_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4188 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r6_binop_1(A,C,D) -> r6_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t11_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4189 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (m2_filter_1(C,A,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (r2_hidden(k1_domain_1(A,A,D,E),B) & r2_hidden(k1_domain_1(A,A,F,G),B) -> r2_hidden(k1_domain_1(A,A,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,G)),B))))))))))))))))) # label(d2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4190 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) = k6_filter_1(A,B,k4_lattices(A,C,D)) & k3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) = k6_filter_1(A,B,k3_lattices(A,C,D)))))))))) # label(t15_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4191 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r5_binop_1(B,E,F) & r5_binop_1(A,C,D) <-> r5_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t29_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4192 (all A (m1_subset_1(A,f1_s2_filter_1) -> (all B (m1_subset_1(B,f1_s2_filter_1) -> p1_s2_filter_1(k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,A),k2_filter_1(f1_s2_filter_1,f2_s2_filter_1,B)))))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1)) -> (all B (m2_subset_1(B,k1_zfmisc_1(f1_s2_filter_1),k8_eqrel_1(f1_s2_filter_1,f2_s2_filter_1)) -> p1_s2_filter_1(A,B))))) # label(s2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4193 (all A (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> l3_lattices(k5_filter_1(A,B)) & k6_lattices(k5_filter_1(A,B)) = k6_filter_1(A,B,k6_lattices(A)) & v14_lattices(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & -v3_struct_0(k5_filter_1(A,B)))))) # label(t19_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4194 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (v3_filter_0(k8_filter_1(A,B)) <-> v3_filter_0(A) & v3_filter_0(B)))))) # label(t48_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4195 (all A all B all C all D (v10_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k10_filter_1(A,B,C,D),u1_struct_0(k8_filter_1(A,B))))) # label(dt_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4196 (all A all B (-v3_struct_0(A) & v10_lattices(A) & v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) -> r1_filter_1(A,A))) # label(reflexivity_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4197 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k9_filter_0(A,B,k9_filter_0(A,B,C)))))))) # label(t54_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4198 (all A all B (l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_1(A,B)) & v8_lattices(k8_filter_1(A,B)) & v9_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & v7_lattices(k8_filter_1(A,B)) & v6_lattices(k8_filter_1(A,B)) & v5_lattices(k8_filter_1(A,B)) & v4_lattices(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)))) # label(fc3_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4199 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k7_lattices(A,k9_filter_0(A,B,C)) = k9_filter_0(A,B,k7_lattices(A,C)) & k9_filter_0(A,k7_lattices(A,B),C) = k7_lattices(A,k9_filter_0(A,B,C)) & k7_lattices(A,k9_filter_0(A,B,C)) = k3_lattices(A,k4_lattices(A,B,k7_lattices(A,C)),k4_lattices(A,k7_lattices(A,B),C)) & k7_lattices(A,k4_filter_0(A,B,C)) = k4_lattices(A,B,k7_lattices(A,C)))))))) # label(t52_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4200 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) <-> r3_lattices(B,E,F) & r3_lattices(A,C,D)))))))))))))) # label(t37_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4201 (all A all B all C (-v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_subset_1(C,A) & m1_relset_1(B,A,A) -> k6_eqrel_1(A,B,C) = k2_filter_1(A,B,C))) # label(redefinition_k2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4202 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) -> -v3_struct_0(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & v3_lattices(k5_filter_1(A,B)))) # label(dt_k5_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4203 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> k8_filter_1(k1_lattice2(A),k1_lattice2(B)) = k1_lattice2(k8_filter_1(A,B)))))) # label(t49_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4204 (all A all B (v1_relat_1(B) & -v1_xboole_0(A) -> (all C (m2_filter_1(C,A,B) -> v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A))))) # label(dt_m2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4205 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & v1_funct_1(C) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & -v1_xboole_0(A) -> m2_relset_1(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & v1_funct_2(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & v1_funct_1(k3_filter_1(A,B,C)))) # label(dt_k3_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4206 (all A (m1_subset_1(A,f1_s1_filter_1) -> p1_s1_filter_1(k2_filter_1(f1_s1_filter_1,f2_s1_filter_1,A)))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s1_filter_1),k8_eqrel_1(f1_s1_filter_1,f2_s1_filter_1)) -> p1_s1_filter_1(A))) # label(s1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4207 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (m2_filter_1(C,A,B) -> (v2_binop_1(C,A) -> v2_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B))))))))) # label(t5_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4208 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> m1_filter_0(k5_subset_1(u1_struct_0(A),B,C),A))))))) # label(t1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4209 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & -v3_struct_0(B) & v10_lattices(B) & v13_lattices(B) & l3_lattices(B) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A) -> k10_filter_1(A,B,k5_lattices(A),k5_lattices(B)) = k5_lattices(k8_filter_1(A,B))))))) # label(t43_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4210 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (r4_binop_1(A,C,D) & r4_binop_1(B,E,F) <-> r4_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t28_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4211 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (m1_filter_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & m2_relset_1(D,k8_eqrel_1(A,B),k8_eqrel_1(A,B)) -> (D = k3_filter_1(A,B,C) <-> (all E all F (r2_hidden(F,E) & r2_hidden(E,k8_eqrel_1(A,B)) -> k6_eqrel_1(A,B,k1_funct_1(C,F)) = k1_funct_1(D,E))))))))))))) # label(d3_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4212 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v2_binop_1(C,A) & v2_binop_1(D,B) <-> v2_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B))))))))))) # label(t24_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4213 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> v3_filter_0(k5_filter_1(A,B)))))) # label(t20_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4214 (all A (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)) <-> r2_hidden(k4_filter_0(A,C,D),B)))))))))) # label(t16_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4215 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> v10_lattices(k5_filter_1(A,B)) & v17_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & -v3_struct_0(k5_filter_1(A,B)))))) # label(t21_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4216 (all A all B all C (m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k1_filter_1(A,B,C) = k1_filter_1(A,C,B))) # label(commutativity_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4217 (all A (m1_subset_1(A,f1_s6_filter_1) -> (all B (m1_subset_1(B,f1_s6_filter_1) -> (all C (m1_subset_1(C,f1_s6_filter_1) -> (all D (m1_subset_1(D,f2_s6_filter_1) -> (all E (m1_subset_1(E,f2_s6_filter_1) -> (all F (m1_subset_1(F,f2_s6_filter_1) -> p1_s6_filter_1(k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,A,D),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,B,E),k1_domain_1(f1_s6_filter_1,f2_s6_filter_1,C,F)))))))))))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> (all B (m1_subset_1(B,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> (all C (m1_subset_1(C,k2_zfmisc_1(f1_s6_filter_1,f2_s6_filter_1)) -> p1_s6_filter_1(A,B,C))))))) # label(s6_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4218 (all A (m1_subset_1(A,f1_s5_filter_1) -> (all B (m1_subset_1(B,f1_s5_filter_1) -> (all C (m1_subset_1(C,f2_s5_filter_1) -> (all D (m1_subset_1(D,f2_s5_filter_1) -> p1_s5_filter_1(k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,A,C),k1_domain_1(f1_s5_filter_1,f2_s5_filter_1,B,D)))))))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1)) -> (all B (m1_subset_1(B,k2_zfmisc_1(f1_s5_filter_1,f2_s5_filter_1)) -> p1_s5_filter_1(A,B))))) # label(s5_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4219 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,A,A) & -v1_xboole_0(A) -> v1_funct_1(k4_filter_1(A,B,C)) & m2_relset_1(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & v1_funct_2(k4_filter_1(A,B,C),k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)))) # label(dt_k4_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4220 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r1_lattice2(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F)) <-> r1_lattice2(B,E,F) & r1_lattice2(A,C,D)))))))))))))) # label(t31_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4221 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> v1_funct_1(k7_filter_1(A,B,C,D)) & m2_relset_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v1_funct_2(k7_filter_1(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)))) # label(dt_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4222 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & v15_lattices(B) & l3_lattices(B) & v15_lattices(A) & v10_lattices(A) -> (r2_lattices(A,C,D) & r2_lattices(B,E,F) <-> r2_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)))))))))))))))) # label(t45_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4223 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,D,C)),k4_filter_0(A,k3_lattices(A,B,D),C)))))))))) # label(t57_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4224 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B,A) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k6_filter_1(A,B,C),u1_struct_0(k5_filter_1(A,B))))) # label(dt_k6_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4225 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_filter_0(A,B,k4_lattices(A,B,C)) = k4_filter_0(A,B,C) & k4_filter_0(A,k3_lattices(A,B,C),B) = k4_filter_0(A,C,B))))))) # label(t55_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4226 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_filter_1(A,k8_filter_1(k5_filter_1(A,k2_filter_0(A,B)),k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t62_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4227 (all A (m1_subset_1(A,f1_s3_filter_1) -> (all B (m1_subset_1(B,f1_s3_filter_1) -> (all C (m1_subset_1(C,f1_s3_filter_1) -> p1_s3_filter_1(k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,A),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,B),k2_filter_1(f1_s3_filter_1,f2_s3_filter_1,C)))))))) -> (all A (m2_subset_1(A,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> (all B (m2_subset_1(B,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> (all C (m2_subset_1(C,k1_zfmisc_1(f1_s3_filter_1),k8_eqrel_1(f1_s3_filter_1,f2_s3_filter_1)) -> p1_s3_filter_1(A,B,C))))))) # label(s3_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4228 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v12_lattices(B) & v12_lattices(A) <-> v12_lattices(k8_filter_1(A,B))))))) # label(t38_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4229 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,B) -> (all G (v1_funct_2(G,k2_zfmisc_1(A,A),A) & m2_relset_1(G,k2_zfmisc_1(A,A),A) & v1_funct_1(G) -> (all H (v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(B,B),B) & m2_relset_1(H,k2_zfmisc_1(B,B),B) -> k2_binop_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(A,B),k7_filter_1(A,B,G,H),k1_domain_1(A,B,C,E),k1_domain_1(A,B,D,F)) = k1_domain_1(A,B,k2_binop_1(A,A,A,G,C,D),k2_binop_1(B,B,B,H,E,F)))))))))))))))))) # label(t22_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4230 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & v14_lattices(B) & l3_lattices(B) & v10_lattices(B) & v14_lattices(A) & v10_lattices(A) -> k10_filter_1(A,B,k6_lattices(A),k6_lattices(B)) = k6_lattices(k8_filter_1(A,B))))))) # label(t44_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4231 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (v13_lattices(A) & v13_lattices(B) <-> v13_lattices(k8_filter_1(A,B))))))) # label(t40_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4232 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (v15_lattices(k8_filter_1(A,B)) <-> v15_lattices(A) & v15_lattices(B)))))) # label(t42_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4233 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_1(E) -> (all F (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r3_binop_1(B,D,F) & r3_binop_1(A,C,E) <-> r3_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F))))))))))))))) # label(t27_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4234 (all A all B all C all D (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> k7_filter_1(A,B,C,D) = k3_funct_4(C,D))) # label(redefinition_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4235 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(B) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4236 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_filter_1(D,A,B) -> (r1_binop_1(A,C,D) -> r1_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t6_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4237 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> (all D (m1_subset_1(D,u1_struct_0(k5_filter_1(A,B))) -> ((all E (v1_partfun1(E,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(E) & v3_relat_2(E) -> (E = k10_filter_0(A,B) -> k2_filter_1(u1_struct_0(A),E,C) = D))) <-> D = k6_filter_1(A,B,C))))))))))) # label(d6_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4238 (all A all B all C all D (-v3_struct_0(A) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & v10_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v10_lattices(A) -> k10_filter_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4239 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v1_relat_1(k9_filter_1(A)))) # label(dt_k9_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4240 (all A all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_1_0_filter_1(B)) <-> (exists C exists D (m1_subset_1(C,u1_struct_0(B)) & k1_domain_1(u1_struct_0(B),u1_struct_0(B),C,D) = A & r3_lattices(B,C,D) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_1_0_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4241 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v11_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) <-> l3_lattices(B) & v11_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A)))))) # label(t39_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4242 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> g3_lattices(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u2_lattices(A),u2_lattices(B)),k7_filter_1(u1_struct_0(A),u1_struct_0(B),u1_lattices(A),u1_lattices(B))) = k8_filter_1(A,B))))) # label(d7_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4243 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> r1_filter_1(k8_filter_1(A,B),k8_filter_1(B,A)))))) # label(t50_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4244 (all A (-v1_xboole_0(A) -> (all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r1_lattice2(A,C,D) -> r1_lattice2(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t12_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4245 (all A all B all C (l3_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & v10_lattices(A) & -v3_struct_0(A) -> B = k1_filter_1(A,B,B))) # label(idempotence_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4246 (all A (-v3_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v13_lattices(A) -> k6_filter_1(A,B,k5_lattices(A)) = k5_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & v13_lattices(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & -v3_struct_0(k5_filter_1(A,B))))))) # label(t18_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4247 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_subset_1(C,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & -v1_xboole_0(A) -> m2_subset_1(k2_filter_1(A,B,C),k1_zfmisc_1(A),k8_eqrel_1(A,B)))) # label(dt_k2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4248 (all A (m1_subset_1(A,f1_s4_filter_1) -> (all B (m1_subset_1(B,f2_s4_filter_1) -> p1_s4_filter_1(k1_domain_1(f1_s4_filter_1,f2_s4_filter_1,A,B)))))) -> (all A (m1_subset_1(A,k2_zfmisc_1(f1_s4_filter_1,f2_s4_filter_1)) -> p1_s4_filter_1(A))) # label(s4_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4249 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_lattices(A,B,C) <-> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k9_filter_1(A))))))))) # label(t32_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4250 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) -> k1_filter_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4251 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B)) -> r3_lattices(A,D,k3_lattices(A,B,k9_filter_0(A,B,C)))))) & r2_hidden(k3_lattices(A,B,k9_filter_0(A,B,C)),k2_filter_1(u1_struct_0(A),k12_filter_0(A,k2_filter_0(A,C)),B)))))))) # label(t61_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4252 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(C,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) & r2_hidden(E,k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) -> r2_hidden(k3_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D)) & r2_hidden(k4_lattices(A,C,E),k2_filter_1(u1_struct_0(A),k11_filter_0(A,B),D))))))))))))) # label(t60_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4253 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k9_filter_0(A,B,C) = k9_filter_0(A,B,D) -> C = D))))))))) # label(t53_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4254 (all A (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> m2_filter_1(u1_lattices(A),u1_struct_0(A),k11_filter_0(A,B)))))) # label(t14_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4255 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (v10_lattices(C) & l3_lattices(C) & -v3_struct_0(C) -> (r1_filter_1(A,B) & r1_filter_1(B,C) -> r1_filter_1(A,C)))))))) # label(t34_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4256 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (all C (m1_filter_1(C,A,B) -> v1_funct_1(C) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A))))) # label(dt_m1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4257 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m1_subset_1(C,A) -> (all D (m2_filter_1(D,A,B) -> (r2_binop_1(A,C,D) -> r2_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t7_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4258 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_filter_1(D,A,B) -> (r3_binop_1(A,C,D) -> r3_binop_1(k8_eqrel_1(A,B),k2_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t8_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4259 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (r1_filter_1(A,B) <-> r4_wellord1(k9_filter_1(A),k9_filter_1(B))))))) # label(d9_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4260 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m2_filter_1(C,A,B) -> (all D (m2_filter_1(D,A,B) -> (r4_binop_1(A,C,D) -> r4_binop_1(k8_eqrel_1(A,B),k4_filter_1(A,B,C),k4_filter_1(A,B,D))))))))))) # label(t9_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4261 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) -> (all F (m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r1_binop_1(B,D,F) & r1_binop_1(A,C,E) <-> r1_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F))))))))))))))) # label(t25_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4262 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,B,D),C)) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,D,C))) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,k4_lattices(A,D,B),C)) & r3_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,C,D))))))))))) # label(t56_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4263 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_filter_0(A,B,C) = k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C))))))))) # label(t51_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4264 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & v17_lattices(B) & l3_lattices(B) & v10_lattices(B) & v17_lattices(A) & v10_lattices(A) <-> v10_lattices(k8_filter_1(A,B)) & v17_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B))))))) # label(t47_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4265 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k3_relat_1(k9_filter_1(A)) = u1_struct_0(A) & k2_relat_1(k9_filter_1(A)) = u1_struct_0(A) & k1_relat_1(k9_filter_1(A)) = u1_struct_0(A))) # label(t33_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4266 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_filter_0(A,k4_lattices(A,B,C),D) = k4_filter_0(A,B,k4_filter_0(A,C,D)))))))))) # label(t17_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4267 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m2_filter_1(E,A,B) -> k2_filter_1(A,B,k2_binop_1(A,A,A,E,C,D)) = k2_binop_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B),k8_eqrel_1(A,B),k4_filter_1(A,B,E),k2_filter_1(A,B,C),k2_filter_1(A,B,D)))))))))))) # label(t3_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4268 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_filter_0(A,C) = k2_filter_0(A,B) -> C = B))))))) # label(t2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4269 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) -> m1_filter_0(k1_filter_1(A,B,C),A))) # label(dt_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4270 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (r2_hidden(k9_filter_0(A,C,D),B) & r2_hidden(k9_filter_0(A,E,F),B) -> r2_hidden(k9_filter_0(A,k4_lattices(A,C,E),k4_lattices(A,D,F)),B) & r2_hidden(k9_filter_0(A,k3_lattices(A,C,E),k3_lattices(A,D,F)),B)))))))))))))) # label(t59_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4271 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> (all C (m2_filter_1(C,A,B) -> (v1_binop_1(C,A) -> v1_binop_1(k4_filter_1(A,B,C),k8_eqrel_1(A,B))))))))) # label(t4_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4272 (all A (-v1_xboole_0(A) -> (all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (m2_filter_1(C,A,B) -> (all D (m2_relset_1(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & v1_funct_2(D,k2_zfmisc_1(k8_eqrel_1(A,B),k8_eqrel_1(A,B)),k8_eqrel_1(A,B)) & v1_funct_1(D) -> (k4_filter_1(A,B,C) = D <-> (all E all F all G all H (r2_hidden(G,E) & r2_hidden(H,F) & r2_hidden(F,k8_eqrel_1(A,B)) & r2_hidden(E,k8_eqrel_1(A,B)) -> k6_eqrel_1(A,B,k1_binop_1(C,G,H)) = k1_binop_1(D,E,F))))))))))))) # label(d4_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4273 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) & -v3_struct_0(A) -> (all C (v3_lattices(C) & v10_lattices(C) & l3_lattices(C) & -v3_struct_0(C) -> (C = k5_filter_1(A,B) <-> (all D (v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(D,u1_struct_0(A),u1_struct_0(A)) -> (D = k10_filter_0(A,B) -> C = g3_lattices(k8_eqrel_1(u1_struct_0(A),D),k4_filter_1(u1_struct_0(A),D,u2_lattices(A)),k4_filter_1(u1_struct_0(A),D,u1_lattices(A)))))))))))))) # label(d5_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4274 (all A all B (v1_relat_1(B) & -v1_xboole_0(A) -> (exists C m2_filter_1(C,A,B)))) # label(existence_m2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4275 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v14_lattices(A) & v14_lattices(B) <-> v14_lattices(k8_filter_1(A,B))))))) # label(t41_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4276 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_2(D,k2_zfmisc_1(B,B),B) -> (v1_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B)) <-> v1_binop_1(C,A) & v1_binop_1(D,B)))))))))) # label(t23_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4277 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (m1_filter_1(C,A,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (r2_hidden(k1_domain_1(A,A,D,E),B) -> r2_hidden(k1_domain_1(A,A,k8_funct_2(A,A,C,D),k8_funct_2(A,A,C,E)),B))))))))))))) # label(d1_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4278 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,k4_filter_0(A,B,C),k4_filter_0(A,B,D)),k4_filter_0(A,B,k4_lattices(A,C,D))))))))))) # label(t58_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4279 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (all E (m2_relset_1(E,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(B,B),B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) -> (r6_binop_1(B,E,F) & r6_binop_1(A,C,D) <-> r6_binop_1(k2_zfmisc_1(A,B),k7_filter_1(A,B,C,E),k7_filter_1(A,B,D,F))))))))))))))) # label(t30_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4280 (all A all B (l3_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)))) # label(fc2_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.82 4281 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> a_1_0_filter_1(A) = k9_filter_1(A))) # label(d8_filter_1) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4282 (all A (l3_lattices(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k15_lattice3(A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r4_lattice3(A,D,B) -> r1_lattices(A,C,D)))) & r4_lattice3(A,C,B))))))) # label(d21_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4283 (all A all B (l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4284 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k7_lattice3(A))) -> k9_lattice3(A,B) = B)))) # label(d7_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4285 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(k7_lattice3(A),k8_lattice3(A,C),k8_lattice3(A,B)) <-> r1_orders_2(A,B,C)))))))) # label(t9_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4286 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v5_lattice3(B) & v4_lattice3(B) & v10_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k15_lattice3(B,a_3_8_lattice3(A,B,C)) = k4_lattices(B,k15_lattice3(B,A),C) & k15_lattice3(B,a_3_7_lattice3(A,B,C)) = k4_lattices(B,C,k15_lattice3(B,A)))))) # label(t54_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4287 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> k2_lattice3(k1_lattice2(A)) = k6_lattice3(u1_struct_0(A),k2_lattice3(A)) & k7_lattice3(k3_lattice3(A)) = k3_lattice3(k1_lattice2(A)))) # label(t20_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4288 (exists A (m1_subset_1(A,f2_s1_lattice3) & p1_s1_lattice3(A))) -> a_0_0_lattice3 = k1_tarski(f1_s1_lattice3) # label(s1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4289 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B k15_lattice3(A,B) = k16_lattice3(A,a_2_2_lattice3(A,B))))) # label(t37_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4290 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k8_lattice3(A,B) = B)))) # label(d6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4291 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k10_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4292 (all A v4_lattice3(k1_lattice3(A))) # label(t25_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4293 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> ((all B all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k16_lattice3(A,a_3_5_lattice3(A,B,C)),k3_lattices(A,C,k16_lattice3(A,B))))) <-> v6_lattice3(A)))) # label(t36_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4294 (all A all B (l3_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)))) # label(dt_k16_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4295 (all A (v6_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4296 (all A all B all C (-v3_struct_0(B) & v4_lattice3(B) & l3_lattices(B) & v10_lattices(B) -> ((exists D ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & r3_lattices(B,E,D))) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_6_lattice3(B,C))))) # label(fraenkel_a_2_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4297 (all A all B all C all D (m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & -v3_struct_0(B) -> ((exists E (k2_lattices(B,D,E) = A & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_lattice3(B,C,D))))) # label(fraenkel_a_3_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4298 (exists A (l3_lattices(A) & -v3_struct_0(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v5_lattice3(A) & v6_lattice3(A) & v4_lattice3(A) & v10_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A))) # label(rc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4299 (all A (-v3_struct_0(A) & l1_orders_2(A) -> v1_orders_2(k7_lattice3(A)) & -v3_struct_0(k7_lattice3(A)))) # label(fc6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4300 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (r1_tarski(B,k1_zfmisc_1(u1_struct_0(A))) -> k15_lattice3(A,k3_tarski(B)) = k15_lattice3(A,a_2_7_lattice3(A,B)))))) # label(t49_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4301 (all A all B all C (v4_orders_2(A) & v1_lattice3(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> k13_lattice3(A,B,C) = k10_lattice3(A,B,C))) # label(redefinition_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4302 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (v5_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> r3_lattices(A,k4_lattices(A,C,k15_lattice3(A,B)),k15_lattice3(A,a_3_3_lattice3(A,B,C)))))))) # label(t33_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4303 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v4_lattice3(A) <-> (all B exists C (r4_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r4_lattice3(A,D,B) -> r1_lattices(A,C,D)))) & m1_subset_1(C,u1_struct_0(A))))))) # label(d18_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4304 (all A (r2_hidden(A,a_0_1_lattice3) <-> (exists B (m1_subset_1(B,f1_s2_lattice3) & A = f3_s2_lattice3(B) & p1_s2_lattice3(B))))) # label(fraenkel_a_0_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4305 (all A ((exists B (p1_s2_lattice3(B) & k1_funct_1(f4_s2_lattice3,f3_s2_lattice3(B)) = A & m1_subset_1(B,f1_s2_lattice3))) <-> r2_hidden(A,a_0_2_lattice3))) # label(fraenkel_a_0_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4306 (all A all B all C (l3_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_1_lattice3(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & D = A & r3_lattice3(B,D,C)))))) # label(fraenkel_a_2_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4307 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice3(A))) -> (r1_lattices(k1_lattice3(A),B,C) <-> r1_tarski(B,C)))))) # label(t2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4308 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k10_lattice3(A,B,C) = k10_lattice3(A,C,B))))))) # label(t13_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4309 (all A all B all C (v10_lattices(B) & l3_lattices(B) & v4_lattice3(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_5_lattice3(B,C)) <-> (exists D (A = D & (exists E (m1_subset_1(E,u1_struct_0(B)) & r3_lattices(B,D,E) & r2_hidden(E,C))) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4310 (all A (l1_orders_2(A) -> (v2_lattice3(A) -> -v3_struct_0(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4311 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> k7_lattices(k1_lattice3(A),B) = k4_xboole_0(A,B))) # label(t5_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4312 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v3_lattice3(A) -> v2_lattice3(A) & v1_lattice3(A)))) # label(t12_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4313 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (k3_lattice3(A) = k3_lattice3(B) -> g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))))))) # label(t6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4314 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & l1_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4315 $T # label(t39_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4316 (all A all B (-v3_struct_0(A) & v10_lattices(A) & m1_subset_1(B,u1_struct_0(k3_lattice3(A))) & l3_lattices(A) -> m1_subset_1(k5_lattice3(A,B),u1_struct_0(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4317 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k1_zfmisc_1(A),A) & v1_funct_2(B,k1_zfmisc_1(A),A) -> -((all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> k8_funct_2(k1_zfmisc_1(A),A,B,k10_relset_1(k1_zfmisc_1(A),A,B,C)) = k1_funct_1(B,k3_tarski(C)))) & (all C (l3_lattices(C) & v4_lattice3(C) & v10_lattices(C) & v3_lattices(C) & -v3_struct_0(C) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> k15_lattice3(C,D) = k1_funct_1(B,D))) & A = u1_struct_0(C)))) & (all C (m1_subset_1(C,A) -> k8_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)) = C))))))) # label(t56_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4318 (all A (v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4319 (all A all B all C all D (v10_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & -v3_struct_0(B) -> ((exists E (A = k4_lattices(B,D,E) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_3_lattice3(B,C,D))))) # label(fraenkel_a_3_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4320 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_lattice3(A))) -> B = k5_lattice3(A,B))))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4321 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,C) = k16_lattice3(A,k2_struct_0(A,B,C)) & k3_lattices(A,B,C) = k15_lattice3(A,k2_struct_0(A,B,C)))))))) # label(t44_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4322 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C r3_lattices(A,k15_lattice3(A,a_3_2_lattice3(A,B,C)),k4_lattices(A,B,k15_lattice3(A,C)))))))) # label(t32_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4323 (exists A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v2_orders_2(A) & v1_orders_2(A) & l1_orders_2(A))) # label(rc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4324 (all A (r2_hidden(A,a_0_0_lattice3) <-> (exists B (A = f1_s1_lattice3 & p1_s1_lattice3(B) & m1_subset_1(B,f2_s1_lattice3))))) # label(fraenkel_a_0_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4325 (all A all B (l3_lattices(B) & v3_lattices(B) -> (k1_lattice3(A) = B <-> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> k4_subset_1(A,C,D) = k1_binop_1(u2_lattices(B),C,D) & k1_binop_1(u1_lattices(B),C,D) = k5_subset_1(A,C,D))))) & u1_struct_0(B) = k1_zfmisc_1(A)))) # label(d1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4326 (all A all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_lattice3(B))) -> (r1_lattice3(k3_lattice3(B),A,C) <-> r3_lattice3(B,k5_lattice3(B,C),A)))))) # label(t29_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4327 (all A all B (m1_subset_1(B,u1_struct_0(k1_lattice3(A))) -> (all C (m1_subset_1(C,u1_struct_0(k1_lattice3(A))) -> k3_xboole_0(B,C) = k2_lattices(k1_lattice3(A),B,C) & k2_xboole_0(B,C) = k1_lattices(k1_lattice3(A),B,C))))) # label(t1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4328 (all A all B all C all D (-v3_struct_0(C) & v5_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & v4_lattice3(C) & v10_lattices(C) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & r2_hidden(E,B) & A = k4_lattices(C,D,E))) <-> r2_hidden(A,a_3_7_lattice3(B,C,D))))) # label(fraenkel_a_3_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4329 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k15_lattice3(A,a_2_3_lattice3(A,B)) & k16_lattice3(A,a_2_4_lattice3(A,B)) = B)))) # label(t45_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4330 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v4_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)))) # label(fc5_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4331 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) & v3_orders_2(A) -> -v3_struct_0(k14_lattice3(A)) & v3_lattices(k14_lattice3(A)) & v5_lattices(k14_lattice3(A)) & v8_lattices(k14_lattice3(A)) & v9_lattices(k14_lattice3(A)) & v4_lattice3(k14_lattice3(A)) & v10_lattices(k14_lattice3(A)) & v7_lattices(k14_lattice3(A)) & v6_lattices(k14_lattice3(A)) & v4_lattices(k14_lattice3(A)))) # label(fc7_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4332 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> k12_lattice3(A,C,B) = k12_lattice3(A,B,C))) # label(commutativity_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4333 (all A all B (v4_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v1_relat_2(B) -> v1_relat_2(k6_lattice3(A,B)) & v4_relat_2(k6_lattice3(A,B)) & m2_relset_1(k6_lattice3(A,B),A,A) & v1_partfun1(k6_lattice3(A,B),A,A) & v8_relat_2(k6_lattice3(A,B)))) # label(dt_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4334 (all A v5_lattice3(k1_lattice3(A))) # label(t26_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4335 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_hidden(B,C) -> r3_lattices(A,k16_lattice3(A,C),B) & r3_lattices(A,B,k15_lattice3(A,C)))))))) # label(t38_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4336 (all A all B all C (v4_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v2_lattice3(A) -> k11_lattice3(A,B,C) = k12_lattice3(A,B,C))) # label(redefinition_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4337 (all A all B all C (v2_lattice3(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v4_orders_2(A) -> m1_subset_1(k12_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4338 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (exists B (-v3_struct_0(B) & v3_lattices(B) & l3_lattices(B) & k3_lattice3(B) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) & v10_lattices(B))))) # label(t19_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4339 (all A all B all C all D (v6_lattice3(C) & l3_lattices(C) & m1_subset_1(D,u1_struct_0(C)) & v4_lattice3(C) & v10_lattices(C) & -v3_struct_0(C) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & r2_hidden(E,B) & A = k3_lattices(C,D,E))) <-> r2_hidden(A,a_3_9_lattice3(B,C,D))))) # label(fraenkel_a_3_9_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4340 (all A (v2_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> C = k13_lattice3(A,k12_lattice3(A,B,C),C))))))) # label(t17_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4341 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_4_lattice3(B,C)) <-> (exists D (r3_lattices(B,C,D) & D = A & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4342 (all A (l1_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,C,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,B,D))))))) <-> v1_lattice3(A)))) # label(d10_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4343 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B k16_lattice3(A,B) = k15_lattice3(A,a_2_1_lattice3(A,B))))) # label(d22_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4344 (all A (k6_lattices(k1_lattice3(A)) = A & v14_lattices(k1_lattice3(A)))) # label(t4_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4345 (all A all B all C all D (v4_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & v6_lattice3(C) & v10_lattices(C) & -v3_struct_0(C) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & k3_lattices(C,E,D) = A & r2_hidden(E,B))) <-> r2_hidden(A,a_3_10_lattice3(B,C,D))))) # label(fraenkel_a_3_10_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4346 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r1_orders_2(A,D,C))))))))) # label(d9_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4347 (all A all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r2_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) <-> r4_lattice3(B,C,A)))))) # label(t30_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4348 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> -(r3_lattices(A,D,E) & r2_hidden(E,C)))) & r2_hidden(D,B)))) -> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)))))) # label(t48_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4349 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r4_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,D,B)))))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4350 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> v10_lattices(A) & k6_lattices(A) = k15_lattice3(A,u1_struct_0(A)) & l3_lattices(A) & v14_lattices(A) & -v3_struct_0(A))) # label(t51_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4351 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)))) # label(t11_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4352 (all A (k1_xboole_0 = k5_lattices(k1_lattice3(A)) & v13_lattices(k1_lattice3(A)))) # label(t3_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4353 (all A (v3_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4354 (all A all B (v1_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v4_relat_2(B) -> B = k6_lattice3(A,k6_lattice3(A,B)))) # label(involutiveness_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4355 (all A (l1_orders_2(A) -> (v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (v3_lattices(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) <-> B = k14_lattice3(A))))))) # label(d15_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4356 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,B,D)))))))))) # label(d16_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4357 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattice3(A,B,k2_struct_0(A,C,D)) <-> r3_lattices(A,B,k4_lattices(A,C,D))))))))))) # label(t21_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4358 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) -> (r2_hidden(A,a_3_4_lattice3(B,C,D)) <-> (exists E (r2_hidden(E,D) & A = k3_lattices(B,C,E) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4359 (all A all B all C (v4_lattice3(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists D (r4_lattice3(B,D,C) & A = D & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_2_lattice3(B,C))))) # label(fraenkel_a_2_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4360 (all A all B (m1_subset_1(B,u1_struct_0(k7_lattice3(A))) & l1_orders_2(A) -> m1_subset_1(k9_lattice3(A,B),u1_struct_0(A)))) # label(dt_k9_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4361 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> -v3_struct_0(A) & l3_lattices(A) & k5_lattices(A) = k15_lattice3(A,k1_xboole_0) & v13_lattices(A) & v10_lattices(A))) # label(t50_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4362 (all A (l1_orders_2(A) -> (v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (r1_orders_2(A,D,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) & m1_subset_1(D,u1_struct_0(A)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k11_lattice3(A,B,C) = D <-> r1_orders_2(A,D,B) & r1_orders_2(A,D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D))))))))))))))) # label(d14_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4363 (all A all B all C all D (v10_lattices(C) & v4_lattice3(C) & v5_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & -v3_struct_0(C) -> ((exists E (r2_hidden(E,B) & A = k4_lattices(C,E,D) & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_8_lattice3(B,C,D))))) # label(fraenkel_a_3_8_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4364 (all A (l1_orders_2(A) -> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k7_lattice3(k7_lattice3(A)))) # label(t8_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4365 (all A all B all C all D (v10_lattices(B) & v4_lattice3(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_6_lattice3(B,C,D)) <-> (exists E (r3_lattices(B,k4_lattices(B,C,E),D) & A = E & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4366 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & v10_lattices(A) -> m1_subset_1(k4_lattice3(A,B),u1_struct_0(k3_lattice3(A))))) # label(dt_k4_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4367 (all A all B all C (v4_orders_2(A) & v1_lattice3(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> k13_lattice3(A,C,B) = k13_lattice3(A,B,C))) # label(commutativity_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4368 (all A all B (v1_relat_2(B) & v4_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) -> k4_relat_1(B) = k6_lattice3(A,B))) # label(redefinition_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4369 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> v5_lattice3(A)))) # label(t53_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4370 r1_tarski(f2_s2_lattice3,k1_relat_1(f4_s2_lattice3)) -> k9_relat_1(f4_s2_lattice3,a_0_1_lattice3) = a_0_2_lattice3 # label(s2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4371 (all A (v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k12_lattice3(A,B,k13_lattice3(A,B,C)))))))) # label(t18_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4372 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & D = A & r3_lattices(B,D,C))) <-> r2_hidden(A,a_2_3_lattice3(B,C))))) # label(fraenkel_a_2_3_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4373 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k15_lattice3(A,k1_struct_0(A,B)) & B = k16_lattice3(A,k1_struct_0(A,B)))))) # label(t43_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4374 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v5_lattice3(A) <-> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r4_lattice3(A,C,B) & r4_lattice3(A,E,a_3_0_lattice3(A,B,D)) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r4_lattice3(A,F,a_3_0_lattice3(A,B,D)) -> r1_lattices(A,E,F)))) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r4_lattice3(A,F,B) -> r1_lattices(A,C,F)))) -> r1_lattices(A,k2_lattices(A,D,C),E))))))))))) # label(d19_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4375 (all A (v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v3_orders_2(A) -> k10_lattice3(A,B,k10_lattice3(A,C,D)) = k10_lattice3(A,k10_lattice3(A,B,C),D)))))))))) # label(t14_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4376 (all A all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) <-> r3_lattice3(B,C,A)))))) # label(t28_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4377 (all A all B all C (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k11_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k11_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4378 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v1_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4379 (all A all B all C all D (m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & -v3_struct_0(B) -> ((exists E (k1_lattices(B,D,E) = A & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_1_lattice3(B,C,D))))) # label(fraenkel_a_3_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4380 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (k15_lattice3(A,B) = k15_lattice3(A,a_2_5_lattice3(A,B)) & k16_lattice3(A,a_2_6_lattice3(A,B)) = k16_lattice3(A,B))))) # label(t47_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4381 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k3_lattices(A,C,D),B) <-> r4_lattice3(A,B,k2_struct_0(A,C,D))))))))))) # label(t22_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4382 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> ((all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_lattice3(A,F,B) -> r1_lattices(A,F,C)))) & r3_lattice3(A,E,a_3_1_lattice3(A,B,D)) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_lattice3(A,F,a_3_1_lattice3(A,B,D)) -> r1_lattices(A,F,E)))) & r3_lattice3(A,C,B) -> r1_lattices(A,E,k1_lattices(A,D,C))))))))) <-> v6_lattice3(A)))) # label(d20_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4383 (all A all B all C all D (-v3_struct_0(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & v10_lattices(B) -> (r2_hidden(A,a_3_5_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & k3_lattices(B,D,E) = A))))) # label(fraenkel_a_3_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4384 (all A (l1_orders_2(A) -> (v1_lattice3(A) -> -v3_struct_0(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4385 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> k9_filter_1(A) = k2_lattice3(A))) # label(redefinition_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4386 (exists A (-v3_struct_0(A) & v4_orders_2(A) & v1_lattice3(A) & v3_lattice3(A) & v2_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) & v1_orders_2(A) & l1_orders_2(A))) # label(rc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4387 (all A (l1_orders_2(A) -> (v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (m1_subset_1(D,u1_struct_0(A)) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,C,E) & r1_orders_2(A,B,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) & r1_orders_2(A,B,D))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) <-> D = k10_lattice3(A,B,C)))))))))))) # label(d13_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4388 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C r3_lattices(A,k3_lattices(A,B,k16_lattice3(A,C)),k16_lattice3(A,a_3_4_lattice3(A,B,C)))))))) # label(t35_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4389 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_hidden(B,C) & r3_lattice3(A,B,C) -> B = k16_lattice3(A,C))))))) # label(t42_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4390 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r4_lattice3(A,B,C) & r2_hidden(B,C) -> k15_lattice3(A,C) = B)))))) # label(t41_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4391 (all A (l1_orders_2(A) -> v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)))) # label(dt_k7_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4392 (all A all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_lattice3(B))) -> (r2_lattice3(k3_lattice3(B),A,C) <-> r4_lattice3(B,k5_lattice3(B,C),A)))))) # label(t31_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4393 (all A all B (l3_lattices(B) & v17_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r4_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) <-> r3_lattice3(B,C,A)))))) # label(t24_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4394 (all A all B all C all D (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & v4_lattice3(B) -> (r2_hidden(A,a_3_2_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & A = k4_lattices(B,C,E) & r2_hidden(E,D)))))) # label(fraenkel_a_3_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4395 (all A v6_lattice3(k1_lattice3(A))) # label(t27_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4396 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice3(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r1_orders_2(A,C,D))))))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4397 (all A (l1_orders_2(A) -> (v2_lattice3(k7_lattice3(A)) <-> v1_lattice3(A)))) # label(t10_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4398 (all A (l1_orders_2(A) -> k7_lattice3(A) = g1_orders_2(u1_struct_0(A),k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))))) # label(d5_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4399 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattice3(A,B))))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4400 (all A all B (v4_lattice3(B) & v6_lattice3(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_lattices(B,k16_lattice3(B,A),C) = k16_lattice3(B,a_3_10_lattice3(A,B,C)) & k16_lattice3(B,a_3_9_lattice3(A,B,C)) = k3_lattices(B,C,k16_lattice3(B,A)))))) # label(t55_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.83 4401 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (v3_orders_2(A) -> k11_lattice3(A,B,k11_lattice3(A,C,D)) = k11_lattice3(A,k11_lattice3(A,B,C),D)))))))))) # label(t16_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4402 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) & -v3_struct_0(A) -> k4_filter_0(A,B,C) = k15_lattice3(A,a_3_6_lattice3(A,B,C))))))))) # label(t52_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4403 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4404 (all A all B all C (v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v4_orders_2(A) -> m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4405 (all A all B all C (l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists D (A = k15_lattice3(B,D) & r2_hidden(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_2_7_lattice3(B,C))))) # label(fraenkel_a_2_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4406 (all A (-v3_struct_0(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v12_lattices(k1_lattice3(A)) & v16_lattices(k1_lattice3(A)) & v17_lattices(k1_lattice3(A)) & v15_lattices(k1_lattice3(A)) & v14_lattices(k1_lattice3(A)) & v13_lattices(k1_lattice3(A)) & v11_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)))) # label(fc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4407 (all A (l1_orders_2(A) -> -v3_struct_0(k14_lattice3(A)) & v3_lattices(k14_lattice3(A)) & v10_lattices(k14_lattice3(A)) & l3_lattices(k14_lattice3(A)))) # label(dt_k14_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4408 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B all C (r1_tarski(B,C) -> r3_lattices(A,k16_lattice3(A,C),k16_lattice3(A,B)) & r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)))))) # label(t46_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4409 (all A all B (v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r3_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B)) <-> r4_lattice3(B,C,A)))))) # label(t23_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4410 (all A all B all C (v17_lattices(C) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> ((exists D (m1_subset_1(D,u1_struct_0(C)) & r2_hidden(D,B) & k7_lattices(C,D) = A)) <-> r2_hidden(A,a_2_0_lattice3(B,C))))) # label(fraenkel_a_2_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4411 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattice3(A,D,C) -> r3_lattices(A,D,B)))) <-> B = k16_lattice3(A,C))))))) # label(t34_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4412 (all A (v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k11_lattice3(A,C,B) = k11_lattice3(A,B,C))))))) # label(t15_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4413 (all A (l1_orders_2(A) -> (v3_lattice3(A) <-> (all B exists C (m1_subset_1(C,u1_struct_0(A)) & r2_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D))))))))) # label(d12_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4414 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C)) <-> r3_lattices(A,B,C)))))))) # label(t7_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4415 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) -> m1_subset_1(k8_lattice3(A,B),u1_struct_0(k7_lattice3(A))))) # label(dt_k8_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4416 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> v1_relat_2(k2_lattice3(A)) & v4_relat_2(k2_lattice3(A)) & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k2_lattice3(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4417 (all A (l1_orders_2(A) -> (v2_lattice3(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,C) & r1_orders_2(A,E,B) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,B)))))))))) # label(d11_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4418 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r3_lattice3(A,B,C) -> r3_lattices(A,B,k16_lattice3(A,C)))))))) # label(t40_lattice3) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4419 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k2_lattice4(A,k5_setwiseo(u1_struct_0(A),B,C)) = k4_lattices(A,k2_lattice4(A,B),k2_lattice4(A,C)))))))) # label(t30_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4420 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (k2_relat_1(C) = u1_struct_0(B) <-> v2_lattice4(C,A,B)))))))) # label(d3_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4421 (all A all B (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v10_lattices(A) -> (all C (m1_lattice4(C,A,B) -> v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)))))) # label(dt_m1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4422 (all A (-v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A)) -> k3_lattices(A,k2_lattice2(u1_struct_0(A),A,B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) = k2_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C)),D))))))))) # label(t20_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4423 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k1_lattice4(A,B) = k7_setwiseo(u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,k7_grcat_1(A)))))) # label(t15_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4424 (all A (v10_lattices(A) & v16_lattices(A) & l3_lattices(A) & v15_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v17_lattices(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> v17_lattices(A) & r4_lattice4(B,A,C)))))))) # label(t38_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4425 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (m2_lattice4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k3_lattices(A,C,D),B) & r2_hidden(k4_lattices(A,C,D),B))))))))))) # label(d10_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4426 (all A (-v3_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & v14_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,k2_lattice4(A,B),C) = k2_lattice4(A,k8_setwiseo(u1_struct_0(A),u1_struct_0(A),k7_funcop_1(u1_struct_0(A),u1_struct_0(A),u2_lattices(A),k7_grcat_1(A),C),B)))))))) # label(t32_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4427 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m3_lattice4(D,A) -> (r2_hidden(C,D) & r2_hidden(B,D) -> r2_hidden(k4_filter_0(A,B,C),D)))))))))) # label(t40_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4428 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (m3_lattice4(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_lattices(A,C,D),B) & r2_hidden(k7_lattices(A,C),B))))))))))) # label(d14_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4429 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,A,B) -> (r2_lattice4(A,B,C) <-> k6_lattices(B) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k6_lattices(A))))))))) # label(d7_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4430 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (exists B m2_lattice4(B,A)))) # label(existence_m2_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4431 (all A (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(D) -> k3_lattice2(u1_struct_0(A),A,B,k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,D)) = k3_lattice2(u1_struct_0(A),A,k8_setwiseo(u1_struct_0(A),u1_struct_0(A),C,B),D))))))))) # label(t29_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4432 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m3_lattice4(B,A) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B))))) # label(dt_m3_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4433 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k7_lattices(A,k1_lattice4(A,B)) = k3_lattice2(u1_struct_0(A),A,B,k5_lattice4(A)))))) # label(t46_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4434 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k2_lattice4(A,B) = k3_lattice2(u1_struct_0(A),A,B,k7_grcat_1(A)))))) # label(d13_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4435 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v2_filter_0(k1_filter_0(A),A))) # label(t4_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4436 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m3_lattice4(C,A) -> (k3_lattice4(A,B) = C <-> r1_tarski(B,C) & (all D (m3_lattice4(D,A) -> (r1_tarski(B,D) -> r1_tarski(C,D))))))))))) # label(d15_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4437 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & v13_lattices(B) & l3_lattices(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> r3_lattice4(B,A,C) & v13_lattices(A)))))))) # label(t19_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4438 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> m2_lattice4(B,A))))) # label(t11_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4439 (all A (v10_lattices(A) & l3_lattices(A) & v13_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattice4(A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C))) = k3_lattices(A,k1_lattice4(A,B),C))))))) # label(t21_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4440 (all A (-v3_struct_0(A) & l3_lattices(A) & v16_lattices(A) & v15_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v3_filter_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_lattice4(C,B,A) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> r3_lattices(A,k4_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k4_filter_0(B,D,E))),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)))))))))))) # label(t33_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4441 (all A (-v3_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,k2_lattice4(A,B),C) = k2_lattice4(A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C))))))))) # label(t28_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4442 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m3_lattice4(D,A) -> (r2_hidden(C,D) & r2_hidden(B,D) -> r2_hidden(k3_lattices(A,B,C),D)))))))))) # label(t39_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4443 $T # label(t12_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4444 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> m2_lattice4(u1_struct_0(A),A))) # label(t10_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4445 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m3_lattice4(B,A) -> m2_lattice4(B,A))))) # label(t42_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4446 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v1_funct_1(k5_lattice4(A)) & m2_relset_1(k5_lattice4(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k5_lattice4(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k5_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4447 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m1_lattice4(C,A,B) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k7_lattices(A,D)) = k7_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)))) <-> r4_lattice4(A,B,C)))))))) # label(d9_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4448 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,A,B) -> (v3_lattice4(C,A,B) <-> v2_lattice4(C,A,B) & v1_lattice4(C,A,B)))))))) # label(d4_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4449 (all A all B (v17_lattices(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(A,k4_lattice4(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & (exists E (r2_hidden(E,C) & r2_hidden(D,C) & A = k4_filter_0(B,D,E) & m1_subset_1(E,u1_struct_0(B))))))))))) # label(t43_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4450 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_lattice4(A,k2_setwiseo(u1_struct_0(A),B)))))) # label(t16_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4451 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> k7_lattices(A,k6_lattices(A)) = k5_lattices(A))) # label(t36_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4452 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) & l3_lattices(A) & v10_lattices(A) -> m1_subset_1(k1_lattice4(A,B),u1_struct_0(A)))) # label(dt_k1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4453 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (l3_lattices(B) & v14_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> r2_lattice4(B,A,C) & v14_lattices(A)))))))) # label(t25_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4454 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_lattice4(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (exists E (D = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) & m1_subset_1(E,u1_struct_0(A))))))))))))) # label(t9_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4455 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k2_lattice2(u1_struct_0(A),A,B,k7_grcat_1(A)) = k1_lattice4(A,B))))) # label(d12_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4456 $T # label(t13_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4457 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k1_lattice4(A,k5_setwiseo(u1_struct_0(A),B,C)) = k3_lattices(A,k1_lattice4(A,B),k1_lattice4(A,C)))))))) # label(t22_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4458 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v13_lattices(A) -> (all B (m2_lattice4(B,A) -> (r2_hidden(k5_lattices(A),B) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> r2_hidden(k1_lattice4(A,C),B))))))))) # label(t24_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4459 $T # label(d11_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4460 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_lattice4(A,k2_setwiseo(u1_struct_0(A),B)) = B)))) # label(t17_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4461 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,A,B) -> (r3_lattice4(A,B,C) <-> k5_lattices(B) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k5_lattices(A))))))))) # label(d8_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4462 (all A all B all C (v10_lattices(B) & m2_lattice4(C,B) & -v1_xboole_0(C) & l3_lattices(B) & v17_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_1_lattice4(B,C)) <-> (exists D (A = k2_lattice4(B,D) & r1_tarski(D,k4_lattice4(B,C)) & m1_subset_1(D,k5_finsub_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4463 (all A (-v3_struct_0(A) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D ((exists E (m1_subset_1(E,u1_struct_0(A)) & r2_hidden(E,B) & r2_hidden(D,B) & C = k3_lattices(A,k7_lattices(A,D),E))) & m1_subset_1(D,u1_struct_0(A)))) <-> r2_hidden(C,k4_lattice4(A,B))))))))) # label(t44_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4464 (all A (v10_lattices(A) & v16_lattices(A) & l3_lattices(A) & v15_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v3_filter_0(B) -> (all C (m1_lattice4(C,B,A) -> (v3_lattice4(C,B,A) -> v3_filter_0(A) & r1_lattice4(B,A,C)))))))) # label(t35_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4465 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> m1_subset_1(k2_lattice4(A,B),u1_struct_0(A)))) # label(dt_k2_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4466 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k7_lattices(A,k2_lattice4(A,B)) = k2_lattice2(u1_struct_0(A),A,B,k5_lattice4(A)))))) # label(t48_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4467 (all A (v13_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k5_lattices(A) = k1_lattice4(A,k1_setwiseo(u1_struct_0(A))))) # label(t23_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4468 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (B = k5_lattice4(A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k7_lattices(A,C)))))))) # label(d17_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4469 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> (r2_hidden(k6_lattices(A),B) & r2_hidden(k5_lattices(A),B) -> a_2_1_lattice4(A,B) = k3_lattice4(A,B)))))) # label(t50_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4470 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (exists B (-v1_xboole_0(B) & m2_lattice4(B,A))))) # label(rc1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4471 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k3_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),C,k2_setwiseo(u1_struct_0(A),B)),k5_lattice4(A)) = k4_lattices(A,k3_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)),k7_lattices(A,B)))))))) # label(t47_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4472 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & v17_lattices(B) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l3_lattices(B) -> (r2_hidden(A,a_2_0_lattice4(B,C)) <-> (exists D exists E (m1_subset_1(E,u1_struct_0(B)) & A = k4_filter_0(B,D,E) & r2_hidden(E,C) & r2_hidden(D,C) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4473 (all A (l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> k2_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),C,k2_setwiseo(u1_struct_0(A),B)),k5_lattice4(A)) = k3_lattices(A,k2_lattice2(u1_struct_0(A),A,C,k5_lattice4(A)),k7_lattices(A,B)))))))) # label(t45_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4474 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> k6_lattices(A) = k7_lattices(A,k5_lattices(A)))) # label(t37_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4475 (all A (l3_lattices(A) & v14_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A)) -> k3_lattice2(u1_struct_0(A),A,k5_setwiseo(u1_struct_0(A),B,k2_setwiseo(u1_struct_0(A),C)),D) = k4_lattices(A,k3_lattice2(u1_struct_0(A),A,B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)))))))))) # label(t27_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4476 (all A (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m2_lattice4(B,A) -> (r2_hidden(k5_lattices(A),B) & r2_hidden(k6_lattices(A),B) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> -(r1_tarski(C,k4_lattice4(A,B)) & (all D (m1_subset_1(D,k5_finsub_1(u1_struct_0(A))) -> -(r1_tarski(D,k4_lattice4(A,B)) & k2_lattice4(A,D) = k2_lattice2(u1_struct_0(A),A,C,k5_lattice4(A))))))))))))) # label(t49_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4477 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (m1_lattice4(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_lattices(A,D,E)) & k3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k3_lattices(A,D,E))))))))))))) # label(d1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4478 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l3_lattices(A) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m3_lattice4(k3_lattice4(A,B),A))) # label(dt_k3_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4479 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_lattice4(E,A,B) -> (r3_lattices(A,C,D) -> r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D))))))))))))) # label(t7_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4480 $T # label(t1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4481 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_funct_1(C) <-> v1_lattice4(C,A,B)))))))) # label(d2_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4482 (all A all B (-v3_struct_0(A) & v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v10_lattices(A) -> (exists C m1_lattice4(C,A,B)))) # label(existence_m1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4483 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k2_filter_0(A,D),B))) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r2_hidden(E,B) & r3_lattices(A,k4_lattices(A,D,E),C))))))))))))) # label(t6_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4484 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,A,B) -> (r1_lattice4(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k4_filter_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_filter_0(A,D,E))))))))))))) # label(d6_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4485 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(A) -> m3_lattice4(u1_struct_0(A),A))) # label(t41_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4486 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_lattice4(E,A,B) -> (v1_lattice4(E,A,B) -> (r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(B),E,D)) <-> r3_lattices(A,C,D))))))))))))) # label(t8_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4487 (all A all B (-v3_struct_0(A) & v17_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l3_lattices(A) & v10_lattices(A) -> m1_subset_1(k4_lattice4(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4488 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & v11_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (m1_lattice4(C,B,A) -> (v2_lattice4(C,B,A) -> v11_lattices(A)))))))) # label(t18_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4489 (all A (v10_lattices(A) & l3_lattices(A) & v14_lattices(A) & -v3_struct_0(A) -> (all B (m2_lattice4(B,A) -> (r2_hidden(k6_lattices(A),B) -> (all C (m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) -> (r1_tarski(C,B) -> r2_hidden(k2_lattice4(A,C),B))))))))) # label(t31_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4490 (all A all B (l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v17_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v1_xboole_0(k4_lattice4(A,B)))) # label(fc1_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4491 (all A -(A != k1_xboole_0 & (all B -(k1_xboole_0 != B & r1_tarski(B,A) & (all C -(r2_hidden(C,A) & (all D (r2_hidden(D,B) -> r1_tarski(D,C))))) & v6_ordinal1(B))) & (all B -(r2_hidden(B,A) & (all C -(C != B & r1_tarski(B,C) & r2_hidden(C,A))))))) # label(t3_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4492 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_lattice4(A,B) = a_2_0_lattice4(A,B))))) # label(d16_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4493 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) -> k7_setwiseo(u1_struct_0(A),u1_struct_0(A),u1_lattices(A),B,k7_grcat_1(A)) = k2_lattice4(A,B))))) # label(t14_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4494 $T # label(t2_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4495 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (r1_filter_1(A,B) <-> (exists C (v3_lattice4(C,A,B) & m1_lattice4(C,A,B)))))))) # label(d5_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4496 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m2_lattice4(B,A) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4497 (all A (v16_lattices(A) & l3_lattices(A) & v15_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v3_filter_0(B) -> (all C (m1_lattice4(C,B,A) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r3_lattices(A,k4_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F)) & v1_lattice4(C,B,A) -> r3_lattices(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k4_filter_0(B,D,F)))))))))))))))) # label(t34_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4498 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v14_lattices(A) -> k6_lattices(A) = k2_lattice4(A,k1_setwiseo(u1_struct_0(A))))) # label(t26_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4499 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (exists B m3_lattice4(B,A)))) # label(existence_m3_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4500 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (m1_filter_0(C,A) -> r1_tarski(C,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) & r1_tarski(B,k3_filter_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),B,C))))))))) # label(t5_lattice4) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4501 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v9_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) -> v1_funct_2(k4_vectsp_8(A,B),k2_vectsp_8(A,B),k1_zfmisc_1(u1_struct_0(B))) & m2_relset_1(k4_vectsp_8(A,B),k2_vectsp_8(A,B),k1_zfmisc_1(u1_struct_0(B))) & v1_funct_1(k4_vectsp_8(A,B)))) # label(dt_k4_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4502 (all A all B (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(A) -> (exists C m3_vectsp_8(C,A,B)))) # label(existence_m3_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4503 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m2_relset_1(C,k2_vectsp_8(A,B),k1_zfmisc_1(u1_struct_0(B))) & v1_funct_2(C,k2_vectsp_8(A,B),k1_zfmisc_1(u1_struct_0(B))) & v1_funct_1(C) -> (C = k4_vectsp_8(A,B) <-> (all D (m2_vectsp_8(D,A,B,k2_vectsp_8(A,B)) -> (all E (m1_vectsp_4(E,A,B) -> (E = D -> k8_funct_2(k2_vectsp_8(A,B),k1_zfmisc_1(u1_struct_0(B)),C,D) = u1_struct_0(E))))))))))))) # label(d4_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4504 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v11_vectsp_1(C,A) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v6_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) & v3_rlvect_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k1_vectsp_8(A,B)),u1_struct_0(k1_vectsp_8(A,C))) & m2_relset_1(E,u1_struct_0(k1_vectsp_8(A,B)),u1_struct_0(k1_vectsp_8(A,C))) -> ((all F (m1_vectsp_4(F,A,B) & v11_vectsp_1(F,A) -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C))) -> (k2_funct_2(u1_struct_0(B),u1_struct_0(C),D,u1_struct_0(F)) = G -> k1_funct_1(E,F) = k1_vectsp_7(A,C,G)))))) <-> k6_vectsp_8(A,B,C,D) = E))))))))))) # label(d7_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4505 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v4_rlvect_1(C) & v6_rlvect_1(C) & v11_vectsp_1(C,A) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v5_rlvect_1(C) & v3_rlvect_1(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) -> (v1_mod_2(D,A,B,C) & v2_funct_1(D) -> m1_lattice4(k6_vectsp_8(A,B,C,D),k1_vectsp_8(A,B),k1_vectsp_8(A,C))))))))))) # label(t13_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4506 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> u2_lattices(k1_vectsp_8(A,B)) = k5_vectsp_5(A,B))))) # label(t5_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4507 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B all C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v11_vectsp_1(C,A) & v6_rlvect_1(C) & v3_rlvect_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> (r1_rlvect_1(k1_vectsp_7(A,C,D),B) & v1_vectsp_4(D,A,C) -> v1_xboole_0(D) | r2_hidden(B,D)))))))) # label(t10_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4508 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattice3(A,D,B) -> r1_lattices(A,D,C)))) & r3_lattice3(A,C,B) & m1_subset_1(C,u1_struct_0(A)))))) <-> v4_lattice3(A)))) # label(d6_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4509 (all A (v8_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_8(A,B))) -> (all D (m1_subset_1(D,u1_struct_0(k1_vectsp_8(A,B))) -> (all E (m1_vectsp_4(E,A,B) -> (all F (m1_vectsp_4(F,A,B) -> (F = D & C = E -> k3_lattices(k1_vectsp_8(A,B),C,D) = k1_vectsp_5(A,B,E,F)))))))))))))) # label(t7_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4510 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) -> v4_lattice3(k1_vectsp_8(A,B)))))) # label(t9_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4511 (all A all B all C (v7_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & -v1_xboole_0(C) & m1_vectsp_8(C,A,B) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all D (m2_vectsp_8(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m2_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4512 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k2_vectsp_8(A,B))) & -v1_xboole_0(C) -> -v1_xboole_0(k2_funct_2(k2_vectsp_8(A,B),k1_zfmisc_1(u1_struct_0(B)),k4_vectsp_8(A,B),C)))))))) # label(t1_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.84 4513 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k2_vectsp_8(A,B))) & -v1_xboole_0(C) -> (all D (v11_vectsp_1(D,A) & m1_vectsp_4(D,A,B) -> (u1_struct_0(D) = k6_setfam_1(u1_struct_0(B),k2_funct_2(k2_vectsp_8(A,B),k1_zfmisc_1(u1_struct_0(B)),k4_vectsp_8(A,B),C)) <-> k5_vectsp_8(A,B,C) = D))))))))) # label(d5_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4514 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (m4_vectsp_8(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k3_lattices(A,D,E)) = k3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))))))))))))) # label(d9_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4515 (all A (v3_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_8(A,B))) -> (all D (m1_subset_1(D,u1_struct_0(k1_vectsp_8(A,B))) -> (all E (m1_vectsp_4(E,A,B) -> (all F (m1_vectsp_4(F,A,B) -> (D = F & E = C -> k2_vectsp_5(A,B,E,F) = k4_lattices(k1_vectsp_8(A,B),C,D)))))))))))))) # label(t8_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4516 (all A all B (v3_rlvect_1(A) & v4_rlvect_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (exists C m1_vectsp_8(C,A,B)))) # label(existence_m1_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4517 (all A all B (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) & v10_lattices(A) -> (exists C m4_vectsp_8(C,A,B)))) # label(existence_m4_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4518 (all A (v3_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> k1_vectsp_8(A,B) = g3_lattices(k3_vectsp_5(A,B),k5_vectsp_5(A,B),k6_vectsp_5(A,B)))))) # label(d1_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4519 (all A all B all C all D (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l4_vectsp_1(B,A) & v3_rlvect_1(C) & v6_rlvect_1(C) & v11_vectsp_1(C,A) & l4_vectsp_1(C,A) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & m1_relset_1(D,u1_struct_0(B),u1_struct_0(C)) & v1_funct_1(D) & v12_vectsp_1(C,A) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_group_1(A) & v4_rlvect_1(A) -> m2_relset_1(k6_vectsp_8(A,B,C,D),u1_struct_0(k1_vectsp_8(A,B)),u1_struct_0(k1_vectsp_8(A,C))) & v1_funct_2(k6_vectsp_8(A,B,C,D),u1_struct_0(k1_vectsp_8(A,B)),u1_struct_0(k1_vectsp_8(A,C))) & v1_funct_1(k6_vectsp_8(A,B,C,D)))) # label(dt_k6_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4520 (all A all B all C (v3_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & -v10_vectsp_1(A) & -v3_struct_0(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & m1_vectsp_8(C,A,B) & -v1_xboole_0(C) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v9_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists D m2_vectsp_8(D,A,B,C)))) # label(existence_m2_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4521 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (m3_vectsp_8(C,A,B) & m4_vectsp_8(C,A,B) <-> m1_lattice4(C,A,B)))))))) # label(t11_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4522 (all A all B all C (-v3_struct_0(A) & v5_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & v3_rlvect_1(B) & v5_rlvect_1(B) & l4_vectsp_1(B,A) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_vectsp_8(A,B))) & v12_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> v11_vectsp_1(k5_vectsp_8(A,B,C),A) & m1_vectsp_4(k5_vectsp_8(A,B,C),A,B))) # label(dt_k5_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4523 $T # label(dt_m1_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4524 (all A all B all C (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & -v10_vectsp_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & -v1_xboole_0(C) & m1_vectsp_8(C,A,B) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all D (m2_vectsp_8(D,A,B,C) -> m1_vectsp_4(D,A,B))))) # label(dt_m2_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4525 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_lattices(A,D,E)) = k4_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))))) <-> m3_vectsp_8(C,A,B)))))))) # label(d8_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4526 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v11_vectsp_1(B,A) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> k2_vectsp_8(A,B) = k3_vectsp_5(A,B))) # label(redefinition_k2_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4527 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v3_rlvect_1(C) & v6_rlvect_1(C) & v11_vectsp_1(C,A) & v12_vectsp_1(C,A) & l4_vectsp_1(C,A) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) -> (v1_mod_2(D,A,B,C) -> m4_vectsp_8(k6_vectsp_8(A,B,C,D),k1_vectsp_8(A,B),k1_vectsp_8(A,C))))))))))) # label(t12_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4528 (all A (v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> u1_struct_0(k1_vectsp_8(A,B)) = k2_vectsp_8(A,B))))) # label(t3_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4529 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> u1_lattices(k1_vectsp_8(A,B)) = k6_vectsp_5(A,B))))) # label(t4_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4530 (all A all B (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (exists C (m1_vectsp_8(C,A,B) & -v1_xboole_0(C))))) # label(rc1_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4531 (all A all B all C (v4_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & v3_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & m1_subset_1(C,k2_vectsp_8(A,B)) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_vectsp_8(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k3_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4532 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_group_1(A) & v7_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v11_vectsp_1(C,A) & v5_rlvect_1(C) & v3_rlvect_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) -> (v1_mod_2(D,A,B,C) & v2_funct_1(D) -> v2_funct_1(k6_vectsp_8(A,B,C,D))))))))))) # label(t14_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4533 (all A all B (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_rlvect_1(A) -> m1_vectsp_8(k2_vectsp_8(A,B),A,B) & -v1_xboole_0(k2_vectsp_8(A,B)))) # label(dt_k2_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4534 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v5_rlvect_1(B) & -v3_struct_0(B) -> k6_partfun1(u1_struct_0(k1_vectsp_8(A,B))) = k6_vectsp_8(A,B,B,k6_partfun1(u1_struct_0(B))))))) # label(t15_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4535 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & -v3_struct_0(B) & v3_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) & v4_rlvect_1(B) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> v10_lattices(k1_vectsp_8(A,B)) & v15_lattices(k1_vectsp_8(A,B)) & l3_lattices(k1_vectsp_8(A,B)) & v3_lattices(k1_vectsp_8(A,B)) & -v3_struct_0(k1_vectsp_8(A,B)))) # label(dt_k1_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4536 (all A all B (l3_lattices(A) & v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & v10_lattices(A) & -v3_struct_0(A) -> (all C (m3_vectsp_8(C,A,B) -> v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C))))) # label(dt_m3_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4537 (all A all B (-v3_struct_0(A) & v10_lattices(A) & v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) -> (all C (m4_vectsp_8(C,A,B) -> m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C))))) # label(dt_m4_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4538 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v11_vectsp_1(B,A) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_vectsp_8(C,A,B) <-> (all D (r2_hidden(D,C) -> m1_vectsp_4(D,A,B))))))))) # label(d2_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4539 (all A (v3_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_8(A,B))) -> (all D (m1_subset_1(D,u1_struct_0(k1_vectsp_8(A,B))) -> (all E (m1_vectsp_4(E,A,B) & v11_vectsp_1(E,A) -> (all F (m1_vectsp_4(F,A,B) & v11_vectsp_1(F,A) -> (E = C & F = D -> (r1_tarski(u1_struct_0(E),u1_struct_0(F)) <-> r3_lattices(k1_vectsp_8(A,B),C,D))))))))))))))) # label(t6_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4540 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) -> (all C (m2_vectsp_8(C,A,B,k2_vectsp_8(A,B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = k3_vectsp_8(A,B,C) <-> (exists E (u1_struct_0(E) = D & E = C & m1_vectsp_4(E,A,B)))))))))))) # label(d3_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4541 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v11_vectsp_1(B,A) -> (all C (v11_vectsp_1(C,A) & m1_vectsp_4(C,A,B) -> r2_hidden(k1_rlvect_1(B),k1_funct_1(k4_vectsp_8(A,B),C)))))))) # label(t2_vectsp_8) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4542 (all A (l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (F = D & r1_orders_2(B,E,F) & C = E -> r1_orders_2(A,C,D)))))))))))))) # label(t60_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4543 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k13_lattice3(A,B,C) = k1_yellow_0(A,k2_struct_0(A,B,C)))))))) # label(t41_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4544 (all A (l1_orders_2(A) -> (all B all C (r2_yellow_0(A,B) & r2_yellow_0(A,C) & r1_tarski(B,C) -> r1_orders_2(A,k2_yellow_0(A,C),k2_yellow_0(A,B)))))) # label(t35_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4545 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r1_yellow_0(A,k2_struct_0(B,C,D)) & r2_hidden(k1_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) -> k1_yellow_0(B,k2_struct_0(B,C,D)) = k1_yellow_0(A,k2_struct_0(B,C,D)) & r1_yellow_0(B,k2_struct_0(B,C,D))))))))))) # label(t67_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4546 (all A (l1_orders_2(A) -> k1_yellow_0(A,k1_xboole_0) = k3_yellow_0(A))) # label(d11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4547 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B ((exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D)))) & r2_lattice3(A,B,C) & m1_subset_1(C,u1_struct_0(A)))) <-> r1_yellow_0(A,B))))) # label(t15_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4548 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_lattice3(A,k1_xboole_0,B) & r1_lattice3(A,k1_xboole_0,B))))) # label(t6_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4549 (all A (l1_orders_2(A) -> (all B all C (r1_tarski(B,C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) -> r2_lattice3(A,B,D)) & (r1_lattice3(A,C,D) -> r1_lattice3(A,B,D)))))))) # label(t9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4550 (all A (l1_orders_2(A) -> m1_subset_1(k3_yellow_0(A),u1_struct_0(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4551 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (r1_yellow_0(A,C) -> k1_yellow_0(A,C) = k1_yellow_0(B,C)))))))) # label(t26_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4552 (all A (l1_orders_2(A) -> (all B all C (r1_yellow_0(A,B) & r1_yellow_0(A,C) & r1_tarski(B,C) -> r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)))))) # label(t34_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4553 (all A (v3_orders_2(A) & l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,D,C) & r1_lattice3(A,B,C) -> r1_lattice3(A,B,D)))))))) # label(t12_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4554 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_yellow_0(A,B) -> (C = k1_yellow_0(A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D)))) & r2_lattice3(A,B,C))))))) # label(d9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4555 (all A (l1_orders_2(A) -> (v4_orders_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,C,B) & r1_orders_2(A,B,C) -> C = B)))))))) # label(d3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4556 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) -> k1_yellow_0(B,C) = k1_yellow_0(A,C)))))))) # label(t69_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4557 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattice3(A,B,C) -> r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)) & (r1_lattice3(A,B,C) -> r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)) & (r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) -> r1_lattice3(A,B,C)) & (r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) -> r2_lattice3(A,B,C)))))) # label(t5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4558 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (v3_lattice3(A) & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> v3_lattice3(B)))))) # label(t3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4559 (all A (l1_orders_2(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (C = E & r2_hidden(E,u1_struct_0(B)) & r2_hidden(F,u1_struct_0(B)) & r1_orders_2(A,C,D) & F = D -> r1_orders_2(B,E,F)))))))))))))) # label(t61_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4560 (all A (l1_orders_2(A) -> (exists B (m1_yellow_0(B,A) & v4_yellow_0(B,A) & v1_orders_2(B))))) # label(rc3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4561 (exists A (-v3_struct_0(A) & v1_orders_2(A) & l1_orders_2(A) & u1_struct_0(A) = f1_s1_yellow_0 & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) <-> p1_s1_yellow_0(B,C)))))))) # label(s1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4562 (all A (v2_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) & v5_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (E = C & F = D -> k12_lattice3(A,E,F) = k12_lattice3(B,C,D)))))))))))))) # label(t70_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4563 (all A (l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> (all D ((r1_lattice3(A,D,C) -> r1_lattice3(A,D,B)) & (r2_lattice3(A,D,B) -> r2_lattice3(A,D,C))))))))))) # label(t4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4564 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B all C (r1_yellow_0(A,C) & r1_yellow_0(A,k2_xboole_0(B,C)) & r1_yellow_0(A,B) -> k1_yellow_0(A,k2_xboole_0(B,C)) = k10_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)))))) # label(t36_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4565 (all A (l1_orders_2(A) & v4_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_yellow_0(A,k2_tarski(B,C)))))) <-> v2_lattice3(A)))) # label(t21_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4566 (all A (v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,B,C) = k2_yellow_0(A,k2_struct_0(A,B,C)))))))) # label(t40_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4567 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) | r2_yellow_0(A,B) -> k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))))))) # label(t52_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4568 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B all C (r1_yellow_0(A,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) <-> r2_lattice3(A,C,D)))) -> r1_yellow_0(A,C))))) # label(t46_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4569 (all A (l1_orders_2(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) -> (all C (v4_yellow_0(C,A) & m1_yellow_0(C,A) -> (u1_struct_0(C) = u1_struct_0(B) -> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))))))))) # label(t58_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4570 (all A (l1_orders_2(A) -> (all B (r1_yellow_0(A,B) <-> (exists C (r2_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r1_orders_2(A,C,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_lattice3(A,B,E) -> r1_orders_2(A,D,E)))) -> C = D))) & m1_subset_1(C,u1_struct_0(A)))))))) # label(d7_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4571 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> ((all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) -> r2_yellow_0(A,B))) <-> v2_lattice3(A)))) # label(t55_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4572 (all A (l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (B = k1_yellow_0(A,C) <-> r2_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) -> r1_orders_2(A,B,D)))))))))) # label(t32_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4573 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) -> v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4574 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (E = C & F = D -> (r2_orders_2(A,C,D) -> r2_orders_2(B,E,F)) & (r1_orders_2(A,C,D) -> r1_orders_2(B,E,F)))))))))))))))) # label(t1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4575 (all A (l1_orders_2(A) -> (v2_yellow_0(A) & v1_yellow_0(A) -> v3_yellow_0(A)))) # label(cc5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4576 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) & r2_yellow_0(A,k2_struct_0(A,C,D)) & r2_hidden(C,u1_struct_0(B)) -> r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B))))))) <-> v5_yellow_0(B,A)))))) # label(d16_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4577 (all A (l1_orders_2(A) -> (all B all C all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) & r2_lattice3(A,B,D) -> r2_lattice3(A,k2_xboole_0(B,C),D)) & (r1_lattice3(A,B,D) & r1_lattice3(A,C,D) -> r1_lattice3(A,k2_xboole_0(B,C),D)))))) # label(t10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4578 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (exists B (m1_yellow_0(B,A) & -v3_struct_0(B) & v7_yellow_0(B,A) & v8_yellow_0(B,A) & v6_yellow_0(B,A) & v5_yellow_0(B,A) & v4_yellow_0(B,A) & v1_orders_2(B))))) # label(rc5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4579 (all A all B (m2_relset_1(B,A,A) -> B = k1_toler_1(B,A))) # label(t56_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4580 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) <-> r1_lattice3(A,B,D)))) & r2_yellow_0(A,B) -> k2_yellow_0(A,B) = k2_yellow_0(A,C))))) # label(t49_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4581 (all A all B (m1_relset_1(B,k1_tarski(A),k1_tarski(A)) -> v3_realset2(g1_orders_2(k1_tarski(A),B)) & v1_orders_2(g1_orders_2(k1_tarski(A),B)) & -v3_struct_0(g1_orders_2(k1_tarski(A),B)))) # label(fc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4582 (all A (l1_orders_2(A) -> m1_subset_1(k4_yellow_0(A),u1_struct_0(A)))) # label(dt_k4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4583 (all A (l1_orders_2(A) & v2_yellow_0(A) & v4_orders_2(A) & -v3_struct_0(A) -> r1_yellow_0(A,u1_struct_0(A)) & r2_yellow_0(A,k1_xboole_0))) # label(t43_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4584 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v2_orders_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,B,B)))))) # label(d1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4585 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) <-> r2_lattice3(A,C,D)))) & r1_yellow_0(A,B) -> k1_yellow_0(A,C) = k1_yellow_0(A,B))))) # label(t47_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4586 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k10_lattice3(A,B,C) = D & r1_yellow_0(A,k2_tarski(B,C)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,C,E) & r1_orders_2(A,B,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) & r1_orders_2(A,B,D)) & (r1_orders_2(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,B,E) & r1_orders_2(A,C,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) -> D = k10_lattice3(A,B,C) & r1_yellow_0(A,k2_tarski(B,C))))))))))) # label(t18_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4587 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (m1_yellow_0(B,A) <-> r1_tarski(u1_struct_0(B),u1_struct_0(A)) & r1_tarski(u1_orders_2(B),u1_orders_2(A))))))) # label(d13_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4588 (all A (l1_orders_2(A) -> k2_yellow_0(A,k1_xboole_0) = k4_yellow_0(A))) # label(d12_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4589 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v8_yellow_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r1_yellow_0(A,C) -> r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)))))))))) # label(d19_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4590 (all A (l1_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_yellow_0(A,B) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))) & r1_lattice3(A,B,C) <-> k2_yellow_0(A,B) = C)))))) # label(d10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4591 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_yellow_0(A,k1_struct_0(A,B)) & r1_yellow_0(A,k1_struct_0(A,B)))))) # label(t38_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4592 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (k16_lattice3(k14_lattice3(A),B) = k2_yellow_0(A,B) & k15_lattice3(k14_lattice3(A),B) = k1_yellow_0(A,B))))) # label(t28_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4593 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B all C (r2_yellow_0(A,k2_xboole_0(B,C)) & r2_yellow_0(A,C) & r2_yellow_0(A,B) -> k11_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) = k2_yellow_0(A,k2_xboole_0(B,C)))))) # label(t37_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4594 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v1_yellow_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,k3_yellow_0(A),B))))) # label(t44_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4595 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v8_yellow_0(B,A) -> v6_yellow_0(B,A)))))) # label(cc10_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4596 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) -> (v7_yellow_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_yellow_0(A,C) -> r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)))))))))) # label(d18_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4597 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (k1_yellow_0(k3_lattice3(A),B) = k15_lattice3(A,B) & k2_yellow_0(k3_lattice3(A),B) = k16_lattice3(A,B))))) # label(t29_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4598 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v7_yellow_0(B,A) -> v5_yellow_0(B,A)))))) # label(cc9_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4599 (all A (l1_orders_2(A) -> (v1_yellow_0(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & r1_lattice3(A,u1_struct_0(A),B)))))) # label(d4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4600 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A) & v4_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A))))) # label(t57_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4601 (all A (l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,C,E) & r1_orders_2(A,B,E) -> r1_orders_2(A,D,E)))) & r1_orders_2(A,C,D) <-> D = k13_lattice3(A,B,C)))))))))) # label(t22_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4602 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) -> v4_yellow_0(B,A) & v4_orders_2(B)))))) # label(cc8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4603 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (r2_yellow_0(A,C) -> k2_yellow_0(B,C) = k2_yellow_0(A,C)))))))) # label(t27_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4604 (all A all B (l1_orders_2(A) -> m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)))) # label(dt_k1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4605 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C ((r2_yellow_0(A,C) -> r2_yellow_0(B,C)) & (r1_yellow_0(A,C) -> r1_yellow_0(B,C))))))))) # label(t14_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4606 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,k2_tarski(C,D),B) -> r1_orders_2(A,B,D) & r1_orders_2(A,B,C)) & (r1_orders_2(A,B,D) & r1_orders_2(A,B,C) -> r1_lattice3(A,k2_tarski(C,D),B)) & (r1_orders_2(A,D,B) & r1_orders_2(A,C,B) -> r2_lattice3(A,k2_tarski(C,D),B)) & (r2_lattice3(A,k2_tarski(C,D),B) -> r1_orders_2(A,C,B) & r1_orders_2(A,D,B)))))))))) # label(t8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4607 (all A (-v3_struct_0(A) & l1_orders_2(A) -> -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4608 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> (r1_lattice3(A,C,D) -> r1_lattice3(B,C,E)) & (r2_lattice3(A,C,D) -> r2_lattice3(B,C,E)))))))))))) # label(t2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4609 (all A (l1_orders_2(A) -> (exists B m1_yellow_0(B,A)))) # label(existence_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4610 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_yellow_0(A,k2_struct_0(A,C,D)) & r2_hidden(D,u1_struct_0(B)) & r2_hidden(C,u1_struct_0(B)) -> r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B))))))) <-> v6_yellow_0(B,A)))))) # label(d17_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4611 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_lattice3(A) -> v2_lattice3(A) & v1_lattice3(A) & -v3_struct_0(A)))) # label(cc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4612 (all A (l1_orders_2(A) & v3_orders_2(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r2_lattice3(A,B,C) -> r2_lattice3(A,B,D)))))))) # label(t11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4613 (all A (l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) -> v4_yellow_0(B,A) & v3_orders_2(B)))))) # label(cc7_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4614 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C ((B = k1_yellow_0(A,C) & r1_yellow_0(A,C) -> r2_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) -> r1_orders_2(A,B,D))))) & ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) -> r1_orders_2(A,B,D)))) & r2_lattice3(A,C,B) -> r1_yellow_0(A,C) & B = k1_yellow_0(A,C)))))))) # label(t30_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4615 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r1_lattice3(A,C,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) -> r1_orders_2(A,D,B)))) <-> B = k2_yellow_0(A,C))))))) # label(t33_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4616 (all A (-v3_struct_0(A) & l1_orders_2(A) & v1_yellow_0(A) & v4_orders_2(A) -> r1_yellow_0(A,k1_xboole_0) & r2_yellow_0(A,u1_struct_0(A)))) # label(t42_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4617 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B ((r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) -> r1_yellow_0(A,B)) & (r2_yellow_0(A,B) -> r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))) & (r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) -> r2_yellow_0(A,B)) & (r1_yellow_0(A,B) -> r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))))))) # label(t50_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4618 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) & -v3_struct_0(B) -> (all C all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> (r2_lattice3(A,C,D) -> r2_lattice3(B,C,E)) & (r1_lattice3(A,C,D) -> r1_lattice3(B,C,E))))))))))) # label(t62_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4619 (exists A (l1_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_yellow_0(A) & v3_yellow_0(A) & v1_yellow_0(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A))) # label(rc2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4620 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (exists B (-v3_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A))))) # label(rc4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4621 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> m1_subset_1(C,u1_struct_0(A)))))))) # label(t59_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4622 (all A (l1_orders_2(A) -> (v2_yellow_0(A) <-> (exists B (r2_lattice3(A,u1_struct_0(A),B) & m1_subset_1(B,u1_struct_0(A))))))) # label(d5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4623 (all A all B (l1_orders_2(A) -> m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)))) # label(dt_k2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4624 (all A (v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v6_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = D & C = E -> k13_lattice3(A,E,F) = k13_lattice3(B,C,D)))))))))))))) # label(t71_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4625 (all A (v3_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) & v4_yellow_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) & r2_yellow_0(A,C) -> r2_yellow_0(B,C) & k2_yellow_0(B,C) = k2_yellow_0(A,C)))))))) # label(t64_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4626 (all A (l1_orders_2(A) -> (all B (r2_yellow_0(A,B) <-> (exists C (m1_subset_1(C,u1_struct_0(A)) & r1_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_lattice3(A,B,E) -> r1_orders_2(A,E,D)))) -> C = D))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))))))))) # label(d8_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4627 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_yellow_0(A,B))) -> v3_lattice3(A)))) # label(t53_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.85 4628 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (v1_lattice3(A) <-> (all B (-v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_yellow_0(A,B)))))) # label(t54_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4629 (all A (l1_orders_2(A) & v4_orders_2(A) -> (v1_lattice3(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_yellow_0(A,k2_tarski(B,C))))))))) # label(t20_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4630 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) | r1_yellow_0(A,B) -> k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))))))) # label(t51_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4631 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) <-> r1_lattice3(A,C,D)))) & r2_yellow_0(A,B) -> r2_yellow_0(A,C))))) # label(t48_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4632 (all A (l1_orders_2(A) -> (v2_yellow_0(A) & v1_yellow_0(A) <-> v3_yellow_0(A)))) # label(d6_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4633 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r3_orders_2(A,B,C) <-> k12_lattice3(A,B,C) = B))))))) # label(t25_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4634 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) -> k2_yellow_0(B,C) = k2_yellow_0(A,C)))))))) # label(t68_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4635 (all A (l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) <-> u1_orders_2(B) = k1_toler_1(u1_orders_2(A),u1_struct_0(B))))))) # label(d14_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4636 (all A (l1_orders_2(A) -> (v3_orders_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r1_orders_2(A,B,C) -> r1_orders_2(A,B,D))))))))))) # label(d2_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4637 (all A (v3_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) & v4_yellow_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r1_yellow_0(A,C) & r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) -> k1_yellow_0(A,C) = k1_yellow_0(B,C) & r1_yellow_0(B,C)))))))) # label(t65_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4638 (all A (v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) & v6_yellow_0(B,A) & -v3_struct_0(B) -> v3_orders_2(B) & v4_orders_2(B) & v6_yellow_0(B,A) & v4_yellow_0(B,A) & v1_lattice3(B) & -v3_struct_0(B)))))) # label(cc12_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4639 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_yellow_0(A,k1_struct_0(A,B)) = B & k2_yellow_0(A,k1_struct_0(A,B)) = B)))) # label(t39_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4640 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice3(A,k1_tarski(C),B) -> r1_orders_2(A,B,C)) & (r1_orders_2(A,B,C) -> r1_lattice3(A,k1_tarski(C),B)) & (r2_lattice3(A,k1_tarski(C),B) -> r1_orders_2(A,C,B)) & (r1_orders_2(A,C,B) -> r2_lattice3(A,k1_tarski(C),B)))))))) # label(t7_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4641 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (E = D -> (r2_lattice3(B,C,E) -> r2_lattice3(A,C,D)) & (r1_lattice3(B,C,E) -> r1_lattice3(A,C,D))))))))))))) # label(t63_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4642 (all A (l1_orders_2(A) -> (v3_yellow_0(A) -> v2_yellow_0(A) & v1_yellow_0(A)))) # label(cc4_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4643 (all A all B (l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_orders_2(k5_yellow_0(A,B)) & v4_yellow_0(k5_yellow_0(A,B),A) & m1_yellow_0(k5_yellow_0(A,B),A))) # label(dt_k5_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4644 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v1_orders_2(C) & m1_yellow_0(C,A) & v4_yellow_0(C,A) -> (u1_struct_0(C) = B <-> k5_yellow_0(A,B) = C))))))) # label(d15_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4645 (exists A (v3_realset2(A) & v3_lattice3(A) & v2_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & v1_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4646 (all A (v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) & v5_yellow_0(B,A) & -v3_struct_0(B) -> v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) & -v3_struct_0(B)))))) # label(cc11_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4647 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v2_yellow_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_orders_2(A,B,k4_yellow_0(A)))))) # label(t45_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4648 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,D,B) & r1_orders_2(A,D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,C) & r1_orders_2(A,E,B) -> r1_orders_2(A,E,D)))) <-> D = k12_lattice3(A,B,C)))))))))) # label(t23_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4649 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (v1_yellow_0(A) -> v1_yellow_0(B)) & (v2_yellow_0(A) -> v2_yellow_0(B))))))) # label(t13_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4650 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_lattice3(A) -> -v3_struct_0(A) & v3_yellow_0(A)))) # label(cc3_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4651 (all A (l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_yellow_0(B,A) -> v4_yellow_0(B,A) & v2_orders_2(B)))))) # label(cc6_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4652 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_yellow_0(A,k2_struct_0(B,C,D)) & r2_hidden(k2_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) -> k2_yellow_0(B,k2_struct_0(B,C,D)) = k2_yellow_0(A,k2_struct_0(B,C,D)) & r2_yellow_0(B,k2_struct_0(B,C,D))))))))))) # label(t66_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4653 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,D,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,C) & r1_orders_2(A,E,B) -> r1_orders_2(A,E,D)))) & r1_orders_2(A,D,C) -> r2_yellow_0(A,k2_tarski(B,C)) & k11_lattice3(A,B,C) = D) & (k11_lattice3(A,B,C) = D & r2_yellow_0(A,k2_tarski(B,C)) -> r1_orders_2(A,D,B) & r1_orders_2(A,D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,E,B) & r1_orders_2(A,E,C) -> r1_orders_2(A,E,D))))))))))))) # label(t19_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.84/6.86 4654 (all A (l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k13_lattice3(A,B,C) <-> r1_orders_2(A,C,B)))))))) # label(t24_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4655 (all A (l1_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (r2_yellow_0(A,B) & r1_yellow_0(A,B))))) # label(t17_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4656 (all A (l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (((all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) -> r1_orders_2(A,D,B)))) & r1_lattice3(A,C,B) -> r2_yellow_0(A,C) & B = k2_yellow_0(A,C)) & (r2_yellow_0(A,C) & B = k2_yellow_0(A,C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) -> r1_orders_2(A,D,B)))) & r1_lattice3(A,C,B)))))))) # label(t31_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4657 (all A (v4_orders_2(A) & l1_orders_2(A) -> (all B (r2_yellow_0(A,B) <-> (exists C (r1_lattice3(A,B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))) & m1_subset_1(C,u1_struct_0(A)))))))) # label(t16_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4658 (all A (l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> l1_orders_2(B))))) # label(dt_m1_yellow_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4659 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) -> (v1_lattice3(A) | v2_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v13_waybel_0(C,A) & v2_waybel_0(C,A) & v2_waybel_0(B,A) & v13_waybel_0(B,A) -> v2_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t45_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4660 (exists A (l1_orders_2(A) & -v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v3_yellow_0(A) & v2_yellow_0(A) & v1_lattice3(A) & v4_orders_2(A))) # label(rc13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4661 (all A all B (l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k12_waybel_0(A,B)))) # label(fc20_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4662 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r1_yellow_0(A,D)))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r2_hidden(k1_yellow_0(A,D),C)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(r1_yellow_0(A,E) & D = k1_yellow_0(A,E)))) & r2_hidden(D,C)))) -> (r1_yellow_0(A,C) <-> r1_yellow_0(A,B))))))))) # label(t53_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4663 (all A all B (v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & -v3_struct_0(A) -> -v1_xboole_0(k4_waybel_0(A,B)))) # label(fc7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4664 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> (all C ((exists D (m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_orders_2(B,D,E) -> r2_hidden(k3_waybel_0(A,B,E),C)))))) <-> r1_waybel_0(A,B,C))))))) # label(d11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4665 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) & -v3_struct_0(B) -> ((exists D (k2_yellow_0(B,D) = A & r2_yellow_0(B,D) & m1_subset_1(D,k1_zfmisc_1(C)) & v1_finset_1(D))) <-> r2_hidden(A,a_2_3_waybel_0(B,C))))) # label(fraenkel_a_2_3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.86 4666 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (v1_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(D,A) & -v1_xboole_0(D) -> r4_waybel_0(A,B,C,D))) -> v22_waybel_0(C,A,B)))))))) # label(t73_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4667 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k4_waybel_0(A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) <-> (exists E (r2_hidden(E,B) & r1_orders_2(A,D,E) & m1_subset_1(E,u1_struct_0(A)))))))))))))) # label(d15_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4668 (all A (v2_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v5_yellow_0(k5_yellow_0(A,B),A) <-> -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) & v2_waybel_0(B,A)))))) # label(t63_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4669 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_yellow_0(A,k6_waybel_0(A,B)) & k1_yellow_0(A,k6_waybel_0(A,B)) = B)))) # label(t34_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4670 (all A (v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r2_hidden(k2_yellow_0(A,D),C)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(r2_yellow_0(A,E) & k2_yellow_0(A,E) = D)))))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,C,D) <-> r1_lattice3(A,B,D))))))))))) # label(t57_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4671 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_yellow_0(A,k7_waybel_0(A,B)) = B & r2_yellow_0(A,k7_waybel_0(A,B)))))) # label(t39_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4672 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_lattice3(A) & v2_orders_2(A) -> v2_orders_2(A) & v25_waybel_0(A) & v24_waybel_0(A) & -v3_struct_0(A)))) # label(cc10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4673 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & m1_yellow_0(B,A) & v4_waybel_0(B,A) & v4_yellow_0(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_waybel_0(C,B) -> (r1_yellow_0(A,C) -> k1_xboole_0 = C | r1_yellow_0(B,C) & k1_yellow_0(A,C) = k1_yellow_0(B,C)))))))) # label(t7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4674 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_waybel_0(A,B) = k4_waybel_0(A,k1_struct_0(A,B)))))) # label(d17_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4675 (all A (l1_struct_0(A) -> (exists B (v2_orders_2(B) & v7_waybel_0(B) & v6_waybel_0(B,A) & v4_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) & l1_waybel_0(B,A))))) # label(rc5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4676 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> (v10_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(B)) -> (exists D (m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_orders_2(B,D,E) -> r1_orders_2(A,k3_waybel_0(A,B,C),k3_waybel_0(A,B,E)))))))))))))) # label(t11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4677 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r2_hidden(k1_yellow_0(A,D),C)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(r1_yellow_0(A,E) & D = k1_yellow_0(A,E))))))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (D != k1_xboole_0 -> r1_yellow_0(A,D)))) -> v1_waybel_0(C,A)))))))) # label(t51_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4678 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_waybel_0(A,B) = a_2_0_waybel_0(A,B))))) # label(t14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4679 (all A (-v3_struct_0(A) & l1_orders_2(A) -> -v1_xboole_0(k2_pre_topc(A)) & v13_waybel_0(k2_pre_topc(A),A) & v12_waybel_0(k2_pre_topc(A),A))) # label(fc15_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4680 (all A all B (v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_yellow_0(A) & -v3_struct_0(A) -> -v1_xboole_0(k13_waybel_0(A,B)))) # label(fc19_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4681 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (v12_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(C,A) & -v1_xboole_0(C) -> (r1_tarski(B,C) -> r1_tarski(k4_waybel_0(A,k12_waybel_0(A,B)),C)))) & r1_tarski(B,k4_waybel_0(A,k12_waybel_0(A,B))))))) # label(t61_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4682 (all A (l1_struct_0(A) -> (exists B l1_waybel_0(B,A)))) # label(existence_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4683 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v4_waybel_0(B,A) <-> (all C (v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> (r1_yellow_0(A,C) -> C = k1_xboole_0 | r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)))))))))) # label(d4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4684 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v12_waybel_0(B,A) & v13_waybel_0(B,A))))) # label(rc8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4685 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k12_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4686 (all A (v1_lattice3(A) & l1_orders_2(A) -> v1_waybel_0(k2_pre_topc(A),A) & -v1_xboole_0(k2_pre_topc(A)))) # label(fc2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4687 (all A (v2_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v2_waybel_0(k1_struct_0(A,B),A) & v1_waybel_0(k1_struct_0(A,B),A))))) # label(t5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4688 (all A (v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) & -v1_xboole_0(B) -> (v6_yellow_0(k5_yellow_0(A,B),A) <-> -v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A)))))) # label(t64_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4689 (all A all B all C all D (l1_struct_0(A) & m1_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) & v1_funct_1(D) & m1_relset_1(C,B,B) -> l1_waybel_0(g1_waybel_0(A,B,C,D),A) & v6_waybel_0(g1_waybel_0(A,B,C,D),A))) # label(dt_g1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4690 (all A (v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) -> (v1_waybel_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(B)) & v1_finset_1(C) -> (C != k1_xboole_0 -> r2_hidden(k1_yellow_0(A,C),B))))))))) # label(t42_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4691 (all A (v2_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k5_waybel_0(A,B)) & r1_tarski(B,k4_waybel_0(A,B)))))) # label(t16_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4692 (all A (l1_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) & v12_waybel_0(B,A))))) # label(rc7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4693 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) -> m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4694 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (v10_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_waybel_0(A,B,a_3_0_waybel_0(A,B,C))))))))) # label(d13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4695 (all A all B (l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_orders_2(A) & -v3_struct_0(A) -> v13_waybel_0(k5_waybel_0(A,B),A))) # label(fc12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4696 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,u1_struct_0(C)) & l1_waybel_0(C,B) & -v3_struct_0(C) & l1_orders_2(B) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & k3_waybel_0(B,C,E) = A & r1_orders_2(B,k3_waybel_0(B,C,D),k3_waybel_0(B,C,E)))) <-> r2_hidden(A,a_3_0_waybel_0(B,C,D))))) # label(fraenkel_a_3_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4697 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v13_waybel_0(B,A) <-> r1_tarski(k5_waybel_0(A,B),B)))))) # label(t24_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4698 (all A (l1_struct_0(A) -> (exists B (v6_waybel_0(B,A) & l1_waybel_0(B,A))))) # label(rc4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4699 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (v9_waybel_0(B,A) <-> v5_waybel_0(k2_waybel_0(A,B),B,A)))))) # label(d10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4700 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> u1_waybel_0(A,B) = k2_waybel_0(A,B))))) # label(d7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4701 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> k9_waybel_0(A) = a_1_1_waybel_0(A))) # label(d24_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4702 $T # label(dt_k9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4703 $T # label(dt_k10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4704 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (exists B (m1_yellow_0(B,A) & -v3_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) & v4_waybel_0(B,A) & v3_waybel_0(B,A) & v8_yellow_0(B,A) & v7_yellow_0(B,A) & v5_yellow_0(B,A))))) # label(rc3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4705 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4706 (all A all B all C all D (l1_struct_0(A) & v1_funct_1(D) & m1_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(C,B,B) -> (all E all F all G all H (g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H) -> F = B & G = C & D = H & E = A)))) # label(free_g1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4707 (all A all B (-v3_struct_0(A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v13_waybel_0(k5_waybel_0(A,B),A) & v2_waybel_0(k5_waybel_0(A,B),A))) # label(fc17_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4708 (all A (l1_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) & v2_waybel_0(B,A))))) # label(rc1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4709 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_hidden(k1_yellow_0(A,D),C)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(r1_yellow_0(A,E) & k1_yellow_0(A,E) = D))) & r2_hidden(D,C)))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r1_yellow_0(A,D)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,C,D) <-> r2_lattice3(A,B,D))))))))))) # label(t52_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4710 (all A all B (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_orders_2(A) & v2_orders_2(A) -> v2_waybel_0(k13_waybel_0(A,B),A))) # label(fc23_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4711 (all A all B all C (l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & D = A & (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & r1_orders_2(B,D,E))))) <-> r2_hidden(A,a_2_0_waybel_0(B,C))))) # label(fraenkel_a_2_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4712 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (-(-v3_struct_0(B) & -v3_struct_0(A)) -> (v23_waybel_0(C,A,B) <-> v3_struct_0(B) & v3_struct_0(A))) & -(-v3_struct_0(A) & -(v2_funct_1(C) & v5_orders_3(C,A,B) & (exists D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v5_orders_3(D,B,A) & D = k2_funct_1(C) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D))) <-> v23_waybel_0(C,A,B)) & -v3_struct_0(B)))))))) # label(d38_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4713 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_waybel_0(A,B)) <-> r1_orders_2(A,C,B)))))))) # label(t17_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4714 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> v2_waybel_0(k7_waybel_0(A,B),A) & -v1_xboole_0(k7_waybel_0(A,B)))) # label(fc10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4715 (all A all B (v4_orders_2(A) & l1_orders_2(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k13_waybel_0(A,B)))) # label(fc21_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4716 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v18_waybel_0(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r4_waybel_0(A,B,C,D)))))))))) # label(d33_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4717 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (l1_orders_2(C) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & l1_orders_2(D) -> (g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C)) -> (all E (v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) -> (E = F -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) -> (all H (m1_subset_1(H,k1_zfmisc_1(u1_struct_0(C))) -> (G = H -> (r4_waybel_0(A,B,E,G) -> r4_waybel_0(C,D,F,H)) & (r3_waybel_0(A,B,E,G) -> r3_waybel_0(C,D,F,H))))))))))))))))))))) # label(t65_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4718 (all A (v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k13_lattice3(A,C,D),B)))))) <-> v1_waybel_0(B,A)))))) # label(t40_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4719 $T # label(dt_k8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4720 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> a_1_0_waybel_0(A) = k8_waybel_0(A))) # label(d23_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4721 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(D,A) -> v1_xboole_0(D) | r3_waybel_0(A,B,C,D)))) <-> v21_waybel_0(C,A,B)))))))) # label(d36_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4722 (all A all B (v2_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k6_waybel_0(A,B)) & v1_waybel_0(k6_waybel_0(A,B),A))) # label(fc9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4723 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) & v1_waybel_0(B,A) -> ((exists C (k6_waybel_0(A,C) = B & m1_subset_1(C,u1_struct_0(A)))) <-> v14_waybel_0(B,A)))))) # label(t48_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4724 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r3_waybel_0(A,B,C,D) <-> (r2_yellow_0(A,D) -> k2_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k2_yellow_0(A,D)) & r2_yellow_0(B,k4_pre_topc(A,B,C,D)))))))))))) # label(d30_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4725 (all A (v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r2_hidden(D,B) -> r2_hidden(k12_lattice3(A,C,D),B))))))))))) # label(t41_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4726 r1_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,a_0_0_waybel_0) <-> (exists A ((all B (m1_subset_1(B,u1_struct_0(f2_s1_waybel_0)) -> (r1_orders_2(f2_s1_waybel_0,A,B) -> p1_s1_waybel_0(k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B))))) & m1_subset_1(A,u1_struct_0(f2_s1_waybel_0)))) # label(s1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4727 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v23_waybel_0(C,A,B) -> (all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (D = k2_funct_1(C) -> v23_waybel_0(D,B,A))))))))))) # label(t68_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4728 (all A all B (l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> m1_subset_1(k13_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4729 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v7_yellow_0(B,A) -> v3_waybel_0(B,A)))))) # label(cc1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4730 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v23_waybel_0(C,A,B) -> v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) & u1_struct_0(A) = k2_relat_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(k2_funct_1(C))))))))) # label(t67_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4731 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> (exists B (v1_finset_1(B) & v2_waybel_0(B,A) & v1_waybel_0(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4732 (all A all B all C (-v3_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(C)) & r1_yellow_0(B,D) & k1_yellow_0(B,D) = A & v1_finset_1(D))) <-> r2_hidden(A,a_2_2_waybel_0(B,C))))) # label(fraenkel_a_2_2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4733 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_waybel_0(A,k1_struct_0(A,B)) = k7_waybel_0(A,B))))) # label(d18_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4734 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,B) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(E,B) & r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E)))) & r2_hidden(C,B)))))) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v1_waybel_0(C,A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = k5_setfam_1(u1_struct_0(A),B) -> v1_waybel_0(C,A))))))))) # label(t46_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4735 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k13_waybel_0(A,B)) & r1_tarski(B,k12_waybel_0(A,B)))))) # label(t50_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4736 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_yellow_0(A,B) <-> r2_yellow_0(A,k5_waybel_0(A,B))))))) # label(t37_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4737 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) -> k10_waybel_0(A) = k2_xboole_0(k8_waybel_0(A),k1_tarski(k1_xboole_0)))) # label(d25_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4738 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_yellow_0(B,A) -> (v8_yellow_0(B,A) -> v4_waybel_0(B,A)))))) # label(cc2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4739 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v12_waybel_0(B,A) & v1_waybel_0(B,A))))) # label(rc9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4740 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v1_xboole_0(k5_waybel_0(A,B)))) # label(fc8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4741 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l1_waybel_0(B,A) & -v3_struct_0(B) & l1_struct_0(A) & -v3_struct_0(A) -> m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)))) # label(dt_k3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4742 (all A (l1_orders_2(A) -> (v2_orders_2(A) & v25_waybel_0(A) & v2_yellow_0(A) & v4_orders_2(A) & -v3_struct_0(A) -> v4_orders_2(A) & v2_yellow_0(A) & v1_lattice3(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.87 4743 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_yellow_0(A,B) -> k2_yellow_0(A,k5_waybel_0(A,B)) = k2_yellow_0(A,B)))))) # label(t38_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4744 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (v2_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r3_waybel_0(A,B,C,D))) & (all D (-v1_xboole_0(D) & v2_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r3_waybel_0(A,B,C,D))) -> v17_waybel_0(C,A,B)))))))) # label(t71_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4745 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v13_waybel_0(B,A) & v13_waybel_0(C,A) -> v13_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & v13_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t29_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4746 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v23_waybel_0(C,A,B) <-> v2_funct_1(C) & k2_relat_1(C) = u1_struct_0(B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) <-> r1_orders_2(A,D,E))))))))))))) # label(t66_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4747 (all A (v3_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_tarski(k6_waybel_0(A,B),k6_waybel_0(A,C))))))))) # label(t21_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4748 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & -v3_struct_0(B) & l1_struct_0(A) -> m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)))) # label(dt_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4749 (all A (l1_orders_2(A) -> v5_orders_2(k1_pre_topc(A),A) & v1_finset_1(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v2_waybel_0(k1_pre_topc(A),A) & v1_waybel_0(k1_pre_topc(A),A) & v5_membered(k1_pre_topc(A)) & v1_xboole_0(k1_pre_topc(A)))) # label(fc1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4750 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,B,C) | r1_orders_2(A,C,B))))) <-> v16_waybel_0(A)))) # label(d29_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4751 (all A all B all C (l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & (exists E (m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,C))))) <-> r2_hidden(A,a_2_1_waybel_0(B,C))))) # label(fraenkel_a_2_1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4752 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(B)) & v1_finset_1(C) -> (exists D (r2_hidden(D,B) & r2_lattice3(A,C,D) & m1_subset_1(D,u1_struct_0(A)))))) <-> v1_waybel_0(B,A) & -v1_xboole_0(B)))))) # label(t1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4753 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) -> m1_subset_1(k4_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4754 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(C,B) & r1_orders_2(A,D,C) -> r2_hidden(D,B)))))) <-> v12_waybel_0(B,A)))))) # label(d19_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4755 (all A all B (l1_struct_0(A) & l1_waybel_0(B,A) -> m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(u1_waybel_0(A,B)))) # label(dt_u1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4756 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) -> (v2_lattice3(A) | v1_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_waybel_0(B,A) & v1_waybel_0(C,A) & v12_waybel_0(C,A) & v12_waybel_0(B,A) -> v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A))))))))) # label(t44_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4757 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D & v1_waybel_0(C,A) -> v1_waybel_0(D,B))))))))))) # label(t3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4758 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r1_yellow_0(A,D)))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (k1_xboole_0 != D -> r2_hidden(k1_yellow_0(A,D),C)))) & r1_yellow_0(A,B) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(D = k1_yellow_0(A,E) & r1_yellow_0(A,E))))))) -> k1_yellow_0(A,C) = k1_yellow_0(A,B)))))))) # label(t54_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4759 (all A (-v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)) & v16_waybel_0(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)) & -v3_struct_0(k7_lattice3(A)))) # label(fc24_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4760 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v2_waybel_0(C,A) & C = D -> v2_waybel_0(D,B))))))))))) # label(t4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4761 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice3(A,B,C) <-> r1_lattice3(A,k5_waybel_0(A,B),C)))))))) # label(t36_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4762 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r3_waybel_0(A,B,C,D))) <-> v17_waybel_0(C,A,B)))))))) # label(d32_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4763 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> (all C (-r2_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) <-> r1_waybel_0(A,B,C))))))) # label(t9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4764 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(B,A) <-> v2_waybel_0(k5_waybel_0(A,B),A)))))) # label(t35_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4765 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) <-> r2_hidden(C,k7_waybel_0(A,B))))))))) # label(t18_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4766 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> (all C all D (r1_tarski(C,D) -> (r2_waybel_0(A,B,C) -> r2_waybel_0(A,B,D)) & (r1_waybel_0(A,B,C) -> r1_waybel_0(A,B,D)))))))) # label(t8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4767 (all A (l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (exists B (v7_waybel_0(B) & v10_waybel_0(B,A) & v11_waybel_0(B,A) & v9_waybel_0(B,A) & v8_waybel_0(B,A) & v6_waybel_0(B,A) & -v3_struct_0(B) & l1_waybel_0(B,A))))) # label(rc6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4768 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (v24_waybel_0(A) <-> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) -> r1_yellow_0(A,B)))))) # label(t75_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4769 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r2_hidden(E,B) & r1_orders_2(A,C,E) & r1_orders_2(A,D,E)))) & r2_hidden(C,B)))))) <-> v1_waybel_0(B,A)))))) # label(d1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4770 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> (v13_waybel_0(C,A) -> v13_waybel_0(D,B)) & (v12_waybel_0(C,A) -> v12_waybel_0(D,B)))))))))))) # label(t25_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4771 (all A all B (l1_orders_2(A) & l1_orders_2(B) & -v3_struct_0(B) & -v3_struct_0(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_1(C) & v17_waybel_0(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v21_waybel_0(C,A,B)))))) # label(cc6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4772 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (-v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(D,A) & v2_waybel_0(D,A) -> r3_waybel_0(A,B,C,D))) -> v5_orders_3(C,A,B)))))))) # label(t69_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4773 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v12_waybel_0(C,A)))) -> v12_waybel_0(k5_setfam_1(u1_struct_0(A),B),A) & m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t26_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4774 (all A (l1_orders_2(A) -> (v25_waybel_0(A) & v2_orders_2(A) & -v3_struct_0(A) -> v1_yellow_0(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4775 (exists A (l1_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A))) # label(rc12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4776 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) & v3_waybel_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v2_waybel_0(C,B) -> (r2_yellow_0(A,C) -> k2_yellow_0(B,C) = k2_yellow_0(A,C) & r2_yellow_0(B,C) | k1_xboole_0 = C))))))) # label(t6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4777 (all A (l1_orders_2(A) -> (v3_realset2(A) & v2_orders_2(A) & -v3_struct_0(A) -> v2_orders_2(A) & v16_waybel_0(A) & -v3_struct_0(A)))) # label(cc5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4778 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k6_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4779 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_0(A,B,C,k2_struct_0(A,D,E)))))) <-> v20_waybel_0(C,A,B)))))))) # label(d35_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4780 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_waybel_0(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(C,B) & r2_hidden(D,B) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(r1_orders_2(A,E,D) & r1_orders_2(A,E,C) & r2_hidden(E,B)))))))))))))) # label(d2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4781 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,B) | v3_lattice3(A) -> k1_yellow_0(A,k12_waybel_0(A,B)) = k1_yellow_0(A,B)))))) # label(t55_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4782 (all A (l1_orders_2(A) & v1_yellow_0(A) & -v3_struct_0(A) -> v2_waybel_0(k2_pre_topc(A),A) & -v1_xboole_0(k2_pre_topc(A)))) # label(fc5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4783 $T # label(dt_k11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4784 (all A all B (-v3_struct_0(A) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v1_waybel_0(k4_waybel_0(A,B),A) & v12_waybel_0(k4_waybel_0(A,B),A))) # label(fc16_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4785 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_orders_2(A) -> v12_waybel_0(k4_waybel_0(A,B),A))) # label(fc11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4786 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_waybel_0(A,B) = k6_waybel_0(A,C) -> B = C))))))) # label(t19_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4787 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (D != k1_xboole_0 -> r2_hidden(k2_yellow_0(A,D),C)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(B)) & v1_finset_1(E) -> -(r2_yellow_0(A,E) & k2_yellow_0(A,E) = D))) & r2_hidden(D,C)))) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) -> (r2_yellow_0(A,C) <-> r2_yellow_0(A,B))))))))) # label(t58_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4788 (all A (-v3_struct_0(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (exists B (-v1_xboole_0(B) & v13_waybel_0(B,A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4789 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> k11_waybel_0(A) = k2_xboole_0(k9_waybel_0(A),k1_tarski(k1_xboole_0)))) # label(d26_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4790 (all A (v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,k4_waybel_0(A,B)) <-> r1_yellow_0(A,B)))))) # label(t32_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4791 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> r2_yellow_0(A,B))) <-> v25_waybel_0(A)))) # label(t76_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4792 (all A (l1_orders_2(A) & v2_yellow_0(A) & -v3_struct_0(A) -> v1_waybel_0(k2_pre_topc(A),A) & -v1_xboole_0(k2_pre_topc(A)))) # label(fc3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4793 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) -> (v7_waybel_0(B) & v9_waybel_0(B,A) & -v3_struct_0(B) -> -v3_struct_0(B) & v7_waybel_0(B) & v11_waybel_0(B,A)))))) # label(cc4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4794 (all A (v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_waybel_0(B,A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> ((exists C (r2_hidden(C,B) & r2_lattice3(A,B,C) & m1_subset_1(C,u1_struct_0(A)))) <-> v14_waybel_0(B,A)))))) # label(d21_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4795 (all A (l1_orders_2(A) -> (v1_waybel_0(k2_pre_topc(A),A) <-> v7_waybel_0(A)))) # label(d6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4796 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(B)) -> (exists D (m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,u1_struct_0(B)) -> (r1_orders_2(B,D,E) -> r1_orders_2(A,k3_waybel_0(A,B,E),k3_waybel_0(A,B,C))))))))) <-> v11_waybel_0(B,A)))))) # label(t12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4797 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k5_waybel_0(A,B) = C <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) <-> (exists E (m1_subset_1(E,u1_struct_0(A)) & r2_hidden(E,B) & r1_orders_2(A,E,D))))))))))))) # label(d16_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4798 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_waybel_0(B,A) <-> v1_waybel_0(k4_waybel_0(A,B),A)))))) # label(t30_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4799 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(E,B) & r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E)))) & r2_hidden(D,B) & r2_hidden(C,B)))))) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v2_waybel_0(C,A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k5_setfam_1(u1_struct_0(A),B) = C -> v2_waybel_0(C,A))))))))) # label(t47_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4800 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> ((r1_yellow_0(A,D) -> k1_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k1_yellow_0(A,D)) & r1_yellow_0(B,k4_pre_topc(A,B,C,D))) <-> r4_waybel_0(A,B,C,D)))))))))) # label(d31_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4801 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v5_waybel_0(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,D,E) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (G = k1_funct_1(C,E) & k1_funct_1(C,D) = F -> r1_orders_2(B,G,F)))))))))))))))))) # label(d5_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.88 4802 (all A (l1_orders_2(A) -> (v4_orders_2(A) & v25_waybel_0(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v2_orders_2(A) & v2_lattice3(A) & v4_orders_2(A)))) # label(cc13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4803 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v19_waybel_0(C,A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> r3_waybel_0(A,B,C,k2_struct_0(A,D,E))))))))))))) # label(d34_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4804 (all A all B (l1_struct_0(A) & l1_waybel_0(B,A) -> (v6_waybel_0(B,A) -> B = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B))))) # label(abstractness_v6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4805 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v13_waybel_0(C,A)))) -> v13_waybel_0(k5_setfam_1(u1_struct_0(A),B),A) & m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t28_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4806 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (-v1_xboole_0(D) & v2_waybel_0(D,A) & v13_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r3_waybel_0(A,B,C,D))) -> v21_waybel_0(C,A,B)))))))) # label(t70_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4807 (all A all B (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_lattice3(A) & v4_orders_2(A) -> v1_waybel_0(k12_waybel_0(A,B),A))) # label(fc22_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4808 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v12_waybel_0(B,A) <-> r1_tarski(k4_waybel_0(A,B),B)))))) # label(t23_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4809 (all A (r2_hidden(A,a_0_0_waybel_0) <-> (exists B (p1_s1_waybel_0(k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B)) & A = k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B) & m1_subset_1(B,u1_struct_0(f2_s1_waybel_0)))))) # label(fraenkel_a_0_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4810 (all A all B (-v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) -> ((exists C (v2_waybel_0(C,B) & C = A & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v13_waybel_0(C,B) & -v1_xboole_0(C))) <-> r2_hidden(A,a_1_1_waybel_0(B))))) # label(fraenkel_a_1_1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4811 (all A all B (-v3_struct_0(A) & l1_waybel_0(B,A) & -v3_struct_0(B) & l1_struct_0(A) -> v1_funct_1(k2_waybel_0(A,B)) & v1_funct_2(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(k2_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)))) # label(dt_k2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4812 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = D -> k4_waybel_0(B,D) = k4_waybel_0(A,C) & k5_waybel_0(B,D) = k5_waybel_0(A,C))))))))))) # label(t13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4813 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_waybel_0(B,A) -> (-v3_struct_0(B) & v7_waybel_0(B) & v8_waybel_0(B,A) -> v10_waybel_0(B,A) & v7_waybel_0(B) & -v3_struct_0(B)))))) # label(cc3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4814 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k7_waybel_0(A,B) = k7_waybel_0(A,C) -> B = C))))))) # label(t20_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4815 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C (-r1_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) <-> r2_waybel_0(A,B,C))))))) # label(t10_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4816 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (-v1_xboole_0(B) & v2_waybel_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(B)) & v1_finset_1(C) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & r1_lattice3(A,C,D) & r2_hidden(D,B)))))))))) # label(t2_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4817 (all A (v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v2_waybel_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(B)) & v1_finset_1(C) -> (C != k1_xboole_0 -> r2_hidden(k2_yellow_0(A,C),B))))))))) # label(t43_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4818 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> a_2_3_waybel_0(A,B) = k13_waybel_0(A,B))))) # label(d28_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4819 (all A (v2_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (exists B (v1_waybel_0(B,A) & v13_waybel_0(B,A) & v12_waybel_0(B,A) & v2_waybel_0(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc11_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4820 (all A all B (l1_orders_2(B) & -v3_struct_0(B) & l1_orders_2(A) & -v3_struct_0(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_1(C) & v18_waybel_0(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(C,A,B) & v20_waybel_0(C,A,B)))))) # label(cc7_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4821 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(C,B,B) & l1_struct_0(A) -> v6_waybel_0(g1_waybel_0(A,B,C,D),A) & -v3_struct_0(g1_waybel_0(A,B,C,D)))) # label(fc6_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4822 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,B) -> k1_yellow_0(A,k4_waybel_0(A,B)) = k1_yellow_0(A,B)))))) # label(t33_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4823 (all A (v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_waybel_0(B,A) -> (v15_waybel_0(B,A) <-> (exists C (k7_waybel_0(A,C) = B & m1_subset_1(C,u1_struct_0(A))))))))) # label(t49_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4824 (all A (l1_orders_2(A) & v2_lattice3(A) -> -v1_xboole_0(k2_pre_topc(A)) & v2_waybel_0(k2_pre_topc(A),A))) # label(fc4_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4825 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & l1_orders_2(B) & l1_orders_2(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) & v1_funct_1(C) -> v1_funct_1(C) & v2_funct_1(C) & v5_orders_3(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))))))) # label(cc8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4826 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v13_waybel_0(B,A) & v2_waybel_0(B,A) & -v1_xboole_0(B) -> ((exists C (m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) & r1_lattice3(A,B,C))) <-> v15_waybel_0(B,A)))))) # label(d22_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4827 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) & r2_hidden(C,B) -> r2_hidden(D,B)))))) <-> v13_waybel_0(B,A)))))) # label(d20_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4828 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(D = k2_yellow_0(A,E) & r2_yellow_0(A,E))))))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_hidden(k2_yellow_0(A,D),C)))) -> v2_waybel_0(C,A)))))))) # label(t56_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4829 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k12_waybel_0(A,B) = a_2_2_waybel_0(A,B))))) # label(d27_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4830 (all A (v2_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r2_yellow_0(A,B) | v3_lattice3(A) -> k2_yellow_0(A,k13_waybel_0(A,B)) = k2_yellow_0(A,B)))))) # label(t60_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4831 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (v8_waybel_0(B,A) <-> v5_orders_3(k2_waybel_0(A,B),B,A)))))) # label(d9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4832 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (v1_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(D,A) & -v1_xboole_0(D) -> r4_waybel_0(A,B,C,D))) -> v5_orders_3(C,A,B)))))))) # label(t72_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4833 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_waybel_0(A,B,C) = k1_waybel_0(B,A,u1_waybel_0(A,B),C))))))) # label(d8_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4834 (all A (l1_orders_2(A) -> (v1_lattice3(A) & v24_waybel_0(A) & v1_yellow_0(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v3_orders_2(A) & v2_orders_2(A)))) # label(cc12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4835 (all A (l1_struct_0(A) -> (all B (l1_waybel_0(B,A) -> l1_orders_2(B))))) # label(dt_l1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4836 (all A all B all C all D (-v3_struct_0(A) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & -v3_struct_0(B) & l1_struct_0(A) -> k1_funct_1(C,D) = k1_waybel_0(A,B,C,D))) # label(redefinition_k1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4837 (all A (v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(B,k5_waybel_0(A,k13_waybel_0(A,B))) & (all C (-v1_xboole_0(C) & v2_waybel_0(C,A) & v13_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k5_waybel_0(A,k13_waybel_0(A,B)),C)))))))) # label(t62_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4838 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & v3_orders_2(A) -> v12_waybel_0(k6_waybel_0(A,B),A))) # label(fc13_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4839 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattice3(A,k4_waybel_0(A,B),C) <-> r2_lattice3(A,B,C)))))))) # label(t31_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4840 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_yellow_0(B,A) -> (v3_waybel_0(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v2_waybel_0(C,B) -> (r2_yellow_0(A,C) -> r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) | k1_xboole_0 = C)))))))) # label(d3_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4841 (all A all B (v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & -v3_struct_0(B) -> (r2_hidden(A,a_1_0_waybel_0(B)) <-> (exists C (A = C & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v12_waybel_0(C,B) & v1_waybel_0(C,B) & -v1_xboole_0(C)))))) # label(fraenkel_a_1_0_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4842 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v12_waybel_0(C,A) & v12_waybel_0(B,A) -> v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & v12_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t27_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4843 (all A all B (-v3_struct_0(A) & v4_orders_2(A) & v1_yellow_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) -> -v1_xboole_0(k12_waybel_0(A,B)))) # label(fc18_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4844 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_waybel_0(A,B) = a_2_1_waybel_0(A,B))))) # label(t15_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4845 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(D,A) & -v1_xboole_0(D) -> r4_waybel_0(A,B,C,D))) & (all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> r4_waybel_0(A,B,C,D))) -> v18_waybel_0(C,A,B)))))))) # label(t74_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4846 (all A all B all C all D (-v3_struct_0(C) & m1_subset_1(D,u1_struct_0(C)) & l1_waybel_0(C,B) & l1_orders_2(B) & -v3_struct_0(B) -> ((exists E (r1_orders_2(B,k3_waybel_0(B,C,E),k3_waybel_0(B,C,D)) & k3_waybel_0(B,C,E) = A & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_1_waybel_0(B,C,D))))) # label(fraenkel_a_3_1_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4847 (all A (l1_orders_2(A) -> (v2_orders_2(A) & v24_waybel_0(A) & v1_lattice3(A) -> -v3_struct_0(A) & v2_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A)))) # label(cc9_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4848 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice3(A,B,D) -> r1_orders_2(A,D,C)))) & r1_lattice3(A,B,C))))) <-> v25_waybel_0(A)))) # label(d40_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4849 (all A (l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (v24_waybel_0(A) <-> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_lattice3(A,B,D) -> r3_orders_2(A,C,D)))) & r2_lattice3(A,B,C)))))))) # label(d39_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4850 (all A (l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_tarski(k7_waybel_0(A,C),k7_waybel_0(A,B))))))))) # label(t22_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4851 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_waybel_0(B,A) & -v3_struct_0(B) -> (all C ((all D (m1_subset_1(D,u1_struct_0(B)) -> (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(k3_waybel_0(A,B,E),C) & r1_orders_2(B,D,E))))) <-> r2_waybel_0(A,B,C))))))) # label(d12_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4852 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_waybel_0(B,A) -> ((all C (m1_subset_1(C,u1_struct_0(B)) -> r1_waybel_0(A,B,a_3_1_waybel_0(A,B,C)))) <-> v11_waybel_0(B,A)))))) # label(d14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4853 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & v3_orders_2(A) & -v3_struct_0(A) -> v13_waybel_0(k7_waybel_0(A,B),A))) # label(fc14_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4854 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((all D (v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != D -> r2_yellow_0(A,D)))) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r2_hidden(D,C) & (all E (v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) -> -(k2_yellow_0(A,E) = D & r2_yellow_0(A,E))))))) & r2_yellow_0(A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(B)) & v1_finset_1(D) -> (k1_xboole_0 != D -> r2_hidden(k2_yellow_0(A,D),C)))) -> k2_yellow_0(A,B) = k2_yellow_0(A,C)))))))) # label(t59_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4855 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v22_waybel_0(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v1_waybel_0(D,A) -> v1_xboole_0(D) | r4_waybel_0(A,B,C,D))))))))))) # label(d37_waybel_0) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4856 (all A all B (l1_orders_2(A) & l1_orders_2(B) -> v1_orders_2(k7_yellow_1(A,B)) & v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)))) # label(dt_k7_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4857 (all A (v1_relat_1(A) -> (v1_yellow_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> l1_orders_2(B)))))) # label(d3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4858 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) & v1_orders_2(C) -> (C = k7_yellow_1(A,B) <-> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (r2_hidden(D,u1_struct_0(C)) <-> v5_orders_3(D,A,B) & r2_hidden(D,k1_funct_2(u1_struct_0(A),u1_struct_0(B))))))))))))) # label(d6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4859 (all A (v1_orders_2(k3_yellow_1(A)) & l1_orders_2(k3_yellow_1(A)))) # label(dt_k3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4860 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k3_yellow_0(k2_yellow_1(u1_pre_topc(A))) = k1_xboole_0)) # label(t23_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4861 (all A all B (m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_yellow_1(A))) -> (r3_orders_2(k3_yellow_1(A),B,C) <-> r1_tarski(B,C)))))) # label(t2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4862 (all A k1_yellow_1(A) = k1_wellord2(A)) # label(redefinition_k1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4863 (all A all B all C (v1_yellow_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> k1_funct_1(B,C) = k4_yellow_1(A,B,C))) # label(redefinition_k4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4864 (all A (-v3_struct_0(A) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A) -> -v3_struct_0(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v1_yellow_0(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)))) # label(fc3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4865 (all A all B (l1_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> v1_orders_2(k6_yellow_1(A,B)) & v2_orders_2(k6_yellow_1(A,B)) & -v3_struct_0(k6_yellow_1(A,B)))) # label(fc12_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4866 (all A all B (-v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) -> v3_orders_2(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & -v3_struct_0(k6_yellow_1(A,B)))) # label(fc15_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4867 (all A (-v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)))) # label(fc8_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4868 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> (r2_hidden(k2_xboole_0(B,C),A) -> k2_xboole_0(B,C) = k10_lattice3(k2_yellow_1(A),B,C)))))))) # label(t8_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4869 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> v4_yellow_0(k2_yellow_1(B),k3_yellow_1(A)) & m1_yellow_0(k2_yellow_1(B),k3_yellow_1(A)))) # label(t5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4870 (all A (-v1_xboole_0(A) -> ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k2_xboole_0(B,C),A))) -> v1_lattice3(k2_yellow_1(A))))) # label(t11_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4871 (all A (v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & -v3_struct_0(k3_yellow_1(A)))) # label(fc7_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4872 (all A all B (m1_pboole(B,A) & v1_yellow_1(B) -> (all C (l1_orders_2(C) & v1_orders_2(C) -> ((all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (r2_hidden(D,k4_card_3(k12_pralg_1(A,B))) -> ((exists F (v1_relat_1(F) & (exists G (v1_funct_1(G) & F = D & (all H -((all I (l1_orders_2(I) -> (all J (m1_subset_1(J,u1_struct_0(I)) -> (all K (m1_subset_1(K,u1_struct_0(I)) -> -(k1_funct_1(B,H) = I & J = k1_funct_1(F,H) & r1_orders_2(I,J,K) & K = k1_funct_1(G,H)))))))) & r2_hidden(H,A))) & G = E & v1_relat_1(G))) & v1_funct_1(F))) <-> r1_orders_2(C,D,E))))))) & u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B)) <-> k5_yellow_1(A,B) = C))))) # label(d4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4873 (all A (l1_orders_2(A) & -v3_struct_0(A) -> v3_realset2(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & -v3_struct_0(k6_yellow_1(k1_xboole_0,A)))) # label(fc13_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4874 (all A k1_xboole_0 = k3_yellow_0(k3_yellow_1(A))) # label(t18_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4875 (all A all B (l1_orders_2(B) -> u1_struct_0(k6_yellow_1(A,B)) = k1_funct_2(A,u1_struct_0(B)))) # label(t28_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4876 (all A all B (v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & -v3_struct_0(B) & -v1_xboole_0(A) -> -v3_struct_0(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v2_lattice3(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)))) # label(fc17_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4877 (all A all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) -> -v3_struct_0(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)))) # label(fc16_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4878 (all A (-v1_xboole_0(A) -> (v1_yellow_0(k2_yellow_1(A)) -> r2_hidden(k1_setfam_1(A),A)))) # label(t16_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4879 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> u1_struct_0(A) = k4_yellow_0(k2_yellow_1(u1_pre_topc(A))))) # label(t24_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4880 (all A (m1_pboole(A,k1_xboole_0) & v1_yellow_1(A) -> k5_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))))) # label(t26_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4881 (all A (l1_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_tarski(B,C) <-> r1_orders_2(A,B,C)))))) -> u1_orders_2(A) = k1_yellow_1(u1_struct_0(A))))) # label(t10_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4882 (all A (l1_orders_2(k2_yellow_1(A)) & v1_orders_2(k2_yellow_1(A)))) # label(dt_k2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4883 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> (r3_orders_2(k2_yellow_1(A),B,C) <-> r1_tarski(B,C)))))))) # label(t3_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4884 (all A (-v1_xboole_0(A) -> (v1_lattice3(k2_yellow_1(A)) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> r1_tarski(k2_xboole_0(B,C),k10_lattice3(k2_yellow_1(A),B,C))))))))) # label(t6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4885 (all A all B (l1_orders_2(B) -> v1_orders_2(k6_yellow_1(A,B)) & l1_orders_2(k6_yellow_1(A,B)))) # label(dt_k6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4886 (all A (v8_relat_2(k1_yellow_1(A)) & m2_relset_1(k1_yellow_1(A),A,A) & v1_partfun1(k1_yellow_1(A),A,A) & v4_relat_2(k1_yellow_1(A)) & v1_relat_2(k1_yellow_1(A)))) # label(dt_k1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4887 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v2_yellow_0(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v3_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v3_yellow_0(k3_lattice3(A)) & v1_yellow_0(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4888 (all A all B (l1_orders_2(B) -> v1_funct_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc10_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4889 (all A k3_yellow_1(A) = k3_lattice3(k1_lattice3(A))) # label(d2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4890 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)))) # label(fc1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4891 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> (r2_hidden(k3_xboole_0(B,C),A) -> k3_xboole_0(B,C) = k11_lattice3(k2_yellow_1(A),B,C)))))))) # label(t9_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4892 (all A (-v1_xboole_0(A) -> (r2_hidden(k1_xboole_0,A) -> k1_xboole_0 = k3_yellow_0(k2_yellow_1(A))))) # label(t13_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4893 (all A all B (-v3_struct_0(B) & l1_orders_2(B) -> v1_orders_2(k6_yellow_1(A,B)) & -v3_struct_0(k6_yellow_1(A,B)))) # label(fc11_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4894 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) -> k1_yellow_0(k3_yellow_1(A),B) = k3_tarski(B))) # label(t21_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4895 (all A k2_yellow_1(A) = g1_orders_2(A,k1_yellow_1(A))) # label(d1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.94/6.89 4896 (all A (-v1_xboole_0(A) -> (v2_lattice3(k2_yellow_1(A)) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) -> r1_tarski(k11_lattice3(k2_yellow_1(A),B,C),k3_xboole_0(B,C))))))))) # label(t7_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.89 4897 (all A (l1_orders_2(A) -> k6_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))))) # label(t27_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.89 4898 (all A all B (l1_orders_2(B) -> k5_yellow_1(A,k2_pre_circ(A,B)) = k6_yellow_1(A,B))) # label(d5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.89 4899 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(A)))) & -v1_xboole_0(B) -> k2_yellow_0(k3_yellow_1(A),B) = k1_setfam_1(B))) # label(t20_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.89 4900 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(k2_yellow_1(u1_pre_topc(A))) & v1_orders_2(k2_yellow_1(u1_pre_topc(A))) & v1_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v2_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v3_lattice3(k2_yellow_1(u1_pre_topc(A))) & -v3_realset2(k2_yellow_1(u1_pre_topc(A))) & v2_lattice3(k2_yellow_1(u1_pre_topc(A))) & v1_lattice3(k2_yellow_1(u1_pre_topc(A))) & v3_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v4_orders_2(k2_yellow_1(u1_pre_topc(A))) & v3_orders_2(k2_yellow_1(u1_pre_topc(A))) & v2_orders_2(k2_yellow_1(u1_pre_topc(A))))) # label(fc9_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.89 4901 (all A (-v1_xboole_0(A) -> v1_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & -v3_struct_0(k2_yellow_1(A)))) # label(fc6_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.89 4902 (all A all B (m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_yellow_1(A))) -> k13_lattice3(k3_yellow_1(A),B,C) = k2_xboole_0(B,C) & k12_lattice3(k3_yellow_1(A),B,C) = k3_xboole_0(B,C))))) # label(t17_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4903 (all A (l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_orders_2(k6_yellow_1(k1_xboole_0,A)) & v1_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v2_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v3_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v1_lattice3(k6_yellow_1(k1_xboole_0,A)) & v2_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) & v3_lattice3(k6_yellow_1(k1_xboole_0,A)) & v4_orders_2(k6_yellow_1(k1_xboole_0,A)) & v2_orders_2(k6_yellow_1(k1_xboole_0,A)) & -v3_struct_0(k6_yellow_1(k1_xboole_0,A)))) # label(fc14_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4904 (all A (k1_yellow_1(A) = u1_orders_2(k2_yellow_1(A)) & u1_struct_0(k2_yellow_1(A)) = A)) # label(t1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4905 (all A k2_yellow_1(k1_zfmisc_1(A)) = k3_yellow_1(A)) # label(t4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4906 (all A (v1_yellow_1(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(A) & v2_pralg_1(A) & v1_funct_1(A))) # label(cc1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4907 (all A all B (m1_pboole(B,A) & v1_yellow_1(B) -> l1_orders_2(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)))) # label(dt_k5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4908 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A))))) -> k1_yellow_0(k2_yellow_1(u1_pre_topc(A)),B) = k3_tarski(B))))) # label(t22_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4909 (all A all B (-v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) & v1_lattice3(B) & -v1_xboole_0(A) -> v1_orders_2(k6_yellow_1(A,B)) & v1_lattice3(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & -v3_struct_0(k6_yellow_1(A,B)))) # label(fc18_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4910 (all A (-v1_xboole_0(A) -> ((all B all C (r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k3_xboole_0(B,C),A))) -> v2_lattice3(k2_yellow_1(A))))) # label(t12_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4911 (all A A = k4_yellow_0(k3_yellow_1(A))) # label(t19_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4912 (all A (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_lattices(A) -> -v3_struct_0(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_yellow_0(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)))) # label(fc2_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4913 (all A (-v1_xboole_0(A) -> (r2_hidden(k3_tarski(A),A) -> k4_yellow_0(k2_yellow_1(A)) = k3_tarski(A)))) # label(t14_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4914 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A))))) <-> v1_tops_2(B,A)))))) # label(t25_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4915 (all A all B all C (-v1_xboole_0(A) & v1_yellow_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) -> l1_orders_2(k4_yellow_1(A,B,C)))) # label(dt_k4_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4916 (all A (-v1_xboole_0(A) -> (v2_yellow_0(k2_yellow_1(A)) -> r2_hidden(k3_tarski(A),A)))) # label(t15_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4917 (all A (v4_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v1_orders_2(k2_yellow_1(A)))) # label(fc5_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4918 (all A exists B (m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_yellow_1(B) & v2_pralg_1(B))) # label(rc1_yellow_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4919 (all A (v2_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> v2_orders_2(k2_yellow_1(k8_waybel_0(A))) & v1_lattice3(k2_yellow_1(k8_waybel_0(A))) & v4_orders_2(k2_yellow_1(k8_waybel_0(A))) & v3_orders_2(k2_yellow_1(k8_waybel_0(A))) & v1_orders_2(k2_yellow_1(k8_waybel_0(A))) & -v3_struct_0(k2_yellow_1(k8_waybel_0(A))))) # label(fc5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4920 (all A (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v2_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v7_yellow_0(B,A) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & v1_lattice3(B) & v2_orders_2(B))))) # label(t32_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4921 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & v1_funct_1(B) -> (k4_yellow_2(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C) = k6_waybel_0(A,C)))))))) # label(d4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4922 $T # label(t9_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4923 (all A (v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> k2_pre_topc(A) = k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0) & r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),k1_xboole_0))) # label(t49_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4924 (all A (v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v2_waybel_0(C,A) & v13_waybel_0(C,A)))) -> v2_waybel_0(k6_setfam_1(u1_struct_0(A),B),A) & m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t41_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4925 (all A all B all C (l1_struct_0(B) & m1_relset_1(C,A,u1_struct_0(B)) & v1_funct_2(C,A,u1_struct_0(B)) & v1_funct_1(C) & -v3_struct_0(B) -> k2_relat_1(C) = k8_yellow_2(A,B,C))) # label(redefinition_k8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4926 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & l1_orders_2(C) -> (all D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) -> (v5_orders_3(E,B,C) & v5_orders_3(D,A,B) -> v5_orders_3(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t14_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4927 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> v1_funct_1(k4_yellow_2(A)) & v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & m2_relset_1(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))))) # label(dt_k4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4928 (all A all B (v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r2_hidden(C,A) -> r3_orders_2(B,C,k1_yellow_0(B,A)) & r3_orders_2(B,k2_yellow_0(B,A),C)))))) # label(t24_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4929 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_yellow_0(A,B))) -> (all B (r1_yellow_0(A,B) & k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))))))) # label(t29_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4930 (all A (v3_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,u1_struct_0(A)) & v1_funct_2(D,C,u1_struct_0(A)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,C) -> r3_orders_2(A,k7_yellow_2(C,A,D,E),B))) -> r3_orders_2(A,k5_yellow_2(A,D),B)))))))))) # label(t56_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4931 (all A (v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B all C (r1_yellow_0(A,B) & r1_yellow_0(A,C) -> r1_yellow_0(A,k2_xboole_0(B,C)) & k13_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) = k1_yellow_0(A,k2_xboole_0(B,C)))))) # label(t3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4932 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u1_struct_0(k2_yellow_2(A,B,C))) -> (exists E (m1_subset_1(E,u1_struct_0(A)) & D = k1_waybel_0(A,B,C,E))))))))))) # label(t12_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4933 (all A all B all C all D (-v3_struct_0(B) & v1_funct_1(C) & m1_subset_1(D,A) & m1_relset_1(C,A,u1_struct_0(B)) & v1_funct_2(C,A,u1_struct_0(B)) & l1_struct_0(B) & -v1_xboole_0(A) -> m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)))) # label(dt_k7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4934 (all A all B all C (-v3_struct_0(B) & l1_struct_0(B) & m1_relset_1(C,A,u1_struct_0(B)) & v1_funct_2(C,A,u1_struct_0(B)) & v1_funct_1(C) -> m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4935 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))))) # label(t54_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4936 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,k6_waybel_0(A,B)) <-> r2_lattice3(A,C,B)))))))) # label(t1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4937 (all A (v1_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v5_orders_3(B,A,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_1_yellow_2(A,B) = C -> v3_orders_2(k5_yellow_0(A,C)) & v2_lattice3(k5_yellow_0(A,C)) & v3_lattice3(k5_yellow_0(A,C)) & l1_orders_2(k5_yellow_0(A,C)) & v1_lattice3(k5_yellow_0(A,C)) & v4_orders_2(k5_yellow_0(A,C)) & v2_orders_2(k5_yellow_0(A,C)))))))))) # label(t31_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4938 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v1_yellow_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k8_waybel_0(A))))) & -v1_xboole_0(B) -> r2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) & k2_yellow_0(k2_yellow_1(k8_waybel_0(A)),B) = k1_setfam_1(B))))) # label(t48_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4939 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v21_waybel_0(B,A,A) -> v5_orders_3(B,A,A)))))) # label(t19_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4940 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v2_lattice3(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v18_waybel_0(C,A,B) -> v8_yellow_0(k2_yellow_2(A,B,C),B)))))))) # label(t34_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4941 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r2_yellow_0(A,B))) -> (all B (r2_yellow_0(A,B) & k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))))))) # label(t28_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4942 (all A (v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v1_waybel_0(C,A) & v12_waybel_0(C,A)))) -> m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t40_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4943 (all A all B (v2_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (-v1_xboole_0(A) & v12_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) & v1_waybel_0(A,B) <-> m1_subset_1(A,u1_struct_0(k2_yellow_1(k8_waybel_0(B))))))) # label(t43_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4944 (all A all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) -> (r2_hidden(A,k1_relat_1(k3_yellow_2(B))) <-> -v1_xboole_0(A) & v12_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) & v1_waybel_0(A,B)))) # label(t52_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4945 (all A all B all C (l1_orders_2(B) & v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & -v3_struct_0(B) & l1_orders_2(A) & -v3_struct_0(A) -> v1_orders_2(k2_yellow_2(A,B,C)) & m1_yellow_0(k2_yellow_2(A,B,C),B) & v4_yellow_0(k2_yellow_2(A,B,C),B))) # label(dt_k2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4946 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> m2_relset_1(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) & v1_funct_1(k3_yellow_2(A)))) # label(dt_k3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4947 (all A (v1_relat_1(A) -> (all B all C (r1_tarski(B,C) -> r1_tarski(k2_wellord1(A,B),k2_wellord1(A,C)))))) # label(t5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4948 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v11_quantal1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_waybel_0(A,A,B,C) = k1_waybel_0(A,A,B,k1_waybel_0(A,A,B,C))))))))) # label(t20_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4949 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B r2_yellow_0(A,B)) <-> (all B r1_yellow_0(A,B))))) # label(t25_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4950 (all A all B all C (l1_struct_0(A) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) -> k1_yellow_2(A,B,C) = k2_relat_1(C))) # label(redefinition_k1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4951 (all A (l1_orders_2(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> k11_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) = k3_xboole_0(B,C))))))) # label(t45_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4952 (all A all B all C all D (l1_orders_2(B) & m1_subset_1(D,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) & m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) & v1_lattice3(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (r2_hidden(A,a_3_0_yellow_2(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & -(-r2_hidden(E,C) & (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> -(r2_hidden(G,D) & k13_lattice3(B,F,G) = E & r2_hidden(F,C)))))) & -r2_hidden(E,D)) & E = A))))) # label(fraenkel_a_3_0_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4953 (all A (-v3_struct_0(A) & l1_orders_2(A) -> v5_orders_3(k7_grcat_1(A),A,A))) # label(t13_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4954 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v3_orders_2(A) & v2_yellow_0(A) & v25_waybel_0(A) & v24_waybel_0(A) & v4_orders_2(A) & v2_orders_2(A) -> -v3_struct_0(A) & v2_orders_2(A) & v2_yellow_0(A) & v25_waybel_0(A) & v3_lattice3(A) & v2_lattice3(A) & v1_lattice3(A) & v24_waybel_0(A) & v3_yellow_0(A) & v1_yellow_0(A) & v4_orders_2(A) & v3_orders_2(A)))) # label(cc1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4955 (all A all B (v1_relat_1(B) & l1_orders_2(A) & -v3_struct_0(A) -> m1_subset_1(k5_yellow_2(A,B),u1_struct_0(A)))) # label(dt_k5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4956 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) -> (all C (v4_yellow_0(C,A) & m1_yellow_0(C,A) & -v3_struct_0(C) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) -> (D = E -> (v1_waybel_0(D,B) -> v1_waybel_0(E,C)) & (v2_waybel_0(D,B) -> v2_waybel_0(E,C)))))))))))))) # label(t8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4957 (all A (-v3_struct_0(A) & l1_orders_2(A) & v24_waybel_0(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A))) # label(t53_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4958 (all A all B all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_struct_0(B) & l1_struct_0(A) -> m1_subset_1(k1_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))))) # label(dt_k1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4959 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_lattice3(A,D,E) & v5_orders_3(C,A,B) -> r2_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E))))))))))))) # label(t16_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4960 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v13_waybel_0(C,A)))) -> v13_waybel_0(k6_setfam_1(u1_struct_0(A),B),A) & m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)))))))) # label(t39_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4961 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,k7_waybel_0(A,B)) <-> r1_lattice3(A,C,B)))))))) # label(t2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4962 (all A (v3_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> v1_orders_2(k2_yellow_1(k8_waybel_0(A))) & v4_orders_2(k2_yellow_1(k8_waybel_0(A))) & v2_yellow_0(k2_yellow_1(k8_waybel_0(A))) & v25_waybel_0(k2_yellow_1(k8_waybel_0(A))) & v2_lattice3(k2_yellow_1(k8_waybel_0(A))) & v3_lattice3(k2_yellow_1(k8_waybel_0(A))) & v1_lattice3(k2_yellow_1(k8_waybel_0(A))) & v24_waybel_0(k2_yellow_1(k8_waybel_0(A))) & v3_yellow_0(k2_yellow_1(k8_waybel_0(A))) & v1_yellow_0(k2_yellow_1(k8_waybel_0(A))) & v3_orders_2(k2_yellow_1(k8_waybel_0(A))) & v2_orders_2(k2_yellow_1(k8_waybel_0(A))) & -v3_struct_0(k2_yellow_1(k8_waybel_0(A))))) # label(fc6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4963 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v12_waybel_0(C,A)))) -> m1_subset_1(k6_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(k6_setfam_1(u1_struct_0(A),B),A)))))) # label(t38_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4964 (all A (l1_orders_2(A) -> (all B (v4_yellow_0(B,A) & m1_yellow_0(B,A) -> (all C (m1_yellow_0(C,A) & v4_yellow_0(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> r1_tarski(u1_orders_2(B),u1_orders_2(C))))))))) # label(t6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4965 (all A (l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v22_waybel_0(B,A,A) -> v5_orders_3(B,A,A)))))) # label(t18_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4966 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v2_orders_2(A) -> v3_lattice3(k2_yellow_1(k8_waybel_0(A))))) # label(t50_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4967 (all A (l1_orders_2(A) & -v3_struct_0(A) -> ((all B r2_yellow_0(A,B)) -> v3_lattice3(A)))) # label(t27_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4968 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (v1_relat_1(B) -> k5_yellow_2(A,B) = k1_yellow_0(A,k2_relat_1(B)))))) # label(d5_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4969 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v11_quantal1(B) -> a_2_0_yellow_2(A,B) = k1_yellow_2(A,A,B)))))) # label(t21_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4970 (all A (l1_orders_2(A) & -v3_struct_0(A) -> v11_quantal1(k7_grcat_1(A)))) # label(t23_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4971 (all A all B (l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,A,u1_struct_0(B)) & v1_funct_2(C,A,u1_struct_0(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,u1_struct_0(B)) & v1_funct_2(D,A,u1_struct_0(B)) -> ((all E -((all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> -(F = k1_funct_1(C,E) & k1_funct_1(D,E) = G & r1_orders_2(B,F,G)))))) & r2_hidden(E,A))) <-> r1_yellow_2(A,B,C,D)))))))) # label(d1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4972 (all A all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_1(C) -> (v11_quantal1(C) & r1_tarski(A,k1_yellow_2(B,B,C)) -> k4_pre_topc(B,B,C,A) = A))))) # label(t22_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4973 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v5_orders_3(C,A,B) -> v1_waybel_0(k4_pre_topc(A,B,C,D),B)))))))))) # label(t17_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4974 (all A (v2_orders_2(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) -> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & a_3_0_yellow_2(A,B,C) = D & k4_waybel_0(A,D) = k10_lattice3(k2_yellow_1(k8_waybel_0(A)),B,C) & r1_yellow_0(k2_yellow_1(k8_waybel_0(A)),k2_struct_0(k2_yellow_1(k8_waybel_0(A)),B,C)))))))))) # label(t46_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4975 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> k5_yellow_0(B,k1_yellow_2(A,B,C)) = k2_yellow_2(A,B,C))))))) # label(d2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4976 (all A (v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v1_yellow_0(A) & v3_orders_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k8_waybel_0(A))) -> -v1_xboole_0(k1_setfam_1(B)) & v1_waybel_0(k1_setfam_1(B),A) & v12_waybel_0(k1_setfam_1(B),A) & m1_subset_1(k1_setfam_1(B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t47_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4977 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) -> (all B all C (r2_yellow_0(A,C) & r2_yellow_0(A,B) -> k12_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) = k2_yellow_0(A,k2_xboole_0(B,C)) & r2_yellow_0(A,k2_xboole_0(B,C)))))) # label(t4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4978 (all A all B (-v3_struct_0(B) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (m1_subset_1(C,u1_struct_0(k2_yellow_1(k8_waybel_0(B)))) -> (r2_hidden(A,C) -> m1_subset_1(A,u1_struct_0(B))))))) # label(t44_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4979 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> k1_relat_1(k3_yellow_2(A)) = k8_waybel_0(A) & m1_subset_1(k1_yellow_2(k2_yellow_1(k8_waybel_0(A)),A,k3_yellow_2(A)),k1_zfmisc_1(u1_struct_0(A))))) # label(t51_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4980 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) & v2_lattice3(A) & v1_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v11_quantal1(B) & v22_waybel_0(B,A,A) -> v4_waybel_0(k2_yellow_2(A,A,B),A) & v1_lattice3(k2_yellow_2(A,A,B)) & l1_orders_2(k2_yellow_2(A,A,B)) & v3_lattice3(k2_yellow_2(A,A,B)) & v2_lattice3(k2_yellow_2(A,A,B)) & v4_orders_2(k2_yellow_2(A,A,B)) & v3_orders_2(k2_yellow_2(A,A,B)) & v2_orders_2(k2_yellow_2(A,A,B))))))) # label(t37_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4981 (all A all B all C (v2_orders_2(B) & v3_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & l1_orders_2(B) & v3_lattice3(B) & v2_lattice3(B) & v1_lattice3(B) & v4_orders_2(B) -> ((exists D (D = k1_waybel_0(B,B,C,D) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_1_yellow_2(B,C))))) # label(fraenkel_a_2_1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4982 (all A (v2_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,C,u1_struct_0(A)) & v1_funct_2(D,C,u1_struct_0(A)) -> ((all E (m1_subset_1(E,C) -> r3_orders_2(A,B,k7_yellow_2(C,A,D,E)))) -> r3_orders_2(A,B,k6_yellow_2(A,D))))))))))) # label(t57_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4983 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> u1_struct_0(k2_yellow_2(A,B,C)) = k1_yellow_2(A,B,C))))))) # label(t11_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4984 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> -v1_xboole_0(k8_waybel_0(A)))) # label(fc3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4985 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & l1_struct_0(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & D = k1_waybel_0(B,B,C,D))) <-> r2_hidden(A,a_2_0_yellow_2(B,C))))) # label(fraenkel_a_2_0_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4986 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v24_waybel_0(A) & v3_orders_2(A) & -v3_struct_0(A) -> v1_relat_1(k3_yellow_2(A)) & v1_funct_1(k3_yellow_2(A)) & v5_orders_3(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) & v1_funct_2(k3_yellow_2(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)))) # label(fc7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4987 (all A (v2_orders_2(A) & v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v17_waybel_0(C,A,B) -> v7_yellow_0(k2_yellow_2(A,B,C),B)))))))) # label(t35_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4988 (all A (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_lattice3(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v8_yellow_0(B,A) & m1_yellow_0(B,A) & v4_yellow_0(B,A) -> v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v3_lattice3(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B))))) # label(t33_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4989 (all A all B (v1_relat_1(B) & l1_orders_2(A) & -v3_struct_0(A) -> m1_subset_1(k6_yellow_2(A,B),u1_struct_0(A)))) # label(dt_k6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4990 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B r1_yellow_0(A,B)) -> v3_lattice3(A)))) # label(t26_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4991 (all A all B all C all D (l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_subset_1(D,A) & m1_relset_1(C,A,u1_struct_0(B)) & -v3_struct_0(B) & -v1_xboole_0(A) -> k1_funct_1(C,D) = k7_yellow_2(A,B,C,D))) # label(redefinition_k7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4992 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> v1_funct_1(k4_yellow_2(A)) & v5_orders_3(k4_yellow_2(A),A,k2_yellow_1(k8_waybel_0(A))) & v1_funct_2(k4_yellow_2(A),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) & v1_relat_1(k4_yellow_2(A)))) # label(fc8_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4993 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v2_orders_2(A) -> -v3_struct_0(k2_yellow_1(k8_waybel_0(A))) & v2_orders_2(k2_yellow_1(k8_waybel_0(A))) & v2_lattice3(k2_yellow_1(k8_waybel_0(A))) & v4_orders_2(k2_yellow_1(k8_waybel_0(A))) & v3_orders_2(k2_yellow_1(k8_waybel_0(A))) & v1_orders_2(k2_yellow_1(k8_waybel_0(A))))) # label(fc4_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4994 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> r1_orders_2(B,k1_waybel_0(A,B,C,E),k1_waybel_0(A,B,D,E)))) <-> r1_yellow_2(u1_struct_0(A),B,C,D)))))))))) # label(t10_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4995 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (v5_orders_3(C,A,B) & r1_lattice3(A,D,E) -> r1_lattice3(B,k4_pre_topc(A,B,C,D),k1_waybel_0(A,B,C,E))))))))))))) # label(t15_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4996 (all A all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (-v3_struct_0(C) & m1_yellow_0(C,B) -> (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) & v1_waybel_0(A,C) -> v1_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B)))) & (v2_waybel_0(A,C) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) -> v2_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B)))))))) # label(t7_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4997 (all A all B all C (-v3_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_orders_2(B) & l1_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(k2_yellow_2(A,B,C)) & v4_yellow_0(k2_yellow_2(A,B,C),B) & v1_orders_2(k2_yellow_2(A,B,C)))) # label(fc2_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4998 (all A (-v3_struct_0(A) & l1_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r2_yellow_0(A,B))) -> v3_lattice3(A)))) # label(t30_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 4999 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A)) -> (B = k3_yellow_2(A) <-> (all C (v1_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(C,A) & -v1_xboole_0(C) -> k1_yellow_0(A,C) = k1_funct_1(B,C)))))))) # label(d3_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5000 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (v1_relat_1(B) -> k6_yellow_2(A,B) = k2_yellow_0(A,k2_relat_1(B)))))) # label(d6_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5001 (all A (v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v2_orders_2(A) -> (all B (v2_orders_2(B) & v4_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & v2_lattice3(B) & v1_lattice3(B) & v3_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v18_waybel_0(C,A,B) | v17_waybel_0(C,A,B) -> v3_orders_2(k2_yellow_2(A,B,C)) & v1_lattice3(k2_yellow_2(A,B,C)) & l1_orders_2(k2_yellow_2(A,B,C)) & v3_lattice3(k2_yellow_2(A,B,C)) & v2_lattice3(k2_yellow_2(A,B,C)) & v4_orders_2(k2_yellow_2(A,B,C)) & v2_orders_2(k2_yellow_2(A,B,C))))))))) # label(t36_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5002 (all A (v2_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v3_orders_2(A) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,u1_struct_0(A)) & v1_funct_2(D,B,u1_struct_0(A)) -> r3_orders_2(A,k6_yellow_2(A,D),k7_yellow_2(B,A,D,C)) & r3_orders_2(A,k7_yellow_2(B,A,D,C),k5_yellow_2(A,D)))))))))) # label(t55_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5003 (all A (v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v1_waybel_0(B,A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) & v12_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(C,A) -> -v1_xboole_0(k5_subset_1(u1_struct_0(A),B,C)) & v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) & m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(A))))))))) # label(t42_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5004 (all A all B (-v3_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & l1_orders_2(A) -> -v3_struct_0(k5_yellow_0(A,B)) & v1_orders_2(k5_yellow_0(A,B)) & v4_yellow_0(k5_yellow_0(A,B),A))) # label(fc1_yellow_2) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5005 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v11_quantal1(B) -> k7_grcat_1(k2_yellow_2(A,A,B)) = k7_funct_2(u1_struct_0(k2_yellow_2(A,A,B)),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,A,B)),k3_waybel_1(A,A,B),k2_waybel_1(A,A,B))))))) # label(t36_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5006 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (exists B (v1_relat_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & -v1_xboole_0(B) & v1_funct_1(B) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)))))) # label(rc1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5007 (all A all B all C (-v3_struct_0(A) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_orders_2(B) & -v3_struct_0(B) & l1_orders_2(A) -> v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & v2_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & v1_partfun1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & -v1_xboole_0(k2_waybel_1(A,B,C)) & v1_funct_1(k2_waybel_1(A,B,C)) & v1_relat_1(k2_waybel_1(A,B,C)))) # label(fc6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5008 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) <-> (all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k6_waybel_0(A,E))))) & v5_orders_3(D,B,A)))))))))) # label(t12_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5009 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (v5_orders_3(C,A,B) & v5_orders_3(D,B,A) & r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) & r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A)) -> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(t20_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.90 5010 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(B)) & l1_orders_2(B) -> ((exists E (E = A & r1_orders_2(B,k11_lattice3(B,C,E),D) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_waybel_1(B,C,D))))) # label(fraenkel_a_3_0_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5011 (all A (l1_orders_2(A) & v1_yellow_0(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,B)))))))))) # label(t86_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5012 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v8_waybel_1(B,A) & r1_yellow_0(A,C) & r1_tarski(C,k8_yellow_2(u1_struct_0(A),A,B)) -> k1_yellow_0(A,C) = k7_yellow_2(u1_struct_0(A),A,B,k1_yellow_0(A,C))))))))) # label(t31_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5013 (all A (-v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> (all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_orders_2(B,E,k7_yellow_2(u1_struct_0(A),B,C,F)) <-> r3_orders_2(A,k7_yellow_2(u1_struct_0(B),A,D,E),F)))))) & v5_orders_3(D,B,A) & v5_orders_3(C,A,B) <-> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(t9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5014 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v1_yellow_0(A) & v9_waybel_1(A) -> k7_waybel_1(A,k4_yellow_0(A)) = k3_yellow_0(A) & k4_yellow_0(A) = k7_waybel_1(A,k3_yellow_0(A))))) # label(t83_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5015 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> B = k7_funct_2(u1_struct_0(A),u1_struct_0(k2_yellow_2(A,A,B)),u1_struct_0(A),k2_waybel_1(A,A,B),k3_waybel_1(A,A,B)))))) # label(t35_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5016 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k1_struct_0(B,E))))) -> k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C) = k7_grcat_1(B)))))))))) # label(t24_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5017 (all A all B all C all D (l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_orders_2(A) -> k1_waybel_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5018 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v5_orders_3(B,A,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_0_waybel_1(A,B) = C -> v8_yellow_0(k5_yellow_0(A,C),A))))))))) # label(t52_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5019 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m1_subset_1(D,u1_struct_0(k2_yellow_2(A,B,C))) -> D = k7_yellow_2(u1_struct_0(k2_yellow_2(A,B,C)),B,k3_waybel_1(A,B,C),D))))))))) # label(t34_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5020 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> (v2_funct_1(D) <-> v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)))))))))))) # label(t26_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5021 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> -(v7_waybel_1(B,A) & (all C (v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,u1_struct_0(C),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(E) -> -(v3_waybel_1(k1_waybel_1(C,A,D,E),C,A) & k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),E,D) = B)))))))))))) # label(t40_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5022 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v7_waybel_1(B,A) -> v3_waybel_1(k1_waybel_1(k2_yellow_2(A,A,B),A,k3_waybel_1(A,A,B),k2_waybel_1(A,A,B)),k2_yellow_2(A,A,B),A)))))) # label(t39_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5023 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) -> v1_funct_1(k5_waybel_1(A,B)) & m2_relset_1(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k5_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5024 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v7_waybel_1(B,A) -> v7_yellow_0(k2_yellow_2(A,A,B),A)) & (v8_waybel_1(B,A) -> v8_yellow_0(k2_yellow_2(A,A,B),A)))))) # label(t56_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5025 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v10_waybel_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r6_waybel_1(A,B,C) & m1_subset_1(C,u1_struct_0(A))))))))) # label(d24_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5026 (all A all B (v4_orders_2(A) & -v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v4_waybel_1(C,A,B) & v1_funct_1(C) -> v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v21_waybel_0(C,A,B) & v19_waybel_0(C,A,B) & v17_waybel_0(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5027 (all A all B all C (-v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & l1_orders_2(B) & v3_orders_2(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & r3_orders_2(B,D,k7_yellow_2(u1_struct_0(B),B,C,D)) & A = D)) <-> r2_hidden(A,a_2_0_waybel_1(B,C))))) # label(fraenkel_a_2_0_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5028 (all A all B all C (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) -> m1_subset_1(k6_waybel_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5029 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v5_orders_3(C,A,B) & r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A)) & r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) & v5_orders_3(D,B,A) -> k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) = C & D = k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D))))))))))) # label(t21_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5030 (all A all B all C all D (v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & v2_lattice3(B) -> (r2_hidden(A,a_3_2_waybel_1(B,C,D)) <-> (exists E (r3_orders_2(B,k12_lattice3(B,C,E),D) & A = E & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5031 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k7_waybel_1(A,B) = k6_waybel_1(A,B,k3_yellow_0(A)))))) # label(d22_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5032 (all A all B all C all D (v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & A = k12_lattice3(B,D,E))) <-> r2_hidden(A,a_3_5_waybel_1(B,C,D))))) # label(fraenkel_a_3_5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5033 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = a_2_1_waybel_1(A,B) -> (all D (m2_relset_1(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & v1_funct_2(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & v1_funct_1(D) -> (k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C) = D -> v8_waybel_1(D,k5_yellow_0(A,C))))))))))))) # label(t51_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5034 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v7_waybel_1(B,A) & v1_funct_1(B) -> v1_funct_1(B) & v6_waybel_1(B,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(B)))))) # label(cc3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5035 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v5_orders_3(B,A,A) -> (all C (v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) -> -(v3_waybel_1(k1_waybel_1(A,C,D,E),A,C) & k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) = B))))))) | v8_waybel_1(B,A)))))) # label(t44_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5036 (all A (l1_orders_2(A) -> (v3_orders_2(A) & v4_orders_2(A) & v3_yellow_0(A) & v10_waybel_1(A) & v2_waybel_1(A) & v2_lattice3(A) & v1_lattice3(A) & v2_orders_2(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v2_waybel_1(A) & v11_waybel_1(A) & v10_waybel_1(A) & v3_yellow_0(A) & v1_lattice3(A) & v4_orders_2(A)))) # label(cc9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5037 (all A (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A))) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_yellow_0(A,a_3_3_waybel_1(A,B,C)) = k12_lattice3(A,C,k1_yellow_0(A,B)))))))))) # label(t66_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5038 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) <-> v2_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A))) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A)))) # label(d19_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5039 (all A (-v3_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_orders_2(A,B,k7_waybel_1(A,C)) <-> r1_orders_2(A,C,k7_waybel_1(A,B)))))))))) # label(t84_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5040 $T # label(t1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5041 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> (v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) <-> v2_funct_1(C))))))))))) # label(t29_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5042 (all A (l1_orders_2(A) & v1_yellow_0(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_yellow_0(A) = k11_lattice3(A,B,C) <-> r1_orders_2(A,C,k7_waybel_1(A,B)))))))))) # label(t85_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5043 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v8_waybel_1(B,A) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & -v1_xboole_0(B) & v1_funct_1(B)))))) # label(cc4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5044 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v1_yellow_0(A) & v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r4_waybel_1(A,k7_waybel_1(A,B),a_2_2_waybel_1(A,B))))))) # label(t82_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5045 (all A (v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_waybel_1(A,a_3_2_waybel_1(A,B,C))))))))) # label(t65_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5046 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(C) -> (C = k4_waybel_1(A,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> k7_yellow_2(u1_struct_0(A),A,C,D) = k11_lattice3(A,B,D)))))))))) # label(d18_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5047 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v9_waybel_1(A) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(C) -> (k5_waybel_1(A,B) = C <-> v3_waybel_1(k1_waybel_1(A,A,C,k4_waybel_1(A,B)),A,A))))))))) # label(d20_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5048 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> k3_xboole_0(a_2_0_waybel_1(A,B),a_2_1_waybel_1(A,B)) = k8_yellow_2(u1_struct_0(A),A,B)))))) # label(t45_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5049 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_pre_topc(A,A,k4_waybel_1(A,B),C) = a_3_1_waybel_1(A,B,C))))))) # label(t64_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5050 (all A all B all C (-v3_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_orders_2(B) & l1_orders_2(A) & -v3_struct_0(A) -> v1_funct_2(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) & m2_relset_1(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) & v1_funct_1(k3_waybel_1(A,B,C)))) # label(dt_k3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5051 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> -v1_xboole_0(a_2_0_waybel_1(A,B)) & m1_subset_1(a_2_0_waybel_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(a_2_1_waybel_1(A,B),k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(a_2_1_waybel_1(A,B))))))) # label(t46_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5052 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> (exists B (m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & -v1_xboole_0(B) & v6_waybel_1(B,A) & v7_waybel_1(B,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B))))) # label(rc2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5053 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) & v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k1_struct_0(A,E)))))))))))))) # label(t27_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5054 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D))))))))))) # label(t2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5055 (all A all B all C all D (v3_orders_2(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) & v3_lattice3(B) & v4_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_4_waybel_1(B,C,D)) <-> (exists E (k12_lattice3(B,D,E) = A & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5056 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> ((exists C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)))) <-> r5_waybel_1(A,B)))))) # label(d8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5057 (all A all B all C all D (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) & v1_funct_1(C) & l1_orders_2(B) & l1_orders_2(A) -> m1_waybel_1(k1_waybel_1(A,B,C,D),A,B))) # label(dt_k1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5058 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (v2_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> r1_yellow_2(u1_struct_0(B),B,k7_grcat_1(B),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) & r1_yellow_2(u1_struct_0(A),A,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D),k7_grcat_1(A))))))))))) # label(t19_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5059 (all A (-v3_struct_0(A) & l1_orders_2(A) & v1_yellow_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k7_waybel_1(A,k10_lattice3(A,B,C)) = k11_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C))))))))) # label(t87_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5060 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (C = a_2_0_waybel_1(A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & m2_relset_1(D,u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) -> (k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C) = D -> v7_waybel_1(D,k5_yellow_0(A,C))))))))))))) # label(t50_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5061 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k6_waybel_1(A,C,D),k6_waybel_1(A,B,D)))))))))))) # label(t78_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5062 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) & -v3_struct_0(A) -> v18_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) & v3_waybel_1(k1_waybel_1(A,k2_yellow_1(k8_waybel_0(A)),k4_yellow_2(A),k3_yellow_2(A)),A,k2_yellow_1(k8_waybel_0(A))))) # label(t60_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5063 (all A all B (-v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) -> v1_funct_1(k4_waybel_1(A,B)) & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5064 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) -> (v5_waybel_1(C,A,B) <-> (exists D (v1_funct_1(D) & v3_waybel_1(k1_waybel_1(A,B,D,C),A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))))))))))) # label(d12_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5065 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) -> (k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D) = k7_grcat_1(A) -> v2_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v2_funct_1(C)))))))))) # label(t25_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5066 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,C,D) -> r1_orders_2(A,k6_waybel_1(A,B,C),k6_waybel_1(A,B,D)))))))))))) # label(t79_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5067 (all A (v2_orders_2(A) & v3_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> v3_lattice3(k2_yellow_2(A,A,B))))))) # label(t57_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5068 (all A all B all C (-v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & l1_orders_2(B) & v2_orders_2(B) -> (r2_hidden(A,a_2_1_waybel_1(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,k7_yellow_2(u1_struct_0(B),B,C,D),D)))))) # label(fraenkel_a_2_1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5069 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> C = k2_waybel_1(A,B,C))))))) # label(t32_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5070 (all A (v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & -v3_struct_0(k3_yellow_1(A)))) # label(fc1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5071 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_yellow_0(A) = k6_waybel_1(A,B,B)))))) # label(t73_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5072 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (C = a_2_0_waybel_1(A,B) -> m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C)))))))))))) # label(t48_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5073 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> r5_waybel_1(k2_yellow_2(k2_yellow_1(k8_waybel_0(A)),k2_yellow_1(k8_waybel_0(A)),k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),k3_yellow_2(A),k4_yellow_2(A))),A) & v7_waybel_1(k7_funct_2(u1_struct_0(k2_yellow_1(k8_waybel_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))),k3_yellow_2(A),k4_yellow_2(A)),k2_yellow_1(k8_waybel_0(A))))) # label(t61_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5074 (all A all B (l1_orders_2(A) & l1_orders_2(B) -> (exists C m1_waybel_1(C,A,B)))) # label(existence_m1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5075 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_waybel_1(A,B,k4_yellow_0(A)) = k4_yellow_0(A)))))) # label(t76_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5076 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) -> -(v3_lattice3(B) & (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) -> -((all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,D,E),k5_pre_topc(B,A,C,k6_waybel_0(A,E))))) & v3_waybel_1(k1_waybel_1(A,B,D,C),A,B)))) & v18_waybel_0(C,B,A)))))))) # label(t16_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5077 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (v5_orders_3(C,A,B) & (all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k7_waybel_0(B,E))))) <-> v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(t11_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5078 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v5_orders_3(B,A,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = a_2_1_waybel_1(A,B) -> v7_yellow_0(k5_yellow_0(A,C),A))))))))) # label(t53_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5079 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> k7_grcat_1(k2_yellow_2(A,B,C)) = k3_waybel_1(A,B,C))))))) # label(d17_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5080 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_0_waybel_1(A,B) = C -> (v17_waybel_0(B,A,A) -> v7_yellow_0(k5_yellow_0(A,C),A) & v7_yellow_0(k2_yellow_2(A,A,B),A)) & (v21_waybel_0(B,A,A) -> v3_waybel_0(k5_yellow_0(A,C),A) & v3_waybel_0(k2_yellow_2(A,A,B),A)))))))))) # label(t54_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5081 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) -> (exists B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & v8_waybel_1(B,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(B) & v1_relat_1(B) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)))))) # label(rc3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5082 (all A (-v3_struct_0(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v8_waybel_1(B,A) -> v3_waybel_1(k1_waybel_1(A,k2_yellow_2(A,A,B),k2_waybel_1(A,A,B),k3_waybel_1(A,A,B)),A,k2_yellow_2(A,A,B))))))) # label(t42_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5083 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> -(v17_waybel_0(C,A,B) & (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> -(v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) & (all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k7_waybel_0(B,E)))))))) & v3_lattice3(A)))))))) # label(t15_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5084 (exists A (v1_orders_2(A) & v3_orders_2(A) & v2_lattice3(A) & v2_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5085 (all A (l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (a_2_1_waybel_1(A,B) = C -> (v18_waybel_0(B,A,A) -> v8_yellow_0(k5_yellow_0(A,C),A) & v8_yellow_0(k2_yellow_2(A,A,B),A)) & (v22_waybel_0(B,A,A) -> v4_waybel_0(k5_yellow_0(A,C),A) & v4_waybel_0(k2_yellow_2(A,A,B),A)))))))))) # label(t55_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5086 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) -> v5_waybel_1(D,A,B) & v4_waybel_1(C,A,B)))))))))) # label(t10_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5087 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> (all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (a_2_1_waybel_1(A,B) = C -> v1_funct_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C)) & v1_funct_2(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))) & m2_relset_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(k5_yellow_0(A,C)),u1_struct_0(k5_yellow_0(A,C))))))))))) # label(t49_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5088 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v6_waybel_1(B,A) <-> v11_quantal1(B) & v5_orders_3(B,A,A)))))) # label(d13_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5089 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v2_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_4_waybel_1(A,B,C)))))) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_waybel_1(k4_waybel_1(A,B),A,A)))))) # label(t67_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5090 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (v3_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) -> (v5_waybel_1(C,A,B) -> v18_waybel_0(C,B,A)))))))) # label(t14_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5091 (all A all B all C (l1_orders_2(A) & -v3_struct_0(B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) & l1_orders_2(B) & -v3_struct_0(A) -> v1_funct_1(k2_waybel_1(A,B,C)) & m2_relset_1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))) & v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C))))) # label(dt_k2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5092 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v9_waybel_1(A) -> v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v4_orders_2(A) & -v3_struct_0(A)))) # label(cc5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5093 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r1_yellow_0(A,C) & r2_hidden(k1_yellow_0(A,C),C) & B = k1_yellow_0(A,C) <-> r4_waybel_1(A,B,C))))))) # label(d7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5094 (all A (v3_orders_2(A) & v2_lattice3(A) & v3_yellow_0(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (v2_waybel_1(A) & v10_waybel_1(A) -> v9_waybel_1(A) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k7_waybel_1(A,k7_waybel_1(A,B)) = B))) & (v9_waybel_1(A) & (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k7_waybel_1(A,k7_waybel_1(A,B)))) -> v10_waybel_1(A) & v2_waybel_1(A)))) # label(t90_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5095 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_waybel_1(A,B,C) = k4_yellow_0(A) <-> r1_orders_2(A,B,C))))))))) # label(t72_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5096 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k11_lattice3(A,B,C) = k11_lattice3(A,B,k6_waybel_1(A,B,C))))))))) # label(t80_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5097 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (m1_waybel_1(C,A,B) -> (v3_waybel_1(C,A,B) <-> (exists D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & (exists E (C = k1_waybel_1(A,B,D,E) & v5_orders_3(D,A,B) & (all F (m1_subset_1(F,u1_struct_0(B)) -> (all G (m1_subset_1(G,u1_struct_0(A)) -> (r1_orders_2(A,k7_yellow_2(u1_struct_0(B),A,E,F),G) <-> r1_orders_2(B,F,k7_yellow_2(u1_struct_0(A),B,D,G))))))) & v5_orders_3(E,B,A) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(E))) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))))))))))) # label(d10_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5098 (all A (l1_orders_2(A) -> v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A),A,A))) # label(fc2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5099 (all A (-v3_struct_0(A) & l1_orders_2(A) -> v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v23_waybel_0(k7_grcat_1(A),A,A) & v6_waybel_1(k7_grcat_1(A),A) & v5_orders_3(k7_grcat_1(A),A,A) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(k7_grcat_1(A)))) # label(fc3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5100 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v9_waybel_1(A) -> v2_yellow_0(A) & -v3_struct_0(A)))) # label(cc7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5101 (all A (l1_orders_2(A) -> (v11_waybel_1(A) & -v3_struct_0(A) -> v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v2_yellow_0(A) & v1_lattice3(A) & v3_orders_2(A) & -v3_struct_0(A)))) # label(cc10_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.91 5102 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (v2_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v4_waybel_1(C,A,B) -> v17_waybel_0(C,A,B)))))))) # label(t13_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5103 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_pre_topc(A,A,k4_waybel_1(A,B),k6_waybel_0(A,C)) = a_3_0_waybel_1(A,B,C))))))) # label(t62_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5104 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (r2_yellow_0(A,C) & k2_yellow_0(A,C) = B & r2_hidden(k2_yellow_0(A,C),C) <-> r3_waybel_1(A,B,C))))))) # label(d6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5105 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v7_waybel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,C) & r1_tarski(C,u1_struct_0(k2_yellow_2(A,A,B))) -> k1_yellow_0(k2_yellow_2(A,A,B),C) = k7_yellow_2(u1_struct_0(A),A,B,k1_yellow_0(A,C)) & r1_yellow_0(k2_yellow_2(A,A,B),C)))) & v18_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B))))))) # label(t58_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5106 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r1_orders_2(A,D,E) -> r1_orders_2(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E))))))) <-> v5_orders_3(C,A,B)))))))) # label(d2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5107 (all A (v2_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> v1_relat_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(k7_grcat_1(A),A) & v7_waybel_1(k7_grcat_1(A),A) & v23_waybel_0(k7_grcat_1(A),A,A) & v5_orders_3(k7_grcat_1(A),A,A) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)))) # label(fc4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5108 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all D (v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(D) -> (C = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) & k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(A),D,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)) = D -> v11_quantal1(k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),D,C)) & v11_quantal1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D))))))))))) # label(t22_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5109 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> v2_waybel_1(A)))) # label(t69_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5110 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v2_funct_1(C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k7_yellow_2(u1_struct_0(A),B,C,E) = k7_yellow_2(u1_struct_0(A),B,C,D) -> E = D)))))))))))) # label(d1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5111 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> -((all C (v2_orders_2(C) & l1_orders_2(C) & v4_orders_2(C) & v3_orders_2(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (all E (m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) & v1_funct_1(E) -> -(v3_waybel_1(k1_waybel_1(A,C,D,E),A,C) & B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E)))))))) & v8_waybel_1(B,A)))))) # label(t43_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5112 (all A (v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_yellow_0(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_yellow_0(A,a_3_5_waybel_1(A,B,C)) = k12_lattice3(A,C,k1_yellow_0(A,B))))))) -> v2_waybel_1(A)))) # label(t68_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5113 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (r2_waybel_1(A,B) <-> r2_hidden(k1_yellow_0(A,B),B) & r1_yellow_0(A,B))))) # label(d5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5114 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v9_waybel_1(A) -> v2_waybel_1(A) & -v3_struct_0(A)))) # label(cc6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5115 (all A (-v3_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,k10_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)),k7_waybel_1(A,k11_lattice3(A,B,C)))))))))) # label(t88_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5116 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_waybel_1(A,k10_lattice3(A,B,C),D) = k11_lattice3(A,k6_waybel_1(A,B,D),k6_waybel_1(A,C,D))))))))))) # label(t81_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5117 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v8_waybel_1(B,A) <-> r1_yellow_2(u1_struct_0(A),A,B,k7_grcat_1(A)) & v6_waybel_1(B,A)))))) # label(d15_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5118 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_orders_2(A,C,k6_waybel_1(A,B,C))))))))) # label(t75_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5119 (all A all B all C (v1_funct_1(C) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & l1_struct_0(B) & -v3_struct_0(B) & l1_struct_0(A) & -v3_struct_0(A) -> (v2_funct_1(C) <-> v1_waybel_1(C,A,B)))) # label(redefinition_v1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5120 (all A (l1_orders_2(A) -> (-v3_struct_0(A) & v11_waybel_1(A) -> v1_lattice3(A) & v10_waybel_1(A) & v2_waybel_1(A) & v3_yellow_0(A) & v2_yellow_0(A) & v1_yellow_0(A) & v2_lattice3(A) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A)))) # label(cc8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5121 (all A (-v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v10_waybel_1(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)))) # label(fc9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5122 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k6_waybel_1(A,C,B) = k4_yellow_0(A) & k4_yellow_0(A) = k6_waybel_1(A,B,C) -> B = C)))))))) # label(t74_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5123 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_waybel_1(A,k4_yellow_0(A),B) = B))))) # label(t77_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5124 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C (l1_orders_2(C) -> (r5_waybel_1(A,B) & r5_waybel_1(B,C) -> r5_waybel_1(A,C)))))))) # label(t8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5125 $T # label(dt_m1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5126 (all A (-v3_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) -> (v3_lattice3(B) -> (v18_waybel_0(C,B,A) <-> v5_orders_3(C,B,A) & v5_waybel_1(C,A,B))))))))) # label(t18_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5127 (all A all B (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) -> v1_funct_1(k4_waybel_1(A,B)) & v1_partfun1(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & v5_orders_3(k4_waybel_1(A,B),A,A) & v1_funct_2(k4_waybel_1(A,B),u1_struct_0(A),u1_struct_0(A)) & -v1_xboole_0(k4_waybel_1(A,B)) & v1_relat_1(k4_waybel_1(A,B)))) # label(fc8_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5128 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v10_waybel_1(A) & v2_waybel_1(A) & v3_yellow_0(A) & l1_orders_2(A) & v2_orders_2(A) <-> v11_waybel_1(A)))) # label(d25_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5129 (all A all B all C (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l1_orders_2(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & k3_yellow_0(B) = k11_lattice3(B,C,D))) <-> r2_hidden(A,a_2_2_waybel_1(B,C))))) # label(fraenkel_a_2_2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5130 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (r5_waybel_1(A,B) -> r5_waybel_1(B,A)))))) # label(t7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5131 (all A all B all C all D (v4_orders_2(B) & v2_lattice3(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (r2_hidden(A,a_3_3_waybel_1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & k12_lattice3(B,D,E) = A))))) # label(fraenkel_a_3_3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5132 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> -((all C (v3_orders_2(C) & l1_orders_2(C) & v4_orders_2(C) & v2_orders_2(C) & -v3_struct_0(C) -> (all D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) -> -(v5_orders_3(D,A,C) & v2_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v5_orders_3(E,C,A) & k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(C),E,D) = k7_grcat_1(C) & B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) & v2_funct_1(E)))))))) & v6_waybel_1(B,A)))))) # label(t37_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5133 (all A (-v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) -> (all B (v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v5_orders_3(B,A,A) -> (all C (v4_orders_2(C) & l1_orders_2(C) & v3_orders_2(C) & v2_orders_2(C) & -v3_struct_0(C) -> (all D (v1_funct_2(D,u1_struct_0(C),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) & v1_funct_1(D) -> (all E (v1_funct_2(E,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(E) -> -(v3_waybel_1(k1_waybel_1(C,A,D,E),C,A) & k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),E,D) = B))))))) | v7_waybel_1(B,A)))))) # label(t41_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5134 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k7_yellow_2(u1_struct_0(A),A,k5_waybel_1(A,B),C) = k6_waybel_1(A,B,C))))))) # label(d21_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5135 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) & r1_yellow_2(u1_struct_0(A),A,k7_grcat_1(A),B) <-> v7_waybel_1(B,A)))))) # label(d14_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5136 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (v5_orders_3(C,A,B) -> v5_orders_3(k2_waybel_1(A,B,C),A,k2_yellow_2(A,B,C))))))))) # label(t33_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5137 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (v9_waybel_1(A) -> v2_yellow_0(A)))) # label(t71_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5138 (all A (-v3_struct_0(A) & l1_orders_2(A) & v2_orders_2(A) -> v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v5_orders_3(k7_grcat_1(A),A,A) & v23_waybel_0(k7_grcat_1(A),A,A) & v8_waybel_1(k7_grcat_1(A),A) & v7_waybel_1(k7_grcat_1(A),A) & v6_waybel_1(k7_grcat_1(A),A) & -v1_xboole_0(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_relat_1(k7_grcat_1(A)))) # label(fc5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5139 (exists A (l1_orders_2(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v11_waybel_1(A) & v10_waybel_1(A) & v9_waybel_1(A) & v2_waybel_1(A) & v3_yellow_0(A) & v1_yellow_0(A) & v4_orders_2(A) & -v3_struct_0(A))) # label(rc4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5140 (all A all B (l1_orders_2(A) & -v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v2_orders_2(B) & v4_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v1_funct_1(C) & v5_waybel_1(C,B,A) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> v1_funct_1(C) & -v1_xboole_0(C) & v18_waybel_0(C,A,B) & v20_waybel_0(C,A,B) & v22_waybel_0(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))))))) # label(cc2_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5141 (all A (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> ((all E (m1_subset_1(E,u1_struct_0(A)) -> r4_waybel_1(B,k7_yellow_2(u1_struct_0(A),B,C,E),k5_pre_topc(B,A,D,k1_struct_0(A,E))))) -> k7_grcat_1(A) = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),C,D)))))))))) # label(t28_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5142 (all A all B all C all D (l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,C,E) & r2_hidden(E,D))) <-> r2_hidden(A,a_3_1_waybel_1(B,C,D))))) # label(fraenkel_a_3_1_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5143 (all A (v1_yellow_0(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v1_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> B = k10_lattice3(A,k3_yellow_0(A),B)) & (v2_lattice3(A) -> k3_yellow_0(A) = k11_lattice3(A,k3_yellow_0(A),B)))))) # label(t4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5144 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (r2_yellow_0(A,B) & r2_hidden(k2_yellow_0(A,B),B) <-> r1_waybel_1(A,B))))) # label(d4_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5145 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> ((exists C (v3_orders_2(C) & l1_orders_2(C) & (exists D (v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & (exists E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) & v5_orders_3(D,A,C) & B = k7_funct_2(u1_struct_0(A),u1_struct_0(C),u1_struct_0(A),D,E) & k7_grcat_1(C) = k7_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(C),E,D) & v5_orders_3(E,C,A) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)))) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) & v1_funct_1(D))) & v4_orders_2(C) & v2_orders_2(C) & -v3_struct_0(C))) -> v6_waybel_1(B,A)))))) # label(t38_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5146 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> k2_waybel_1(A,B,C) = k8_relat_1(u1_struct_0(k2_yellow_2(A,B,C)),C))))))) # label(d16_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5147 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v2_waybel_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k10_lattice3(A,k11_lattice3(A,B,C),k11_lattice3(A,B,D)) = k11_lattice3(A,B,k10_lattice3(A,C,D))))))))))) # label(d3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5148 (all A (v3_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,B,C) -> r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D))))))))))) # label(t3_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5149 (all A (l1_orders_2(A) -> (all B (l1_orders_2(B) -> (all C ((exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & (exists E (C = k4_tarski(D,E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(E))))) <-> m1_waybel_1(C,A,B))))))) # label(d9_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5150 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_orders_2(A) & -v3_struct_0(A) -> m1_subset_1(k7_waybel_1(A,B),u1_struct_0(A)))) # label(dt_k7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5151 (all A (v2_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v5_orders_3(k4_waybel_1(A,B),A,A))))) # label(t63_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5152 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> (all B (l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v3_lattice3(A) -> (v17_waybel_0(C,A,B) <-> v5_orders_3(C,A,B) & v4_waybel_1(C,A,B))))))))) # label(t17_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5153 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> (all C (m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) -> (v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> r3_waybel_1(A,k7_yellow_2(u1_struct_0(B),A,D,E),k5_pre_topc(A,B,C,k1_struct_0(B,E)))))))))))))) # label(t23_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5154 (all A (v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & v3_yellow_0(A) & v2_lattice3(A) & v3_orders_2(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> B = k7_waybel_1(A,k7_waybel_1(A,B)))) & v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r6_waybel_1(A,B,k7_waybel_1(A,B))))))) # label(t89_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5155 (all A (v2_orders_2(A) & v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) -> (v2_waybel_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k13_lattice3(A,B,k12_lattice3(A,C,D)) = k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,B,D))))))))))) # label(t6_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5156 (all A (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> (all B (m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(B) -> (v8_waybel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,u1_struct_0(k2_yellow_2(A,A,B))) & r2_yellow_0(A,C) -> r2_yellow_0(k2_yellow_2(A,A,B),C) & k2_yellow_0(k2_yellow_2(A,A,B),C) = k7_yellow_2(u1_struct_0(A),A,B,k2_yellow_0(A,C))))) & v17_waybel_0(k2_waybel_1(A,A,B),A,k2_yellow_2(A,A,B))))))) # label(t59_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5157 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v9_waybel_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_orders_2(A,D,k6_waybel_1(A,C,B)) <-> r1_orders_2(A,k11_lattice3(A,C,D),B))))))))))) # label(t70_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5158 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v4_waybel_1(C,A,B) <-> (exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) & v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)))))))))) # label(d11_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5159 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) -> (v6_waybel_1(B,A) -> k8_yellow_2(u1_struct_0(A),A,B) = k2_relat_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,a_2_0_waybel_1(A,B))) & k8_yellow_2(u1_struct_0(A),A,B) = k2_relat_1(k2_partfun1(u1_struct_0(A),u1_struct_0(A),B,a_2_1_waybel_1(A,B)))))))) # label(t47_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5160 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v7_waybel_1(B,A) & r2_yellow_0(A,C) & r1_tarski(C,k8_yellow_2(u1_struct_0(A),A,B)) -> k2_yellow_0(A,C) = k7_yellow_2(u1_struct_0(A),A,B,k2_yellow_0(A,C))))))))) # label(t30_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5161 (all A (v4_orders_2(A) & l1_orders_2(A) & v2_yellow_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v1_lattice3(A) -> k4_yellow_0(A) = k10_lattice3(A,k4_yellow_0(A),B)) & (v2_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) -> k11_lattice3(A,k4_yellow_0(A),B) = B))))) # label(t5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5162 (all A all B all C (l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & -v3_struct_0(B) & l1_orders_2(A) & -v3_struct_0(A) -> v2_funct_1(k3_waybel_1(A,B,C)) & v5_orders_3(k3_waybel_1(A,B,C),k2_yellow_2(A,B,C),B) & v1_partfun1(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) & v1_funct_2(k3_waybel_1(A,B,C),u1_struct_0(k2_yellow_2(A,B,C)),u1_struct_0(B)) & -v1_xboole_0(k3_waybel_1(A,B,C)) & v1_funct_1(k3_waybel_1(A,B,C)) & v1_relat_1(k3_waybel_1(A,B,C)))) # label(fc7_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5163 (all A all B (l1_orders_2(A) & l1_orders_2(B) -> r5_waybel_1(A,A))) # label(reflexivity_r5_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5164 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k10_lattice3(A,B,C) = k4_yellow_0(A) & k3_yellow_0(A) = k11_lattice3(A,B,C) <-> r6_waybel_1(A,B,C)))))))) # label(d23_waybel_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5165 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v6_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) & -v7_conlat_1(B,A) -> B = k1_binop_1(k10_conlat_1(A),B,k6_conlat_1(A)))))) # label(t44_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5166 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) & v6_conlat_1(B,A) -> (all C (-v7_conlat_1(C,A) & l3_conlat_1(C,A) & v9_conlat_1(C,A) & v6_conlat_1(C,A) -> k1_binop_1(k10_conlat_1(A),B,C) = k1_binop_1(k10_conlat_1(A),C,B))))))) # label(t37_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5167 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (exists B (l3_conlat_1(B,A) & v6_conlat_1(B,A) & -v7_conlat_1(B,A) & v9_conlat_1(B,A) & v11_conlat_1(B,A))))) # label(rc16_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5168 (all A all B (l2_conlat_1(B) & -v3_conlat_1(B) -> (r2_hidden(A,a_1_0_conlat_1(B)) <-> (exists C exists D (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(B))) & m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(B))) & -v7_conlat_1(g3_conlat_1(B,C,D),B) & k8_funct_2(k1_zfmisc_1(u1_conlat_1(B)),k1_zfmisc_1(u2_conlat_1(B)),k1_conlat_1(B),C) = D & C = k8_funct_2(k1_zfmisc_1(u2_conlat_1(B)),k1_zfmisc_1(u1_conlat_1(B)),k2_conlat_1(B),D) & A = g3_conlat_1(B,C,D)))))) # label(fraenkel_a_1_0_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5169 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> -v3_struct_0(k11_conlat_1(A)) & l3_lattices(k11_conlat_1(A)) & v3_lattices(k11_conlat_1(A)))) # label(dt_k11_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5170 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> (v10_conlat_1(B,A) <-> u4_conlat_1(A,B) = u1_conlat_1(A)))))) # label(d14_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5171 (all A all B all C (-v3_conlat_1(B) & m1_subset_1(C,u2_conlat_1(B)) & l2_conlat_1(B) -> ((exists D (m1_subset_1(D,u1_conlat_1(B)) & D = A & r1_conlat_1(B,D,C))) <-> r2_hidden(A,a_2_3_conlat_1(B,C))))) # label(fraenkel_a_2_3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5172 (all A all B (-v3_conlat_1(A) & l2_conlat_1(A) & m1_conlat_1(B,A) -> (exists C m2_conlat_1(C,A,B)))) # label(existence_m2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5173 (all A (-v3_conlat_1(A) & l1_conlat_1(A) -> -v1_xboole_0(u2_conlat_1(A)))) # label(fc1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5174 (all A (v3_conlat_1(A) & l1_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> v8_conlat_1(B,A))))) # label(cc2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5175 (all A all B (l3_conlat_1(B,A) & l1_conlat_1(A) -> m1_subset_1(u4_conlat_1(A,B),k1_zfmisc_1(u1_conlat_1(A))))) # label(dt_u4_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5176 (all A all B (l3_conlat_1(B,A) & l1_conlat_1(A) -> m1_subset_1(u5_conlat_1(A,B),k1_zfmisc_1(u2_conlat_1(A))))) # label(dt_u5_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5177 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> k7_conlat_1(A) = a_1_0_conlat_1(A))) # label(d20_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5178 (all A (l1_orders_2(A) & -v3_struct_0(A) -> (all B (l1_orders_2(B) & -v3_struct_0(B) -> (all C (m1_waybel_1(C,A,B) -> (v5_conlat_1(C,A,B) <-> (exists D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & (exists E (v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & v5_waybel_0(D,A,B) & v5_waybel_0(E,B,A) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (all G (m1_subset_1(G,u1_struct_0(A)) -> (all H (m1_subset_1(H,u1_struct_0(B)) -> (all I (m1_subset_1(I,u1_struct_0(B)) -> r1_orders_2(A,F,k1_waybel_0(B,A,E,k1_waybel_0(A,B,D,F))) & r1_orders_2(B,H,k1_waybel_0(A,B,D,k1_waybel_0(B,A,E,H))))))))))) & k1_waybel_1(A,B,D,E) = C & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(E))) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))))))))))) # label(d10_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5179 (all A all B (l2_conlat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) & -v3_conlat_1(A) -> (exists C m3_conlat_1(C,A,B)))) # label(existence_m3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5180 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (l3_conlat_1(B,A) & v8_conlat_1(B,A) -> -(v6_conlat_1(B,A) & -v7_conlat_1(B,A) & B != k6_conlat_1(A) & B != k5_conlat_1(A) & l3_conlat_1(B,A) & v9_conlat_1(B,A)))))) # label(t28_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5181 (exists A (l2_conlat_1(A) & v4_conlat_1(A))) # label(rc5_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5182 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> (r1_tarski(k12_mcart_1(u1_conlat_1(A),u2_conlat_1(A),B,C),u3_conlat_1(A)) <-> r1_tarski(C,k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))))))))) # label(t10_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5183 (all A (l1_conlat_1(A) -> (exists B (v6_conlat_1(B,A) & l3_conlat_1(B,A))))) # label(rc10_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5184 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> (r1_tarski(k12_mcart_1(u1_conlat_1(A),u2_conlat_1(A),B,C),u3_conlat_1(A)) <-> r1_tarski(B,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C))))))))) # label(t9_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5185 $T # label(dt_u2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5186 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (v9_conlat_1(B,A) & l3_conlat_1(B,A) & -v7_conlat_1(B,A) -> (all C (-v7_conlat_1(C,A) & v9_conlat_1(C,A) & l3_conlat_1(C,A) -> (r1_tarski(u5_conlat_1(A,B),u5_conlat_1(A,C)) <-> r2_conlat_1(A,C,B)))))))) # label(t33_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5187 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))) -> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B) = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))))))) # label(t8_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5188 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,u1_struct_0(k11_conlat_1(A))) -> (all C (m1_subset_1(C,u1_struct_0(k11_conlat_1(A))) -> (r2_conlat_1(A,k12_conlat_1(A,B),k12_conlat_1(A,C)) <-> r3_lattices(k11_conlat_1(A),B,C)))))))) # label(t47_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5189 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v9_conlat_1(B,A) & l3_conlat_1(B,A) & -v7_conlat_1(B,A) & v6_conlat_1(B,A) -> (all C (v6_conlat_1(C,A) & -v7_conlat_1(C,A) & v9_conlat_1(C,A) & l3_conlat_1(C,A) -> (all D (-v7_conlat_1(D,A) & v9_conlat_1(D,A) & l3_conlat_1(D,A) & v6_conlat_1(D,A) -> k1_binop_1(k9_conlat_1(A),k1_binop_1(k9_conlat_1(A),B,C),D) = k1_binop_1(k9_conlat_1(A),B,k1_binop_1(k9_conlat_1(A),C,D)))))))))) # label(t38_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5190 (all A (l1_conlat_1(A) & -v3_conlat_1(A) -> -v1_xboole_0(u1_conlat_1(A)))) # label(fc2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5191 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> v1_funct_2(k9_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) & m2_relset_1(k9_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) & v1_funct_1(k9_conlat_1(A)))) # label(dt_k9_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5192 $T # label(d3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5193 (all A (-v3_conlat_1(A) & l1_conlat_1(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))))))) # label(rc8_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5194 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> u2_conlat_1(A) = k1_funct_1(k1_conlat_1(A),k1_xboole_0))) # label(t18_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5195 (all A all B all C (l1_conlat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> l3_conlat_1(g3_conlat_1(A,B,C),A) & v6_conlat_1(g3_conlat_1(A,B,C),A))) # label(dt_g3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5196 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) & v1_funct_2(B,k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) -> (B = k1_conlat_1(A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) -> a_2_0_conlat_1(A,C) = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),B,C)))))))) # label(d6_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5197 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (-v1_xboole_0(B) -> (m1_conlat_1(B,A) <-> (all C (r2_hidden(C,B) -> -v7_conlat_1(C,A) & v9_conlat_1(C,A) & l3_conlat_1(C,A)))))))) # label(d18_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5198 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (-v7_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) & v6_conlat_1(B,A) -> (all C (v6_conlat_1(C,A) & -v7_conlat_1(C,A) & v9_conlat_1(C,A) & l3_conlat_1(C,A) -> k1_binop_1(k9_conlat_1(A),B,C) = k1_binop_1(k9_conlat_1(A),C,B))))))) # label(t36_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5199 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> (v11_conlat_1(B,A) <-> u5_conlat_1(A,B) = u2_conlat_1(A)))))) # label(d15_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5200 (exists A (l1_conlat_1(A) & v1_conlat_1(A) & -v2_conlat_1(A))) # label(rc2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5201 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> k5_subset_1(u1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C)) = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k4_subset_1(u2_conlat_1(A),B,C)))))))) # label(t17_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5202 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) -> (k1_xboole_0 = u5_conlat_1(A,B) -> v10_conlat_1(B,A)) & (u4_conlat_1(A,B) = k1_xboole_0 -> v11_conlat_1(B,A)))))) # label(t25_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5203 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> v1_funct_1(k10_conlat_1(A)) & m2_relset_1(k10_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) & v1_funct_2(k10_conlat_1(A),k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)))) # label(dt_k10_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5204 (all A (v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) & v4_orders_2(B) & v3_orders_2(B) -> (all C (m1_waybel_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) & v1_funct_1(E) -> (C = k1_waybel_1(A,B,D,E) -> (v5_conlat_1(C,A,B) <-> (all F (m1_subset_1(F,u1_struct_0(A)) -> (all G (m1_subset_1(G,u1_struct_0(B)) -> (r3_orders_2(B,G,k1_waybel_0(A,B,D,F)) <-> r3_orders_2(A,F,k1_waybel_0(B,A,E,G))))))))))))))))))) # label(t13_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5205 (all A all B all C (-v3_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(B))) & l2_conlat_1(B) -> ((exists D (D = A & (all E (m1_subset_1(E,u1_conlat_1(B)) -> (r2_hidden(E,C) -> r1_conlat_1(B,E,D)))) & m1_subset_1(D,u2_conlat_1(B)))) <-> r2_hidden(A,a_2_0_conlat_1(B,C))))) # label(fraenkel_a_2_0_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5206 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (exists B (l3_conlat_1(B,A) & v6_conlat_1(B,A) & v10_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A))))) # label(rc15_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5207 $T # label(t32_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5208 (exists A l1_conlat_1(A)) # label(existence_l1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5209 (all A all B all C (m1_relset_1(C,A,B) -> (all D all E all F (g2_conlat_1(A,B,C) = g2_conlat_1(D,E,F) -> E = B & C = F & D = A)))) # label(free_g2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5210 (exists A (v1_conlat_1(A) & l1_conlat_1(A))) # label(rc1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5211 (all A all B (-v3_conlat_1(A) & l2_conlat_1(A) & m1_conlat_1(B,A) -> (all C (m2_conlat_1(C,A,B) -> -v7_conlat_1(C,A) & l3_conlat_1(C,A) & v9_conlat_1(C,A))))) # label(dt_m2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5212 (exists A (l2_conlat_1(A) & -v2_conlat_1(A) & v4_conlat_1(A))) # label(rc6_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5213 (all A (-v3_conlat_1(A) & l1_conlat_1(A) -> (exists B (-v7_conlat_1(B,A) & v6_conlat_1(B,A) & l3_conlat_1(B,A))))) # label(rc11_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5214 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) -> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k4_subset_1(u1_conlat_1(A),B,C)) = k5_subset_1(u2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),C)))))))) # label(t16_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5215 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (v6_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) -> (all C (-v7_conlat_1(C,A) & v9_conlat_1(C,A) & l3_conlat_1(C,A) & v6_conlat_1(C,A) -> C = k1_binop_1(k10_conlat_1(A),k1_binop_1(k9_conlat_1(A),B,C),C))))))) # label(t40_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5216 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> v5_conlat_1(k1_waybel_1(k3_yellow_1(u1_conlat_1(A)),k3_yellow_1(u2_conlat_1(A)),k3_conlat_1(A),k4_conlat_1(A)),k3_yellow_1(u1_conlat_1(A)),k3_yellow_1(u2_conlat_1(A))))) # label(t15_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5217 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> v1_funct_1(k2_conlat_1(A)) & m2_relset_1(k2_conlat_1(A),k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))) & v1_funct_2(k2_conlat_1(A),k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))))) # label(dt_k2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5218 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> m1_conlat_1(k8_conlat_1(A),A))) # label(dt_k8_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.92 5219 $T # label(dt_l1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5220 (all A all B all C (l2_conlat_1(B) & m1_subset_1(C,u1_conlat_1(B)) & -v3_conlat_1(B) -> (r2_hidden(A,a_2_2_conlat_1(B,C)) <-> (exists D (m1_subset_1(D,u2_conlat_1(B)) & D = A & r1_conlat_1(B,C,D)))))) # label(fraenkel_a_2_2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5221 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (exists B (l3_conlat_1(B,A) & -v7_conlat_1(B,A) & v9_conlat_1(B,A))))) # label(rc13_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5222 (all A (l1_conlat_1(A) -> (exists B l3_conlat_1(B,A)))) # label(existence_l3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5223 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & v3_orders_2(B) & -v3_struct_0(B) -> (all C (m1_waybel_1(C,A,B) -> (v5_conlat_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) -> (C = k1_waybel_1(A,B,D,E) -> k7_funct_2(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),k7_funct_2(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),E,D),E) = E & D = k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),D,E),D))))))))))))) # label(t14_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5224 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) & m2_relset_1(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) & v1_funct_1(B) -> (B = k10_conlat_1(A) <-> (all C (v6_conlat_1(C,A) & l3_conlat_1(C,A) & v9_conlat_1(C,A) & -v7_conlat_1(C,A) -> (all D (v9_conlat_1(D,A) & l3_conlat_1(D,A) & -v7_conlat_1(D,A) & v6_conlat_1(D,A) -> (exists E (m1_subset_1(E,k1_zfmisc_1(u1_conlat_1(A))) & (exists F (E = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k4_subset_1(u1_conlat_1(A),u4_conlat_1(A,C),u4_conlat_1(A,D)))) & k5_subset_1(u2_conlat_1(A),u5_conlat_1(A,C),u5_conlat_1(A,D)) = F & g3_conlat_1(A,E,F) = k1_binop_1(B,C,D) & m1_subset_1(F,k1_zfmisc_1(u2_conlat_1(A)))))))))))))))) # label(d22_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5225 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> (r1_tarski(B,C) -> r1_tarski(k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))))))))) # label(t4_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5226 $T # label(dt_l3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5227 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) & v1_funct_2(B,k2_zfmisc_1(k8_conlat_1(A),k8_conlat_1(A)),k8_conlat_1(A)) & v1_funct_1(B) -> (B = k9_conlat_1(A) <-> (all C (v9_conlat_1(C,A) & l3_conlat_1(C,A) & -v7_conlat_1(C,A) & v6_conlat_1(C,A) -> (all D (v6_conlat_1(D,A) & -v7_conlat_1(D,A) & v9_conlat_1(D,A) & l3_conlat_1(D,A) -> (exists E ((exists F (m1_subset_1(F,k1_zfmisc_1(u2_conlat_1(A))) & k1_binop_1(B,C,D) = g3_conlat_1(A,E,F) & F = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k4_subset_1(u2_conlat_1(A),u5_conlat_1(A,C),u5_conlat_1(A,D)))) & k5_subset_1(u1_conlat_1(A),u4_conlat_1(A,C),u4_conlat_1(A,D)) = E)) & m1_subset_1(E,k1_zfmisc_1(u1_conlat_1(A)))))))))))))) # label(d21_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5228 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (-v7_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) -> r2_conlat_1(A,k6_conlat_1(A),B) & r2_conlat_1(A,B,k5_conlat_1(A)))))) # label(t34_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5229 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (l3_conlat_1(B,A) & v10_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) & v6_conlat_1(B,A) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) & (exists D (m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A))) & D = k1_funct_1(k1_conlat_1(A),k1_funct_1(k2_conlat_1(A),k1_xboole_0)) & k1_funct_1(k2_conlat_1(A),k1_xboole_0) = C & B = g3_conlat_1(A,C,D))))) <-> B = k5_conlat_1(A)))))) # label(d16_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5230 (all A (l1_conlat_1(A) -> (v1_conlat_1(A) -> A = g1_conlat_1(u1_conlat_1(A),u2_conlat_1(A))))) # label(abstractness_v1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5231 (all A all B (m1_subset_1(B,u1_struct_0(k11_conlat_1(A))) & l2_conlat_1(A) & -v3_conlat_1(A) -> v6_conlat_1(k12_conlat_1(A,B),A) & v9_conlat_1(k12_conlat_1(A,B),A) & l3_conlat_1(k12_conlat_1(A,B),A) & -v7_conlat_1(k12_conlat_1(A,B),A))) # label(dt_k12_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5232 (all A (l1_conlat_1(A) & -v3_conlat_1(A) -> (exists B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))))))) # label(rc9_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5233 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (l3_conlat_1(B,A) & v8_conlat_1(B,A) -> -(-v7_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) & -v11_conlat_1(B,A) & -v10_conlat_1(B,A)))))) # label(t27_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5234 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,u1_conlat_1(A)) -> a_2_2_conlat_1(A,B) = k1_funct_1(k1_conlat_1(A),k1_tarski(B)))))) # label(t1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5235 (all A (l2_conlat_1(A) -> (v4_conlat_1(A) -> g2_conlat_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(A)) = A))) # label(abstractness_v4_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5236 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> v1_funct_2(k3_conlat_1(A),u1_struct_0(k3_yellow_1(u1_conlat_1(A))),u1_struct_0(k3_yellow_1(u2_conlat_1(A)))) & m2_relset_1(k3_conlat_1(A),u1_struct_0(k3_yellow_1(u1_conlat_1(A))),u1_struct_0(k3_yellow_1(u2_conlat_1(A)))) & v1_funct_1(k3_conlat_1(A)))) # label(dt_k3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5237 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (r2_hidden(B,k8_conlat_1(A)) <-> v6_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A))))) # label(t35_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5238 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,u2_conlat_1(A)) -> k1_funct_1(k2_conlat_1(A),k1_tarski(B)) = a_2_3_conlat_1(A,B))))) # label(t2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5239 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> (B = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)) <-> (exists C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) & v9_conlat_1(g3_conlat_1(A,B,C),A) & l3_conlat_1(g3_conlat_1(A,B,C),A) & -v7_conlat_1(g3_conlat_1(A,B,C),A)))))))) # label(t21_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5240 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v1_funct_2(B,k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))) & m2_relset_1(B,k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A))) & v1_funct_1(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),B,C) = a_2_1_conlat_1(A,C))) <-> B = k2_conlat_1(A)))))) # label(d7_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5241 (all A (v2_conlat_1(A) & l1_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> v7_conlat_1(B,A))))) # label(cc1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5242 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> -v1_xboole_0(k7_conlat_1(A)))) # label(dt_k7_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5243 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> r1_tarski(B,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))))))) # label(t5_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5244 $T # label(t12_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5245 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (-v7_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) & v6_conlat_1(B,A) -> k1_binop_1(k9_conlat_1(A),B,k5_conlat_1(A)) = B)))) # label(t42_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5246 (all A (l1_conlat_1(A) -> (v2_conlat_1(A) <-> v1_xboole_0(u2_conlat_1(A)) & v1_xboole_0(u1_conlat_1(A))))) # label(d1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5247 (exists A l2_conlat_1(A)) # label(existence_l2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5248 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,u1_struct_0(k11_conlat_1(A))) -> k12_conlat_1(A,B) = B)))) # label(d24_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5249 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))) -> r1_tarski(B,k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))))))) # label(t6_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5250 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (l3_conlat_1(B,A) & v11_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) & v6_conlat_1(B,A) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) & (exists D (k1_funct_1(k1_conlat_1(A),k1_xboole_0) = D & C = k1_funct_1(k2_conlat_1(A),k1_funct_1(k1_conlat_1(A),k1_xboole_0)) & g3_conlat_1(A,C,D) = B & m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A))))))) <-> k6_conlat_1(A) = B))))) # label(d17_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5251 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> (v9_conlat_1(B,A) <-> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),u4_conlat_1(A,B)) = u5_conlat_1(A,B) & u4_conlat_1(A,B) = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),u5_conlat_1(A,B))))))) # label(d13_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5252 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> v3_lattices(k11_conlat_1(A)) & v5_lattices(k11_conlat_1(A)) & v7_lattices(k11_conlat_1(A)) & v9_lattices(k11_conlat_1(A)) & v10_lattices(k11_conlat_1(A)) & v8_lattices(k11_conlat_1(A)) & v6_lattices(k11_conlat_1(A)) & v4_lattices(k11_conlat_1(A)) & -v3_struct_0(k11_conlat_1(A)))) # label(fc4_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5253 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (exists B (v6_conlat_1(B,A) & -v7_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A))))) # label(rc14_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5254 (all A all B (l1_conlat_1(A) & l3_conlat_1(B,A) -> (v6_conlat_1(B,A) -> B = g3_conlat_1(A,u4_conlat_1(A,B),u5_conlat_1(A,B))))) # label(abstractness_v6_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5255 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> -v7_conlat_1(k5_conlat_1(A),A) & l3_conlat_1(k5_conlat_1(A),A) & v10_conlat_1(k5_conlat_1(A),A) & v9_conlat_1(k5_conlat_1(A),A) & v6_conlat_1(k5_conlat_1(A),A))) # label(dt_k5_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5256 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> k1_funct_1(k2_conlat_1(A),k1_xboole_0) = u1_conlat_1(A))) # label(t19_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5257 (all A (l1_conlat_1(A) -> (v3_conlat_1(A) <-> v1_xboole_0(u1_conlat_1(A)) | v1_xboole_0(u2_conlat_1(A))))) # label(d2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5258 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) & -v1_xboole_0(B) & l2_conlat_1(A) & -v3_conlat_1(A) -> (all C (m3_conlat_1(C,A,B) -> -v7_conlat_1(C,A) & l3_conlat_1(C,A) & v9_conlat_1(C,A))))) # label(dt_m3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5259 (all A (l1_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> (v7_conlat_1(B,A) <-> v1_xboole_0(u4_conlat_1(A,B)) & v1_xboole_0(u5_conlat_1(A,B))))))) # label(d11_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5260 (exists A (-v3_conlat_1(A) & v1_conlat_1(A) & l1_conlat_1(A))) # label(rc3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5261 (all A all B (m1_conlat_1(B,A) & l2_conlat_1(A) & -v3_conlat_1(A) -> (all C (m1_subset_1(C,B) <-> m2_conlat_1(C,A,B))))) # label(redefinition_m2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5262 (all A (l1_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> (v8_conlat_1(B,A) <-> v1_xboole_0(u4_conlat_1(A,B)) | v1_xboole_0(u5_conlat_1(A,B))))))) # label(d12_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5263 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) -> (r1_tarski(B,C) -> r1_tarski(k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),C),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))))))))) # label(t3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5264 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (-v7_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & v6_conlat_1(B,A) -> k5_conlat_1(A) = k1_binop_1(k10_conlat_1(A),B,k5_conlat_1(A)))))) # label(t43_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5265 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> v10_lattices(k11_conlat_1(A)) & l3_lattices(k11_conlat_1(A)) & v4_lattice3(k11_conlat_1(A)) & -v3_struct_0(k11_conlat_1(A)))) # label(t48_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5266 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_conlat_1(B,A) -> -v1_xboole_0(B))))) # label(dt_m1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5267 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v9_conlat_1(B,A) & l3_conlat_1(B,A) & -v7_conlat_1(B,A) -> (all C (l3_conlat_1(C,A) & v9_conlat_1(C,A) & -v7_conlat_1(C,A) -> (r2_conlat_1(A,B,C) <-> r1_tarski(u4_conlat_1(A,B),u4_conlat_1(A,C))))))))) # label(d19_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5268 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (v6_conlat_1(B,A) & -v7_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) -> k6_conlat_1(A) = k1_binop_1(k9_conlat_1(A),B,k6_conlat_1(A)))))) # label(t45_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5269 $T # label(d4_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5270 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))) = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))))) # label(t7_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5271 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A))) -> (-v7_conlat_1(g3_conlat_1(A,C,D),A) & v9_conlat_1(g3_conlat_1(A,C,D),A) & r1_tarski(B,D) & l3_conlat_1(g3_conlat_1(A,C,D),A) -> r1_tarski(k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B)),D)))))) & l3_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))),A) & v9_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))),A) & -v7_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))),A))))) # label(t22_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5272 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (-v7_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & v6_conlat_1(B,A) -> (all C (v6_conlat_1(C,A) & v9_conlat_1(C,A) & l3_conlat_1(C,A) & -v7_conlat_1(C,A) -> B = k1_binop_1(k9_conlat_1(A),B,k1_binop_1(k10_conlat_1(A),B,C)))))))) # label(t41_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5273 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> (r1_tarski(B,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),C)) <-> r1_tarski(C,k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))))))))) # label(t11_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5274 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,u1_conlat_1(A)) -> (all C (m1_subset_1(C,u2_conlat_1(A)) -> (r1_conlat_1(A,B,C) <-> r2_hidden(k4_tarski(B,C),u3_conlat_1(A))))))))) # label(d5_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5275 $T # label(t29_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5276 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> -v7_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),A) & (all C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u2_conlat_1(A))) -> (-v7_conlat_1(g3_conlat_1(A,C,D),A) & l3_conlat_1(g3_conlat_1(A,C,D),A) & r1_tarski(B,C) & v9_conlat_1(g3_conlat_1(A,C,D),A) -> r1_tarski(k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),C)))))) & l3_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),A) & v9_conlat_1(g3_conlat_1(A,k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B)),A))))) # label(t20_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5277 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> -v3_struct_0(k11_conlat_1(A)) & v7_lattices(k11_conlat_1(A)) & v9_lattices(k11_conlat_1(A)) & v4_lattice3(k11_conlat_1(A)) & v10_lattices(k11_conlat_1(A)) & v8_lattices(k11_conlat_1(A)) & v6_lattices(k11_conlat_1(A)) & v5_lattices(k11_conlat_1(A)) & v4_lattices(k11_conlat_1(A)) & v3_lattices(k11_conlat_1(A)))) # label(fc5_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5278 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) & -v1_xboole_0(B) & l2_conlat_1(A) & -v3_conlat_1(A) -> (all C (m3_conlat_1(C,A,B) <-> m1_subset_1(C,B))))) # label(redefinition_m3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5279 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> k4_conlat_1(A) = k2_conlat_1(A))) # label(d9_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5280 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(u1_conlat_1(A))) & l3_conlat_1(g3_conlat_1(A,C,B),A) & v9_conlat_1(g3_conlat_1(A,C,B),A) & -v7_conlat_1(g3_conlat_1(A,C,B),A))) <-> B = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B))))))) # label(t23_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5281 (exists A (l1_conlat_1(A) & v1_conlat_1(A) & v3_conlat_1(A) & v2_conlat_1(A))) # label(rc4_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5282 (all A all B all C all D (g1_conlat_1(C,D) = g1_conlat_1(A,B) -> A = C & B = D)) # label(free_g1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5283 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> m2_relset_1(k1_conlat_1(A),k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) & v1_funct_2(k1_conlat_1(A),k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A))) & v1_funct_1(k1_conlat_1(A)))) # label(dt_k1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5284 (all A all B all C (m1_relset_1(C,A,B) -> v4_conlat_1(g2_conlat_1(A,B,C)) & l2_conlat_1(g2_conlat_1(A,B,C)))) # label(dt_g2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5285 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (exists B m1_conlat_1(B,A)))) # label(existence_m1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5286 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> g3_lattices(k8_conlat_1(A),k10_conlat_1(A),k9_conlat_1(A)) = k11_conlat_1(A))) # label(d23_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5287 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> v1_funct_1(k4_conlat_1(A)) & m2_relset_1(k4_conlat_1(A),u1_struct_0(k3_yellow_1(u2_conlat_1(A))),u1_struct_0(k3_yellow_1(u1_conlat_1(A)))) & v1_funct_2(k4_conlat_1(A),u1_struct_0(k3_yellow_1(u2_conlat_1(A))),u1_struct_0(k3_yellow_1(u1_conlat_1(A)))))) # label(dt_k4_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5288 (exists A (v4_conlat_1(A) & -v3_conlat_1(A) & l2_conlat_1(A))) # label(rc7_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5289 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> u5_conlat_1(A,k6_conlat_1(A)) = u2_conlat_1(A) & u1_conlat_1(A) = u4_conlat_1(A,k5_conlat_1(A)))) # label(t24_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5290 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> v10_lattices(k11_conlat_1(A)) & l3_lattices(k11_conlat_1(A)) & -v3_struct_0(k11_conlat_1(A)))) # label(t46_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5291 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) -> (all C (v9_conlat_1(C,A) & l3_conlat_1(C,A) & -v7_conlat_1(C,A) -> (r1_tarski(u5_conlat_1(A,C),u5_conlat_1(A,B)) <-> r2_conlat_1(A,B,C)))))))) # label(t31_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5292 (all A all B (v1_conlat_1(g1_conlat_1(A,B)) & l1_conlat_1(g1_conlat_1(A,B)))) # label(dt_g1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5293 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> v11_conlat_1(k6_conlat_1(A),A) & l3_conlat_1(k6_conlat_1(A),A) & v9_conlat_1(k6_conlat_1(A),A) & -v7_conlat_1(k6_conlat_1(A),A) & v6_conlat_1(k6_conlat_1(A),A))) # label(dt_k6_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5294 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> k8_conlat_1(A) = k7_conlat_1(A))) # label(redefinition_k8_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5295 $T # label(dt_u1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5296 (all A (l2_conlat_1(A) -> l1_conlat_1(A))) # label(dt_l2_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5297 (all A (l2_conlat_1(A) -> m2_relset_1(u3_conlat_1(A),u1_conlat_1(A),u2_conlat_1(A)))) # label(dt_u3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5298 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> k3_conlat_1(A) = k1_conlat_1(A))) # label(d8_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5299 (all A (-v3_conlat_1(A) & l1_conlat_1(A) -> (exists B (l3_conlat_1(B,A) & v8_conlat_1(B,A) & v6_conlat_1(B,A))))) # label(rc12_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5300 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (v6_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) -> (u5_conlat_1(A,B) = k1_xboole_0 -> k5_conlat_1(A) = B) & (k1_xboole_0 = u4_conlat_1(A,B) -> B = k6_conlat_1(A)))))) # label(t26_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5301 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v6_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) -> (all C (v6_conlat_1(C,A) & -v7_conlat_1(C,A) & v9_conlat_1(C,A) & l3_conlat_1(C,A) -> (all D (v6_conlat_1(D,A) & -v7_conlat_1(D,A) & l3_conlat_1(D,A) & v9_conlat_1(D,A) -> k1_binop_1(k10_conlat_1(A),k1_binop_1(k10_conlat_1(A),B,C),D) = k1_binop_1(k10_conlat_1(A),B,k1_binop_1(k10_conlat_1(A),C,D)))))))))) # label(t39_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5302 $T # label(t30_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5303 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> -v1_xboole_0(k7_conlat_1(A)))) # label(fc3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5304 (all A all B all C (l1_conlat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) & m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(A))) -> (all D all E all F (g3_conlat_1(A,B,C) = g3_conlat_1(D,E,F) -> A = D & B = E & F = C)))) # label(free_g3_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5305 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(u2_conlat_1(B))) & l2_conlat_1(B) & -v3_conlat_1(B) -> (r2_hidden(A,a_2_1_conlat_1(B,C)) <-> (exists D (m1_subset_1(D,u1_conlat_1(B)) & (all E (m1_subset_1(E,u2_conlat_1(B)) -> (r2_hidden(E,C) -> r1_conlat_1(B,D,E)))) & D = A))))) # label(fraenkel_a_2_1_conlat_1) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5306 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (v2_lattice6(k1_lattice2(A)) <-> v1_lattice6(A)))) # label(t1_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5307 (all A all B all C (-v3_struct_0(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & v4_lattice3(B) & v10_lattices(B) -> (r2_hidden(A,a_2_2_lattice6(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & D = A & D != C & r3_lattices(B,C,D)))))) # label(fraenkel_a_2_2_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5308 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v9_lattice6(B,A) -> r1_tarski(k5_lattice6(A),B)))))) # label(t27_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5309 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (v1_wellfnd1(k3_lattice3(A)) <-> v1_lattice6(A)))) # label(d3_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5310 (all A (v10_lattices(A) & v2_lattice6(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(C != B & (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r1_lattice6(A,B,D) & r3_lattices(A,C,D)))) & r3_lattices(A,C,B)))))))) # label(t4_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5311 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v5_lattice6(B,A) -> v4_lattice6(B,A)))))) # label(t21_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5312 (all A (v10_lattices(A) & v2_lattice6(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> v9_lattice6(k5_lattice6(A),A))) # label(fc2_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5313 (exists A (v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v13_lattices(A) & v2_lattice6(A) & v4_lattice3(A) & v15_lattices(A) & v14_lattices(A) & v7_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc3_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5314 (all A (v10_lattices(A) & l3_lattices(A) & v14_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r1_lattice6(A,B,k6_lattices(A)))))) # label(t5_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5315 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (C != D -> (r1_lattice6(A,B,C) & r1_lattice6(A,B,D) -> k3_lattices(A,D,C) = B) & (r1_lattice6(A,D,B) & r1_lattice6(A,C,B) -> k4_lattices(A,D,C) = B)))))))))) # label(t2_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5316 (all A (v10_lattices(A) & v4_lattice3(A) & v1_lattice6(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_lattice6(B,A) <-> (exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice6(A,D,B) -> D = C))) & r1_lattice6(A,C,B)))))))) # label(t14_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5317 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_lattice6(A,B,k5_lattices(A)) <-> v5_lattice6(B,A)))))) # label(d10_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5318 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,k4_lattice6(A,B),B) & r3_lattices(A,B,k3_lattice6(A,B)))))) # label(t9_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5319 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l3_lattices(B) -> (r2_hidden(A,a_2_0_lattice6(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & r2_hidden(D,C) & k4_lattice3(B,D) = A))))) # label(fraenkel_a_2_0_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5320 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k4_lattice6(A,B) <-> v4_lattice6(B,A)))))) # label(d9_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5321 (all A (-v3_struct_0(A) & v1_lattice6(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> v8_lattice6(k6_lattice6(A),A))) # label(fc3_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5322 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice6(A,B,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> -(r3_lattices(A,C,D) & B != D & C != D & r3_lattices(A,D,B)))) & r3_lattices(A,C,B) & C != B))))))) # label(d5_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5323 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v10_lattices(A) -> m1_subset_1(k1_lattice6(A,B),k1_zfmisc_1(u1_struct_0(k3_lattice3(A)))))) # label(dt_k1_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5324 (all A (v4_lattice3(A) & v2_lattice6(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((exists C (m1_subset_1(C,u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattice6(A,B,D) -> C = D))) & r1_lattice6(A,B,C))) <-> v4_lattice6(B,A)))))) # label(t15_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5325 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_lattice6(B,A) <-> k3_lattice6(A,B) != B))))) # label(d8_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5326 (all A all B (l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_lattice3(A)))) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k2_lattice6(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_lattice6) # label(axiom) # label(non_clause). [assumption]. 6.99/6.93 5327 (all A (v10_lattices(A) & v4_lattice3(A) & v2_lattice6(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_lattices(A) != B -> (v4_lattice6(B,A) <-> v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A)))))))) # label(t19_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5328 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,k1_zfmisc_1(B)) & k15_lattice3(A,D) = C)))) <-> v8_lattice6(B,A)))))) # label(d13_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5329 (exists A (l3_lattices(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v10_lattices(A) & v15_lattices(A) & v7_lattice6(A) & v4_lattice3(A) & v14_lattices(A) & v13_lattices(A) & v9_lattices(A) & v8_lattices(A) & v5_lattices(A) & -v3_struct_0(A))) # label(rc5_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5330 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> v2_waybel_6(k4_lattice3(A,k6_lattices(A)),k3_lattice3(A)) & k6_lattices(A) = k3_lattice6(A,k6_lattices(A)))) # label(t10_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5331 (all A (l3_lattices(A) & v2_lattice6(A) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r1_lattice6(A,B,C)))))))) # label(t8_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5332 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v2_lattice6(A) <-> v1_wellfnd1(k7_lattice3(k3_lattice3(A)))))) # label(d4_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5333 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v1_lattice6(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k6_lattices(A) -> (v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) <-> v3_lattice6(B,A))))))) # label(t17_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5334 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_lattice3(A)))) -> a_2_1_lattice6(A,B) = k2_lattice6(A,B))))) # label(d2_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5335 (all A all B all C all D (l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & E = A & r2_hidden(E,C) & r3_lattices(B,E,D))) <-> r2_hidden(A,a_3_0_lattice6(B,C,D))))) # label(fraenkel_a_3_0_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5336 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> m1_subset_1(k6_lattice6(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k6_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5337 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> k5_lattices(A) = k4_lattice6(A,k5_lattices(A)) & v3_waybel_6(k4_lattice3(A,k5_lattices(A)),k3_lattice3(A)))) # label(t11_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5338 (exists A (v7_lattices(A) & v9_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v1_lattice6(A) & v4_lattice3(A) & v10_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc2_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5339 (all A all B (-v3_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) -> (r2_hidden(A,a_1_0_lattice6(B)) <-> (exists C (m1_subset_1(C,u1_struct_0(B)) & C = A & v3_lattice6(C,B)))))) # label(fraenkel_a_1_0_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.93 5340 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v4_lattice6(B,A) -> r1_lattice6(A,B,k4_lattice6(A,B)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice6(A,B,C) -> k4_lattice6(A,B) = C)))))))) # label(t13_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5341 (all A (l3_lattices(A) -> (v6_group_1(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v10_lattices(A) & v1_lattice6(A) & v9_lattices(A) & v5_lattices(A) & v4_lattices(A)))) # label(cc2_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5342 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v6_group_1(A) -> v1_orders_2(k3_lattice3(A)) & v1_yellow_0(k3_lattice3(A)) & v2_yellow_0(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v1_wellfnd1(k3_lattice3(A)) & v3_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) & v25_waybel_0(k3_lattice3(A)) & v24_waybel_0(k3_lattice3(A)) & v3_yellow_0(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc1_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5343 (all A (v1_lattice6(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k6_lattices(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r1_lattice6(A,C,B)))))))) # label(t6_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5344 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_lattice6(A,k6_lattices(A),B) <-> v6_lattice6(B,A)))))) # label(d11_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5345 (all A (l3_lattices(A) -> (v10_lattices(A) & v6_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v10_lattices(A) & v2_lattice6(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A)))) # label(cc3_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5346 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> a_1_1_lattice6(A) = k6_lattice6(A))) # label(d16_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5347 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v4_lattice6(B,A) -> v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A))))))) # label(t18_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5348 (all A all B (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) -> m1_subset_1(k3_lattice6(A,B),u1_struct_0(A)))) # label(dt_k3_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5349 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & v4_lattice3(A) & v10_lattices(A) -> m1_subset_1(k4_lattice6(A,B),u1_struct_0(A)))) # label(dt_k4_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5350 (all A all B all C (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_lattice3(B)))) -> ((exists D (m1_subset_1(D,u1_struct_0(k3_lattice3(B))) & k5_lattice3(B,D) = A & r2_hidden(D,C))) <-> r2_hidden(A,a_2_1_lattice6(B,C))))) # label(fraenkel_a_2_1_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5351 (exists A (l3_lattices(A) & -v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v9_lattices(A) & v13_lattices(A) & v14_lattices(A) & v6_group_1(A) & v15_lattices(A) & v10_lattices(A) & v8_lattices(A))) # label(rc1_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5352 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_lattice6(A,B) = a_2_0_lattice6(A,B))))) # label(d1_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5353 (exists A (l3_lattices(A) & -v3_struct_0(A) & v3_lattices(A) & v5_lattices(A) & v6_lattices(A) & v3_realset2(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v4_lattices(A))) # label(rc4_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5354 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_lattice6(B,A) -> r1_lattice6(A,k3_lattice6(A,B),B) & (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattice6(A,C,B) -> k3_lattice6(A,B) = C)))))))) # label(t12_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5355 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v8_lattice6(B,A) -> r1_tarski(k6_lattice6(A),B)))))) # label(t26_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5356 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k16_lattice3(A,a_3_1_lattice6(A,B,C)))) <-> v9_lattice6(B,A)))))) # label(t24_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5357 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> v5_lattice6(D,A)))) & B = k15_lattice3(A,C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) <-> v7_lattice6(A)))) # label(d12_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5358 (all A all B (v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & -v3_struct_0(B) -> ((exists C (A = C & v4_lattice6(C,B) & m1_subset_1(C,u1_struct_0(B)))) <-> r2_hidden(A,a_1_1_lattice6(B))))) # label(fraenkel_a_1_1_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5359 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v9_lattice6(B,A) <-> v4_waybel_6(k1_lattice6(A,B),k3_lattice3(A))))))) # label(t25_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5360 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> k5_lattice6(A) = a_1_0_lattice6(A))) # label(d15_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5361 (all A (v10_lattices(A) & l3_lattices(A) & v6_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(k5_lattices(A) != B & B != k6_lattices(A) & -((v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) -> v3_lattice6(B,A)) & (v4_lattice6(B,A) -> v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A))) & (v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) -> v4_lattice6(B,A)) & (v3_lattice6(B,A) -> v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A))))))))) # label(t20_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5362 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattice6(A,B) = k16_lattice3(A,a_2_2_lattice6(A,B)))))) # label(d6_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5363 (all A (v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -r1_lattice6(A,k5_lattices(A),B))))) # label(t7_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5364 (all A (v10_lattices(A) & l3_lattices(A) & v1_lattice6(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -((all D (m1_subset_1(D,u1_struct_0(A)) -> -(r3_lattices(A,D,C) & r1_lattice6(A,D,B)))) & B != C & r3_lattices(A,B,C)))))))) # label(t3_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5365 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v6_lattice6(B,A) -> v3_lattice6(B,A)))))) # label(t22_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5366 (all A all B all C all D (v10_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_lattice6(B,C,D)) <-> (exists E (r2_hidden(E,C) & r3_lattices(B,D,E) & A = E & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5367 (all A all B all C (l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_3_lattice6(B,C)) <-> (exists D (m1_subset_1(D,u1_struct_0(B)) & D != C & r3_lattices(B,D,C) & D = A))))) # label(fraenkel_a_2_3_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5368 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_lattice6(B,A) -> v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A))))))) # label(t16_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5369 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k16_lattice3(A,D) = C & m1_subset_1(D,k1_zfmisc_1(B)))))) <-> v9_lattice6(B,A)))))) # label(d14_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5370 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v8_lattice6(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k15_lattice3(A,a_3_0_lattice6(A,B,C)) = C))))))) # label(t23_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5371 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v6_group_1(A) & v10_lattices(A) -> -v3_struct_0(A) & v5_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v15_lattices(A) & v4_lattice3(A) & v13_lattices(A) & v7_lattices(A) & v6_lattices(A) & v4_lattices(A)))) # label(cc1_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5372 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattice6(A,B) = k15_lattice3(A,a_2_3_lattice6(A,B)))))) # label(d7_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5373 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> m1_subset_1(k5_lattice6(A),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_lattice6) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5374 (all A all B (-v3_conlat_1(A) & l2_conlat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) -> l3_conlat_1(k2_conlat_2(A,B),A) & v9_conlat_1(k2_conlat_2(A,B),A) & -v7_conlat_1(k2_conlat_2(A,B),A))) # label(dt_k2_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5375 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_conlat_1(A))) -> k1_funct_1(k2_conlat_1(k7_conlat_2(A)),B) = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),B))))) # label(t18_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5376 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) -> v9_conlat_1(k16_lattice3(k11_conlat_1(A),B),A) & v9_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) & l3_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) & -v7_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) & l3_conlat_1(k16_lattice3(k11_conlat_1(A),B),A) & -v7_conlat_1(k16_lattice3(k11_conlat_1(A),B),A))))) # label(t4_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5377 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,u1_conlat_1(A)) -> (all C (m1_subset_1(C,u2_conlat_1(A)) -> -v7_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A) & v9_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A) & l3_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A) & v9_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A) & -v7_conlat_1(k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A) & l3_conlat_1(k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A))))))) # label(t11_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5378 (all A all B (l2_conlat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) & -v3_conlat_1(A) -> -v7_conlat_1(k3_conlat_2(A,B),A) & v9_conlat_1(k3_conlat_2(A,B),A) & l3_conlat_1(k3_conlat_2(A,B),A))) # label(dt_k3_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5379 (all A all B (-v3_conlat_1(A) & l2_conlat_1(A) & l3_conlat_1(B,A) -> l3_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) & v6_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)))) # label(dt_k8_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5380 (all A all B (-v3_conlat_1(A) & v6_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) & l2_conlat_1(A) -> m1_subset_1(k1_conlat_2(A,B),u1_struct_0(k11_conlat_1(A))))) # label(dt_k1_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5381 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) & v1_funct_2(B,u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) -> (B = k4_conlat_2(A) <-> (all C (m1_subset_1(C,u1_conlat_1(A)) -> (exists D ((exists E (E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k6_domain_1(u1_conlat_1(A),C)) & D = k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k6_domain_1(u1_conlat_1(A),C))) & k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),B,C) = g3_conlat_1(A,D,E) & m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(A)))))))))))) # label(d4_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5382 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> m2_relset_1(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) & v1_funct_2(k4_conlat_2(A),u1_conlat_1(A),u1_struct_0(k11_conlat_1(A))) & v1_funct_1(k4_conlat_2(A)))) # label(dt_k4_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5383 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) -> r3_lattices(A,D,E)))))) -> v2_funct_1(C)))))))) # label(l19_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5384 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> m2_relset_1(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) & v1_funct_2(k5_conlat_2(A),u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) & v1_funct_1(k5_conlat_2(A)))) # label(dt_k5_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5385 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> m1_lattice4(k10_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))))) # label(dt_k10_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5386 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) & -v1_xboole_0(B) -> k1_funct_1(k1_conlat_1(A),k1_funct_1(k2_conlat_1(A),k3_tarski(a_2_3_conlat_2(A,B)))) = u5_conlat_1(A,k2_conlat_2(A,B)) & k1_setfam_1(a_2_2_conlat_2(A,B)) = u4_conlat_1(A,k2_conlat_2(A,B)))))) # label(t8_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5387 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (-v7_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) & v6_conlat_1(B,A) -> k16_lattice3(k11_conlat_1(A),a_2_5_conlat_2(A,B)) = B)))) # label(t10_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5388 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) & v1_funct_2(B,u2_conlat_1(A),u1_struct_0(k11_conlat_1(A))) -> (k5_conlat_2(A) = B <-> (all C (m1_subset_1(C,u2_conlat_1(A)) -> (exists D ((exists E (g3_conlat_1(A,D,E) = k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),B,C) & E = k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k6_domain_1(u2_conlat_1(A),C))) & k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k6_domain_1(u2_conlat_1(A),C)) = D & m1_subset_1(E,k1_zfmisc_1(u2_conlat_1(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_conlat_1(A)))))))))))) # label(d5_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5389 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> k3_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k5_conlat_1(A) & k2_conlat_2(A,k2_subset_1(u1_struct_0(k11_conlat_1(A)))) = k6_conlat_1(A))) # label(t6_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5390 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> r1_filter_1(k11_conlat_1(k6_conlat_2(A)),A))) # label(t15_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5391 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> g2_conlat_1(u1_struct_0(A),u1_struct_0(A),k2_lattice3(A)) = k6_conlat_2(A))) # label(d6_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5392 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> k6_lattices(k11_conlat_1(A)) = k5_conlat_1(A) & k6_conlat_1(A) = k5_lattices(k11_conlat_1(A)))) # label(t1_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5393 (all A (v4_conlat_1(A) & l2_conlat_1(A) & -v3_conlat_1(A) -> A = k7_conlat_2(k7_conlat_2(A)))) # label(t17_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5394 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v6_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) & -v7_conlat_1(B,A) -> k15_lattice3(k11_conlat_1(A),a_2_4_conlat_2(A,B)) = B)))) # label(t9_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5395 (all A all B (-v3_conlat_1(A) & l2_conlat_1(A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) & -v7_conlat_1(B,A) -> k9_conlat_2(A,B) = k8_conlat_2(A,B))) # label(redefinition_k9_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5396 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> v9_lattice6(k5_relset_1(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A)),k11_conlat_1(A)) & v8_lattice6(k5_relset_1(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A)),k11_conlat_1(A)))) # label(t12_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5397 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) -> k2_conlat_2(A,B) = k16_lattice3(k11_conlat_1(A),B))))) # label(d2_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5398 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) & -v1_xboole_0(B) -> k1_setfam_1(a_2_3_conlat_2(A,B)) = u5_conlat_1(A,k3_conlat_2(A,B)) & k1_funct_1(k2_conlat_1(A),k1_funct_1(k1_conlat_1(A),k3_tarski(a_2_2_conlat_2(A,B)))) = u4_conlat_1(A,k3_conlat_2(A,B)))))) # label(t7_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5399 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> v3_lattices(k11_conlat_1(A)) & v4_lattices(k11_conlat_1(A)) & v5_lattices(k11_conlat_1(A)) & v13_lattices(k11_conlat_1(A)) & v14_lattices(k11_conlat_1(A)) & v4_lattice3(k11_conlat_1(A)) & v15_lattices(k11_conlat_1(A)) & v10_lattices(k11_conlat_1(A)) & v9_lattices(k11_conlat_1(A)) & v8_lattices(k11_conlat_1(A)) & v7_lattices(k11_conlat_1(A)) & v6_lattices(k11_conlat_1(A)) & -v3_struct_0(k11_conlat_1(A)))) # label(fc1_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5400 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (v6_conlat_1(B,A) & -v7_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) -> B = k1_conlat_2(A,B))))) # label(d1_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5401 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k1_lattice2(A)) & v3_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v4_lattice3(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))) # label(fc2_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5402 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> l2_conlat_1(k6_conlat_2(A)) & v4_conlat_1(k6_conlat_2(A)) & -v3_conlat_1(k6_conlat_2(A)))) # label(dt_k6_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5403 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,u1_conlat_1(A)) -> (all C (m1_subset_1(C,u2_conlat_1(A)) -> (r3_lattices(k11_conlat_1(A),k8_funct_2(u1_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),k8_funct_2(u2_conlat_1(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C)) <-> r1_conlat_1(A,B,C)))))))) # label(t13_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5404 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (u1_struct_0(B) = k5_relset_1(u1_struct_0(A),u1_struct_0(B),C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) <-> r3_lattices(A,D,E)))))) & v2_funct_1(C) -> m1_lattice4(C,A,B)))))))) # label(l20_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5405 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) -> k3_conlat_2(A,B) = k15_lattice3(k11_conlat_1(A),B))))) # label(d3_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5406 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_conlat_1(A)))) -> k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),k5_setfam_1(u1_conlat_1(A),B)) = k1_setfam_1(a_2_0_conlat_2(A,B)))))) # label(t2_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5407 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> -(k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),u5_conlat_1(A,B)) = u4_conlat_1(A,B) & v7_conlat_1(B,A) & k8_funct_2(k1_zfmisc_1(u1_conlat_1(A)),k1_zfmisc_1(u2_conlat_1(A)),k1_conlat_1(A),u4_conlat_1(A,B)) = u5_conlat_1(A,B)))))) # label(l21_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5408 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u2_conlat_1(A)))) & -v1_xboole_0(B) -> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),k5_setfam_1(u2_conlat_1(A),B)) = k1_setfam_1(a_2_1_conlat_2(A,B)))))) # label(t3_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5409 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> k7_conlat_2(A) = g2_conlat_1(u2_conlat_1(A),u1_conlat_1(A),k6_relset_1(u1_conlat_1(A),u2_conlat_1(A),u3_conlat_1(A))))) # label(d7_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5410 (all A all B (-v7_conlat_1(B,A) & v9_conlat_1(B,A) & l3_conlat_1(B,A) & l2_conlat_1(A) & -v3_conlat_1(A) -> l3_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)) & v9_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)) & -v7_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)) & v6_conlat_1(k9_conlat_2(A,B),k7_conlat_2(A)))) # label(dt_k9_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5411 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (v4_lattice3(A) <-> (exists B (-v3_conlat_1(B) & l2_conlat_1(B) & r1_filter_1(k11_conlat_1(B),A)))))) # label(t16_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5412 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> l2_conlat_1(k7_conlat_2(A)) & v4_conlat_1(k7_conlat_2(A)) & -v3_conlat_1(k7_conlat_2(A)))) # label(dt_k7_conlat_2) # label(axiom) # label(non_clause). [assumption]. 7.04/6.94 5413 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) -> (all B (-v3_conlat_1(B) & l2_conlat_1(B) -> ((exists C (m2_relset_1(C,u1_conlat_1(B),u1_struct_0(A)) & (exists D ((all E (m1_subset_1(E,u1_conlat_1(B)) -> (all F (m1_subset_1(F,u2_conlat_1(B)) -> (r3_lattices(A,k8_funct_2(u1_conlat_1(B),u1_struct_0(A),C,E),k8_funct_2(u2_conlat_1(B),u1_struct_0(A),D,F)) <-> r1_conlat_1(B,E,F)))))) & v9_lattice6(k5_relset_1(u2_conlat_1(B),u1_struct_0(A),D),A) & v8_lattice6(k5_relset_1(u1_conlat_1(B),u1_struct_0(A),C),A) & m2_relset_1(D,u2_conlat_1(B),u1_struct_0(A)) & v1_funct_2(D,u2_conlat_1(B),u1_struct_0(A)) & v1_funct_1(D))) & v1_funct_2(C,u1_conlat_1(B),u1_struct_0(A)) & v1_funct_1(C))) <-> r1_filter_1(k11_conlat_1(B),A)))))) # label(t14_conlat_2) # label(axiom) # label(non_clause). [assumption]. 8.11/8.07 5414 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (l3_conlat_1(B,A) -> (all C (l3_conlat_1(C,k7_conlat_2(A)) & v6_conlat_1(C,k7_conlat_2(A)) -> (u5_conlat_1(A,B) = u4_conlat_1(k7_conlat_2(A),C) & u4_conlat_1(A,B) = u5_conlat_1(k7_conlat_2(A),C) <-> C = k8_conlat_2(A,B)))))))) # label(d8_conlat_2) # label(axiom) # label(non_clause). [assumption]. 8.11/8.07 5415 (all A (-v3_conlat_1(A) & l2_conlat_1(A) -> k5_conlat_1(A) = k2_conlat_2(A,k1_pre_topc(k11_conlat_1(A))) & k6_conlat_1(A) = k3_conlat_2(A,k1_pre_topc(k11_conlat_1(A))))) # label(t5_conlat_2) # label(axiom) # label(non_clause). [assumption]. 8.11/8.07 5416 (all A (l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u2_conlat_1(A))) -> k8_funct_2(k1_zfmisc_1(u2_conlat_1(A)),k1_zfmisc_1(u1_conlat_1(A)),k2_conlat_1(A),B) = k1_funct_1(k1_conlat_1(k7_conlat_2(A)),B))))) # label(t19_conlat_2) # label(axiom) # label(non_clause). [assumption]. 8.11/8.07 5417 -(all A (v4_conlat_1(A) & l2_conlat_1(A) & -v3_conlat_1(A) -> (all B (v6_conlat_1(B,A) & -v7_conlat_1(B,A) & l3_conlat_1(B,A) & v9_conlat_1(B,A) -> B = k9_conlat_2(k7_conlat_2(A),k9_conlat_2(A,B)))))) # label(t20_conlat_2) # label(negated_conjecture) # label(non_clause). [assumption]. 8.11/8.07 8.11/8.07 ============================== end of process non-clausal formulas === 8.11/8.07 8.11/8.07 ============================== PROCESS INITIAL CLAUSES =============== 8.11/8.07 8.11/8.07 ============================== PREDICATE ELIMINATION ================= 8.11/8.07 5418 -r2_tarski(A,B) | r2_hidden(k4_tarski(f10(A,B,C),C),f9(A,B)) | -r2_hidden(C,B) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.07 5419 r2_tarski(A,f7(B)) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)) # label(t9_tarski) # label(axiom). [clausify(10)]. 8.11/8.07 Derived: r2_hidden(k4_tarski(f10(A,f7(B),C),C),f9(A,f7(B))) | -r2_hidden(C,f7(B)) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)). [resolve(5418,a,5419,a)]. 8.11/8.07 5420 -r2_tarski(A,B) | r2_hidden(f10(A,B,C),A) | -r2_hidden(C,B) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.07 Derived: r2_hidden(f10(A,f7(B),C),A) | -r2_hidden(C,f7(B)) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)). [resolve(5420,a,5419,a)]. 8.11/8.07 5421 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f9(A,B)) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | C != E | D = F # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.07 Derived: -r2_hidden(k4_tarski(A,B),f9(C,f7(D))) | -r2_hidden(k4_tarski(E,F),f9(C,f7(D))) | A != E | B = F | r2_hidden(C,f7(D)) | -r1_tarski(C,f7(D)). [resolve(5421,a,5419,a)]. 8.11/8.07 5422 -r2_tarski(A,B) | -r2_hidden(k4_tarski(C,D),f9(A,B)) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | C = E | D != F # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.07 Derived: -r2_hidden(k4_tarski(A,B),f9(C,f7(D))) | -r2_hidden(k4_tarski(E,F),f9(C,f7(D))) | A = E | B != F | r2_hidden(C,f7(D)) | -r1_tarski(C,f7(D)). [resolve(5422,a,5419,a)]. 8.11/8.07 5423 -r2_tarski(A,B) | r2_hidden(f11(A,B,C),B) | -r2_hidden(C,A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.07 Derived: r2_hidden(f11(A,f7(B),C),f7(B)) | -r2_hidden(C,A) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)). [resolve(5423,a,5419,a)]. 8.11/8.07 5424 -r2_tarski(A,B) | r2_hidden(k4_tarski(C,f11(A,B,C)),f9(A,B)) | -r2_hidden(C,A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.07 Derived: r2_hidden(k4_tarski(A,f11(B,f7(C),A)),f9(B,f7(C))) | -r2_hidden(A,B) | r2_hidden(B,f7(C)) | -r1_tarski(B,f7(C)). [resolve(5424,a,5419,a)]. 8.11/8.07 5425 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f15(A,B,D),f16(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.07 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(5425,a,5418,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(5425,a,5420,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(5425,a,5421,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(5425,a,5422,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(5425,a,5423,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(5425,a,5424,a)]. 8.11/8.12 5426 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f15(A,B,D),f16(A,B,D)),D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(5426,a,5418,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(5426,a,5420,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(5426,a,5421,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(5426,a,5422,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(5426,a,5423,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f15(B,C,D),f16(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(5426,a,5424,a)]. 8.11/8.12 5427 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(5427,a,5418,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(5427,a,5420,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(5427,a,5421,a)]. 8.11/8.12 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(5427,a,5422,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(5427,a,5423,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(5427,a,5424,a)]. 8.23/8.16 5428 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(5428,a,5418,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(5428,a,5420,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(5428,a,5421,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(5428,a,5422,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(5428,a,5423,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | r2_hidden(k4_tarski(f13(B,C,D),f14(B,C,D)),D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(5428,a,5424,a)]. 8.23/8.16 5429 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) = f13(A,B,D) | f16(A,B,D) = f14(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(5429,a,5418,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(5429,a,5420,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(5429,a,5421,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(5429,a,5422,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(5429,a,5423,a)]. 8.23/8.16 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(5429,a,5424,a)]. 8.23/8.20 5430 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) = f13(A,B,D) | f16(A,B,D) = f14(A,B,D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(5430,a,5418,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(5430,a,5420,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(5430,a,5421,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(5430,a,5422,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(5430,a,5423,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) = f13(B,C,D) | f16(B,C,D) = f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(5430,a,5424,a)]. 8.23/8.20 5431 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) != f13(A,B,D) | f16(A,B,D) != f14(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(f10(B,C,F),F),f9(B,C)) | -r2_hidden(F,C). [resolve(5431,a,5418,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f10(B,C,F),B) | -r2_hidden(F,C). [resolve(5431,a,5420,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F != V7 | V6 = V8. [resolve(5431,a,5421,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | -r2_hidden(k4_tarski(F,V6),f9(B,C)) | -r2_hidden(k4_tarski(V7,V8),f9(B,C)) | F = V7 | V6 != V8. [resolve(5431,a,5422,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(f11(B,C,F),C) | -r2_hidden(F,B). [resolve(5431,a,5423,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | -r2_hidden(E,C) | -r2_hidden(k4_tarski(f17(B,C,D),E),D) | r2_hidden(k4_tarski(F,f11(B,C,F)),f9(B,C)) | -r2_hidden(F,B). [resolve(5431,a,5424,a)]. 8.23/8.20 5432 r2_tarski(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) != f13(A,B,D) | f16(A,B,D) != f14(A,B,D) | r2_hidden(f17(A,B,D),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(f10(B,C,E),E),f9(B,C)) | -r2_hidden(E,C). [resolve(5432,a,5418,a)]. 8.23/8.20 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f10(B,C,E),B) | -r2_hidden(E,C). [resolve(5432,a,5420,a)]. 8.35/8.24 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E != V6 | F = V7. [resolve(5432,a,5421,a)]. 8.35/8.24 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | -r2_hidden(k4_tarski(E,F),f9(B,C)) | -r2_hidden(k4_tarski(V6,V7),f9(B,C)) | E = V6 | F != V7. [resolve(5432,a,5422,a)]. 8.35/8.24 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(f11(B,C,E),C) | -r2_hidden(E,B). [resolve(5432,a,5423,a)]. 8.35/8.24 Derived: -r2_hidden(k4_tarski(A,f12(B,C,D)),D) | -r2_hidden(A,B) | f15(B,C,D) != f13(B,C,D) | f16(B,C,D) != f14(B,C,D) | r2_hidden(f17(B,C,D),B) | r2_hidden(k4_tarski(E,f11(B,C,E)),f9(B,C)) | -r2_hidden(E,B). [resolve(5432,a,5424,a)]. 8.35/8.24 5433 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(5433,a,5418,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(5433,a,5420,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(5433,a,5421,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(5433,a,5422,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(5433,a,5423,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(5433,a,5424,a)]. 8.35/8.24 5434 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(5434,a,5418,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(5434,a,5420,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(5434,a,5421,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(5434,a,5422,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(5434,a,5423,a)]. 8.35/8.24 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f15(A,B,C),f16(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(5434,a,5424,a)]. 8.35/8.28 5435 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(5435,a,5418,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(5435,a,5420,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(5435,a,5421,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(5435,a,5422,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(5435,a,5423,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(5435,a,5424,a)]. 8.35/8.28 5436 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(5436,a,5418,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(5436,a,5420,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(5436,a,5421,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(5436,a,5422,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(5436,a,5423,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | r2_hidden(k4_tarski(f13(A,B,C),f14(A,B,C)),C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(5436,a,5424,a)]. 8.35/8.28 5437 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(5437,a,5418,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(5437,a,5420,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(5437,a,5421,a)]. 8.35/8.28 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(5437,a,5422,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(5437,a,5423,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(5437,a,5424,a)]. 8.35/8.32 5438 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(5438,a,5418,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(5438,a,5420,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(5438,a,5421,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(5438,a,5422,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(5438,a,5423,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) = f13(A,B,C) | f16(A,B,C) = f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(5438,a,5424,a)]. 8.35/8.32 5439 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(f10(A,B,E),E),f9(A,B)) | -r2_hidden(E,B). [resolve(5439,a,5418,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f10(A,B,E),A) | -r2_hidden(E,B). [resolve(5439,a,5420,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E != V6 | F = V7. [resolve(5439,a,5421,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | -r2_hidden(k4_tarski(V6,V7),f9(A,B)) | E = V6 | F != V7. [resolve(5439,a,5422,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(f11(A,B,E),B) | -r2_hidden(E,A). [resolve(5439,a,5423,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | -r2_hidden(D,B) | -r2_hidden(k4_tarski(f17(A,B,C),D),C) | r2_hidden(k4_tarski(E,f11(A,B,E)),f9(A,B)) | -r2_hidden(E,A). [resolve(5439,a,5424,a)]. 8.35/8.32 5440 r2_tarski(A,B) | r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) # label(d6_tarski) # label(axiom). [clausify(11)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(f10(A,B,D),D),f9(A,B)) | -r2_hidden(D,B). [resolve(5440,a,5418,a)]. 8.35/8.32 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f10(A,B,D),A) | -r2_hidden(D,B). [resolve(5440,a,5420,a)]. 8.74/8.66 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D != F | E = V6. [resolve(5440,a,5421,a)]. 8.74/8.66 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | -r2_hidden(k4_tarski(D,E),f9(A,B)) | -r2_hidden(k4_tarski(F,V6),f9(A,B)) | D = F | E != V6. [resolve(5440,a,5422,a)]. 8.74/8.66 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(f11(A,B,D),B) | -r2_hidden(D,A). [resolve(5440,a,5423,a)]. 8.74/8.66 Derived: r2_hidden(f12(A,B,C),B) | f15(A,B,C) != f13(A,B,C) | f16(A,B,C) != f14(A,B,C) | r2_hidden(f17(A,B,C),A) | r2_hidden(k4_tarski(D,f11(A,B,D)),f9(A,B)) | -r2_hidden(D,A). [resolve(5440,a,5424,a)]. 8.74/8.66 5441 r2_tarski(A,f59(B)) | r2_hidden(A,f59(B)) | -r1_tarski(A,f59(B)) # label(t136_zfmisc_1) # label(axiom). [clausify(331)]. 8.74/8.66 Derived: r2_hidden(A,f59(B)) | -r1_tarski(A,f59(B)) | r2_hidden(k4_tarski(f10(A,f59(B),C),C),f9(A,f59(B))) | -r2_hidden(C,f59(B)). [resolve(5441,a,5418,a)]. 8.74/8.66 Derived: r2_hidden(A,f59(B)) | -r1_tarski(A,f59(B)) | r2_hidden(f10(A,f59(B),C),A) | -r2_hidden(C,f59(B)). [resolve(5441,a,5420,a)]. 8.74/8.66 Derived: r2_hidden(A,f59(B)) | -r1_tarski(A,f59(B)) | -r2_hidden(k4_tarski(C,D),f9(A,f59(B))) | -r2_hidden(k4_tarski(E,F),f9(A,f59(B))) | C != E | D = F. [resolve(5441,a,5421,a)]. 8.74/8.66 Derived: r2_hidden(A,f59(B)) | -r1_tarski(A,f59(B)) | -r2_hidden(k4_tarski(C,D),f9(A,f59(B))) | -r2_hidden(k4_tarski(E,F),f9(A,f59(B))) | C = E | D != F. [resolve(5441,a,5422,a)]. 8.74/8.66 Derived: r2_hidden(A,f59(B)) | -r1_tarski(A,f59(B)) | r2_hidden(f11(A,f59(B),C),f59(B)) | -r2_hidden(C,A). [resolve(5441,a,5423,a)]. 8.74/8.66 Derived: r2_hidden(A,f59(B)) | -r1_tarski(A,f59(B)) | r2_hidden(k4_tarski(C,f11(A,f59(B),C)),f9(A,f59(B))) | -r2_hidden(C,A). [resolve(5441,a,5424,a)]. 8.74/8.66 5442 -r2_wellord2(A,B) | r2_tarski(A,B) # label(redefinition_r2_wellord2) # label(axiom). [clausify(1587)]. 8.74/8.66 Derived: -r2_wellord2(A,B) | r2_hidden(k4_tarski(f10(A,B,C),C),f9(A,B)) | -r2_hidden(C,B). [resolve(5442,b,5418,a)]. 8.74/8.66 Derived: -r2_wellord2(A,B) | r2_hidden(f10(A,B,C),A) | -r2_hidden(C,B). [resolve(5442,b,5420,a)]. 8.74/8.66 Derived: -r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,D),f9(A,B)) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | C != E | D = F. [resolve(5442,b,5421,a)]. 8.74/8.66 Derived: -r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,D),f9(A,B)) | -r2_hidden(k4_tarski(E,F),f9(A,B)) | C = E | D != F. [resolve(5442,b,5422,a)]. 8.74/8.66 Derived: -r2_wellord2(A,B) | r2_hidden(f11(A,B,C),B) | -r2_hidden(C,A). [resolve(5442,b,5423,a)]. 8.74/8.66 Derived: -r2_wellord2(A,B) | r2_hidden(k4_tarski(C,f11(A,B,C)),f9(A,B)) | -r2_hidden(C,A). [resolve(5442,b,5424,a)]. 8.74/8.66 5443 r2_wellord2(A,B) | -r2_tarski(A,B) # label(redefinition_r2_wellord2) # label(axiom). [clausify(1587)]. 8.74/8.66 Derived: r2_wellord2(A,f7(B)) | r2_hidden(A,f7(B)) | -r1_tarski(A,f7(B)). [resolve(5443,b,5419,a)]. 8.74/8.66 Derived: r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f15(A,B,D),f16(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D). [resolve(5443,b,5425,a)]. 8.74/8.66 Derived: r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f15(A,B,D),f16(A,B,D)),D) | r2_hidden(f17(A,B,D),A). [resolve(5443,b,5426,a)]. 8.74/8.66 Derived: r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D). [resolve(5443,b,5427,a)]. 8.74/8.66 Derived: r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | r2_hidden(k4_tarski(f13(A,B,D),f14(A,B,D)),D) | r2_hidden(f17(A,B,D),A). [resolve(5443,b,5428,a)]. 8.74/8.66 Derived: r2_wellord2(A,B) | -r2_hidden(k4_tarski(C,f12(A,B,D)),D) | -r2_hidden(C,A) | f15(A,B,D) = f13(A,B,D) | f16(A,B,D) = f14(A,B,D) | -r2_hidden(E,B) | -r2_hidden(k4_tarski(f17(A,B,D),E),D). [rAlarm clock 120.14/120.05 Prover9 interrupted 120.14/120.05 EOF