0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n132.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 06:27:42 CDT 2018 0.03/0.24 % CPUTime : 21.68/22.86 ============================== Prover9 =============================== 21.68/22.86 Prover9 (32) version 2009-11A, November 2009. 21.68/22.86 Process 27437 was started by sandbox2 on n132.star.cs.uiowa.edu, 21.68/22.86 Sat Jul 14 06:28:02 2018 21.68/22.86 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27402_n132.star.cs.uiowa.edu". 21.68/22.86 ============================== end of head =========================== 21.68/22.86 21.68/22.86 ============================== INPUT ================================= 21.68/22.86 21.68/22.86 % Reading from file /tmp/Prover9_27402_n132.star.cs.uiowa.edu 21.68/22.86 21.68/22.86 set(prolog_style_variables). 21.68/22.86 set(auto2). 21.68/22.86 % set(auto2) -> set(auto). 21.68/22.86 % set(auto) -> set(auto_inference). 21.68/22.86 % set(auto) -> set(auto_setup). 21.68/22.86 % set(auto_setup) -> set(predicate_elim). 21.68/22.86 % set(auto_setup) -> assign(eq_defs, unfold). 21.68/22.86 % set(auto) -> set(auto_limits). 21.68/22.86 % set(auto_limits) -> assign(max_weight, "100.000"). 21.68/22.86 % set(auto_limits) -> assign(sos_limit, 20000). 21.68/22.86 % set(auto) -> set(auto_denials). 21.68/22.86 % set(auto) -> set(auto_process). 21.68/22.86 % set(auto2) -> assign(new_constants, 1). 21.68/22.86 % set(auto2) -> assign(fold_denial_max, 3). 21.68/22.86 % set(auto2) -> assign(max_weight, "200.000"). 21.68/22.86 % set(auto2) -> assign(max_hours, 1). 21.68/22.86 % assign(max_hours, 1) -> assign(max_seconds, 3600). 21.68/22.86 % set(auto2) -> assign(max_seconds, 0). 21.68/22.86 % set(auto2) -> assign(max_minutes, 5). 21.68/22.86 % assign(max_minutes, 5) -> assign(max_seconds, 300). 21.68/22.86 % set(auto2) -> set(sort_initial_sos). 21.68/22.86 % set(auto2) -> assign(sos_limit, -1). 21.68/22.86 % set(auto2) -> assign(lrs_ticks, 3000). 21.68/22.86 % set(auto2) -> assign(max_megs, 400). 21.68/22.86 % set(auto2) -> assign(stats, some). 21.68/22.86 % set(auto2) -> clear(echo_input). 21.68/22.86 % set(auto2) -> set(quiet). 21.68/22.86 % set(auto2) -> clear(print_initial_clauses). 21.68/22.86 % set(auto2) -> clear(print_given). 21.68/22.86 assign(lrs_ticks,-1). 21.68/22.86 assign(sos_limit,10000). 21.68/22.86 assign(order,kbo). 21.68/22.86 set(lex_order_vars). 21.68/22.86 clear(print_given). 21.68/22.86 21.68/22.86 % formulas(sos). % not echoed (10578 formulas) 21.68/22.86 21.68/22.86 ============================== end of input ========================== 21.68/22.86 21.68/22.86 % From the command line: assign(max_seconds, 300). 21.68/22.86 21.68/22.86 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 21.68/22.86 21.68/22.86 % Formulas that are not ordinary clauses: 21.68/22.86 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 2 $T # label(t5_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 3 $T # label(t8_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 4 (all A all B r1_tarski(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 5 (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]. 21.68/22.86 6 (all A all B all C (p1_s1_tarski(A,B) & p1_s1_tarski(A,C) -> B = C)) -> (exists A all B (r2_hidden(B,A) <-> (exists C (p1_s1_tarski(C,B) & r2_hidden(C,f1_s1_tarski))))) # label(s1_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 7 $T # label(t1_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 8 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 9 (all A exists B (r2_hidden(A,B) & (all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & (all C -(r2_hidden(C,B) & (all D -((all E (r1_tarski(E,C) -> r2_hidden(E,D))) & r2_hidden(D,B))))) & (all C -(r1_tarski(C,B) & -r2_tarski(C,B) & -r2_hidden(C,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 10 $T # label(t3_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 11 (all A all B (k3_tarski(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D (r2_hidden(D,A) & r2_hidden(C,D))))))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 12 $T # label(t6_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 13 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 14 (all A all B all C ((all D (r2_hidden(D,C) <-> B = D | A = D)) <-> C = k2_tarski(A,B))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 15 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 16 (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]. 21.68/22.86 17 (all A all B k2_tarski(B,A) = k2_tarski(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 18 (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(D,E),C) & r2_hidden(k4_tarski(F,G),C) -> (F = D <-> E = G))) & (all D -((all E -(r2_hidden(k4_tarski(D,E),C) & r2_hidden(E,B))) & r2_hidden(D,A))))))) # label(d6_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 19 (all A all B (B = k1_tarski(A) <-> (all C (r2_hidden(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 20 (all A all B -(r2_hidden(A,B) & (all C -(r2_hidden(C,B) & (all D -(r2_hidden(D,B) & r2_hidden(D,C))))))) # label(t7_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 21 $T # label(t4_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 22 (all A all B ((all C (r2_hidden(C,A) <-> r2_hidden(C,B))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 23 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 24 (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]. 21.68/22.86 25 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 26 (all A all B all C -(-(-r2_hidden(C,B) & r2_hidden(C,A)) & -(-r2_hidden(C,A) & r2_hidden(C,B)) & r2_hidden(C,k2_xboole_0(A,B)) & r1_xboole_0(A,B))) # label(t5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 27 (all A all B k2_xboole_0(B,A) = k2_xboole_0(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 28 (all A all B A = k2_xboole_0(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 29 (all A all B r3_xboole_0(A,A)) # label(reflexivity_r3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 30 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 31 (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]. 21.68/22.86 32 (all A all B (k1_xboole_0 = k3_xboole_0(A,B) <-> r1_xboole_0(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 33 (all A all B all C (-(r2_hidden(A,B) <-> r2_hidden(A,C)) <-> r2_hidden(A,k5_xboole_0(B,C)))) # label(t1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 34 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 35 (all A all B (B = A <-> r1_tarski(A,B) & r1_tarski(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 36 (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f2_s2_xboole_0))) & (all A (p1_s2_xboole_0(A) <-> r2_hidden(A,f1_s2_xboole_0))) -> f1_s2_xboole_0 = f2_s2_xboole_0 # label(s2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 37 (all A all B ((all C (r2_hidden(C,A) <-> p1_s3_xboole_0(C))) & (all C (r2_hidden(C,B) <-> p1_s3_xboole_0(C))) -> B = A)) # label(s3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 38 (all A all B (-((all C -r2_hidden(C,k3_xboole_0(A,B))) & -r1_xboole_0(A,B)) & -((exists C r2_hidden(C,k3_xboole_0(A,B))) & r1_xboole_0(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 39 (all A all B all C ((all D (-r2_hidden(D,A) <-> (r2_hidden(D,B) <-> r2_hidden(D,C)))) -> A = k5_xboole_0(B,C))) # label(t2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 40 (all A all B (r3_xboole_0(A,B) <-> r1_tarski(A,B) | r1_tarski(B,A))) # label(d9_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 41 (all A all B all C (k3_xboole_0(A,B) = C <-> (all D (r2_hidden(D,B) & r2_hidden(D,A) <-> r2_hidden(D,C))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 42 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k5_xboole_0(A,B)) # label(d6_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 43 (all A all B -r2_xboole_0(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 44 (all A all B (r2_xboole_0(A,B) <-> B != A & r1_tarski(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 45 (all A all B all C ((all D (r2_hidden(D,C) <-> -r2_hidden(D,B) & r2_hidden(D,A))) <-> C = k4_xboole_0(A,B))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 46 $T # label(dt_k5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 47 (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]. 21.68/22.86 48 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 49 (all A all B A = k3_xboole_0(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 50 (all A all B (-((exists C (r2_hidden(C,B) & r2_hidden(C,A))) & r1_xboole_0(A,B)) & -(-r1_xboole_0(A,B) & (all C -(r2_hidden(C,A) & r2_hidden(C,B)))))) # label(t3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 51 (all A all B all C ((all D (r2_hidden(D,B) | r2_hidden(D,A) <-> r2_hidden(D,C))) <-> k2_xboole_0(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 52 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 53 (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]. 21.68/22.86 54 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 55 (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]. 21.68/22.86 56 (all A (k1_xboole_0 = A <-> (all B -r2_hidden(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 57 (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]. 21.68/22.86 58 (all A (v1_xboole_0(A) <-> k1_xboole_0 = A)) # label(d5_xboole_0) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 59 (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]. 21.68/22.86 60 (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]. 21.68/22.86 61 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 62 (all A all B -(v1_xboole_0(A) & v1_xboole_0(B) & A != B)) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 63 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 64 (all A k1_xboole_0 = k4_xboole_0(k1_xboole_0,A)) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 65 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 66 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 67 (all A k1_xboole_0 = k3_xboole_0(A,k1_xboole_0)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 68 (all A A = k5_xboole_0(A,k1_xboole_0)) # label(t5_boole) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 69 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)))) # label(t34_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 70 (all A all B all C (r1_tarski(k2_xboole_0(A,B),C) -> r1_tarski(A,C))) # label(t11_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 71 (all A all B r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B))) # label(t89_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 72 (all A all B all C (r1_tarski(A,B) -> r1_xboole_0(A,k4_xboole_0(C,B)))) # label(t85_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 73 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) -> r1_tarski(k5_xboole_0(A,B),C))) # label(t97_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 74 (all A -r2_xboole_0(A,k1_xboole_0)) # label(t62_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 75 (all A all B all C (r2_xboole_0(A,B) & r1_tarski(B,C) -> r2_xboole_0(A,C))) # label(t58_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 76 (all A all B all C k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C)) = k2_xboole_0(A,k3_xboole_0(B,C))) # label(t24_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 77 (all A all B all C k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k3_xboole_0(k3_xboole_0(A,B),C)) = k4_xboole_0(A,k5_xboole_0(B,C))) # label(t102_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 78 (all A all B (-v1_xboole_0(B) -> -(r1_tarski(B,A) & r1_xboole_0(B,A)))) # label(t69_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 79 (all A all B k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B))) # label(t100_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 80 (all A all B r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B))) # label(t96_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 81 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k2_xboole_0(C,B)))) # label(t10_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 82 (all A all B all C k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C))) # label(t42_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 83 (all A all B all C k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t53_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 84 (all A all B (r1_tarski(A,k4_xboole_0(B,A)) -> k1_xboole_0 = A)) # label(t38_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 85 (all A all B all C (r1_tarski(A,B) & r1_tarski(A,C) -> r1_tarski(A,k3_xboole_0(B,C)))) # label(t19_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 86 (all A all B all C -(r1_tarski(A,C) & r1_xboole_0(A,k3_xboole_0(B,C)) & -r1_xboole_0(A,B))) # label(t77_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 87 (all A all B all C all D (r1_xboole_0(C,D) & r1_xboole_0(B,D) & r1_xboole_0(A,D) -> r1_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D))) # label(t114_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 88 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C)) # label(t49_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 89 (all A all B all C k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t23_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 90 (all A all B all C (r1_xboole_0(A,k4_xboole_0(B,C)) -> r1_xboole_0(B,k4_xboole_0(A,C)))) # label(t81_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 91 (all A all B all C all D (r1_xboole_0(C,A) & r1_xboole_0(D,B) & k2_xboole_0(A,B) = k2_xboole_0(C,D) -> B = C)) # label(t72_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 92 (all A all B k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A) # label(t51_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 93 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k5_xboole_0(A,C),B))) # label(t110_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 94 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(A,k4_xboole_0(B,C)))) # label(t80_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 95 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)))) # label(t26_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 96 (all A all B all C (r1_tarski(A,B) -> k3_xboole_0(k2_xboole_0(A,C),B) = k2_xboole_0(A,k3_xboole_0(C,B)))) # label(t30_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 97 (all A all B k4_xboole_0(A,k2_xboole_0(A,B)) = k1_xboole_0) # label(t46_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 98 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)))) # label(t9_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 99 (all A all B all C (r1_xboole_0(A,B) -> k4_xboole_0(k2_xboole_0(C,B),A) = k2_xboole_0(k4_xboole_0(C,A),B))) # label(t87_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 100 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)))) # label(t35_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 101 (all A all B all C k5_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B)) = k3_xboole_0(k5_xboole_0(A,C),B)) # label(t112_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 102 (all A all B all C k3_xboole_0(k4_xboole_0(A,C),B) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(C,B))) # label(t111_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 103 (all A all B k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t94_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 104 (all A all B k2_xboole_0(A,k3_xboole_0(A,B)) = A) # label(t22_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 105 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,B) -> r1_xboole_0(A,C))) # label(t63_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 106 (all A all B all C k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C)))) # label(t99_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 107 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) -> r1_tarski(A,B))) # label(t73_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 108 (all A all B (k1_xboole_0 = k4_xboole_0(A,B) <-> r1_tarski(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 109 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),B))) # label(t109_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 110 (all A r1_xboole_0(A,k1_xboole_0)) # label(t65_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 111 (all A all B r1_tarski(A,k2_xboole_0(A,B))) # label(t7_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 112 (all A all B all C -(-r1_xboole_0(A,B) & r1_xboole_0(A,k4_xboole_0(B,C)) & r1_xboole_0(A,C))) # label(t84_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 113 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)))) # label(t33_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 114 (all A all B (r1_xboole_0(A,B) -> A = k4_xboole_0(k2_xboole_0(A,B),B))) # label(t88_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 115 (all A all B k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 116 (all A all B (r1_xboole_0(A,B) <-> A = k4_xboole_0(A,B))) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 117 (all A all B all C (-v1_xboole_0(C) -> -(r1_tarski(C,B) & r1_xboole_0(A,B) & r1_tarski(C,A)))) # label(t68_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 118 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)))) # label(t13_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 119 (all A all B all C (r1_tarski(A,B) & (all D (r1_tarski(A,D) & r1_tarski(C,D) -> r1_tarski(B,D))) & r1_tarski(C,B) -> k2_xboole_0(A,C) = B)) # label(t14_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 120 (all A all B all C k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C))) # label(t91_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 121 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) & r1_xboole_0(B,D) -> r1_xboole_0(A,C))) # label(t64_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 122 (all A all B k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) = k5_xboole_0(A,B)) # label(t101_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.86 123 (all A all B k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B))) # label(t55_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 124 (all A all B r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B)) # label(t90_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 125 (all A all B r1_tarski(k4_xboole_0(A,B),A)) # label(t36_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 126 (all A r1_tarski(k1_xboole_0,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 127 (all A all B all C k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C)) = k2_xboole_0(k2_xboole_0(A,B),C)) # label(t5_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 128 (all A all B all C -(r1_xboole_0(A,B) & -r1_xboole_0(A,k3_xboole_0(B,C)))) # label(t74_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 129 (all A all B all C (r1_tarski(A,B) & r1_xboole_0(A,C) -> r1_tarski(A,k4_xboole_0(B,C)))) # label(t86_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 130 (all A all B k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t93_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 131 (all A all B all C (r1_tarski(k4_xboole_0(A,B),C) -> r1_tarski(A,k2_xboole_0(B,C)))) # label(t44_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 132 (all A k5_xboole_0(A,A) = k1_xboole_0) # label(t92_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 133 (all A all B -(k1_xboole_0 = k4_xboole_0(B,A) & r2_xboole_0(A,B))) # label(t105_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 134 (all A all B all C k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) = k4_xboole_0(A,k4_xboole_0(B,C))) # label(t52_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 135 (all A all B -(r1_xboole_0(k3_xboole_0(A,B),B) & -r1_xboole_0(A,B))) # label(t75_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 136 (all A all B all C (r1_xboole_0(A,B) -> k3_xboole_0(A,C) = k3_xboole_0(A,k2_xboole_0(B,C)))) # label(t78_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 137 (all A all B (k1_xboole_0 = k2_xboole_0(A,B) -> k1_xboole_0 = A)) # label(t15_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 138 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),B))) # label(t108_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 139 (all A all B all C (r1_xboole_0(B,C) & r1_tarski(A,C) & r1_tarski(A,B) -> k1_xboole_0 = A)) # label(t67_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 140 (all A all B all C (r1_tarski(A,k4_xboole_0(B,C)) -> r1_tarski(A,B) & r1_xboole_0(A,C))) # label(t106_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 141 (all A all B all C r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C))) # label(t31_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 142 (all A all B all C (r1_tarski(A,B) & r2_xboole_0(B,C) -> r2_xboole_0(A,C))) # label(t59_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 143 (all A all B all C (r1_xboole_0(A,B) & r1_xboole_0(C,B) & k2_xboole_0(A,B) = k2_xboole_0(C,B) -> C = A)) # label(t71_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 144 (all A all B (r1_tarski(A,B) -> B = k2_xboole_0(A,k4_xboole_0(B,A)))) # label(t45_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 145 (all A all B all C (r1_tarski(C,B) & r1_tarski(A,B) -> r1_tarski(k2_xboole_0(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 146 (all A all B all C k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C))) # label(t4_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 147 (all A all B all C r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C))) # label(t29_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 148 (all A all B k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B)) = k3_xboole_0(A,B)) # label(t95_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 149 (all A all B -(r2_xboole_0(A,B) & r2_xboole_0(B,A))) # label(t57_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 150 (all A (-(r1_xboole_0(A,A) & k1_xboole_0 != A) & -(-r1_xboole_0(A,A) & A = k1_xboole_0))) # label(t66_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 151 (all A all B all C (r1_tarski(A,k5_xboole_0(B,C)) <-> r1_xboole_0(A,k3_xboole_0(B,C)) & r1_tarski(A,k2_xboole_0(B,C)))) # label(t107_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 152 (all A all B r1_tarski(k3_xboole_0(A,B),A)) # label(t17_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 153 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)))) # label(t27_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 154 (all A all B k4_xboole_0(A,B) = k4_xboole_0(A,k3_xboole_0(A,B))) # label(t47_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 155 (all A all B all C k4_xboole_0(A,k3_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C))) # label(t54_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 156 (all A all B all C (-(-(r1_xboole_0(A,C) & r1_xboole_0(A,B)) & r1_xboole_0(A,k2_xboole_0(B,C))) & -(r1_xboole_0(A,C) & r1_xboole_0(A,B) & -r1_xboole_0(A,k2_xboole_0(B,C))))) # label(t70_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 157 (all A all B all C k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C))) # label(t16_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 158 (all A all B r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A))) # label(t82_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 159 (all A all B (k4_xboole_0(A,B) = k4_xboole_0(B,A) -> A = B)) # label(t32_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 160 (all A all B k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B)) # label(t6_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 161 (all A all B k5_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t98_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 162 (all A all B r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B))) # label(t103_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 163 (all A all B all C (r2_xboole_0(B,C) & r2_xboole_0(A,B) -> r2_xboole_0(A,C))) # label(t56_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 164 (all A all B all C k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C))) # label(t41_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 165 (all A all B all C (r1_tarski(B,C) & r1_tarski(A,B) -> r1_tarski(A,C))) # label(t1_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 166 (all A all B (r1_tarski(A,B) -> A = k3_xboole_0(A,B))) # label(t28_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 167 (all A all B all C (r1_xboole_0(A,B) -> r1_xboole_0(k3_xboole_0(C,A),k3_xboole_0(C,B)))) # label(t76_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 168 (all A all B k3_xboole_0(A,B) = k4_xboole_0(A,k4_xboole_0(A,B))) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 169 (all A all B k3_xboole_0(A,k2_xboole_0(A,B)) = A) # label(t21_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 170 (all A all B all C (r1_tarski(A,C) & (all D (r1_tarski(D,C) & r1_tarski(D,B) -> r1_tarski(D,A))) & r1_tarski(A,B) -> A = k3_xboole_0(B,C))) # label(t20_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 171 (all A all B all C k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C))) # label(t50_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 172 (all A (r1_tarski(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t3_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 173 (all A all B r1_xboole_0(k4_xboole_0(A,B),B)) # label(t79_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 174 (all A (A != k1_xboole_0 -> r2_xboole_0(k1_xboole_0,A))) # label(t61_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 175 (all A all B all C k2_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(B,C)),k3_xboole_0(C,A)) = k3_xboole_0(k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(B,C)),k2_xboole_0(C,A))) # label(t25_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 176 (all A all B all C all D k2_xboole_0(A,k2_xboole_0(k2_xboole_0(B,C),D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D)) # label(t113_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 177 (all A all B (-(A != B & -r2_xboole_0(B,A) & -r2_xboole_0(A,B)) <-> r3_xboole_0(A,B))) # label(t104_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 178 (all A all B (r1_tarski(A,B) -> k2_xboole_0(A,B) = B)) # label(t12_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 179 (all A all B all C (r1_tarski(A,k2_xboole_0(B,C)) -> r1_tarski(k4_xboole_0(A,B),C))) # label(t43_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 180 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 181 (all A all B all C (r1_tarski(A,k3_xboole_0(B,C)) -> r1_tarski(A,B))) # label(t18_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 182 (all A all B -(r2_xboole_0(B,A) & r1_tarski(A,B))) # label(t60_xboole_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 183 (all A all B all C all D -(A != C & D != A & k2_tarski(A,B) = k2_tarski(C,D))) # label(t10_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 184 (all A all B all C (r1_tarski(k2_tarski(A,B),k1_tarski(C)) -> C = A)) # label(t26_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 185 $T # label(t5_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 186 (all A all B (A = k4_xboole_0(A,k1_tarski(B)) <-> -r2_hidden(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 187 (all A all B -(r1_xboole_0(k1_tarski(A),k1_tarski(B)) & B = A)) # label(t16_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 188 $T # label(t61_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 189 (all A all B (k3_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) -> A = B)) # label(t18_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 190 (all A all B all C (k2_tarski(B,C) = k1_tarski(A) -> B = A)) # label(t8_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 191 (all A all B (-r2_hidden(A,B) -> B = k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)))) # label(t141_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 192 (all A all B all C (r2_hidden(B,C) & r2_hidden(A,C) <-> r1_tarski(k2_tarski(A,B),C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 193 (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]. 21.68/22.87 194 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 195 (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]. 21.68/22.87 196 (all A all B (r1_tarski(A,k2_zfmisc_1(B,A)) | r1_tarski(A,k2_zfmisc_1(A,B)) -> A = k1_xboole_0)) # label(t135_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 197 (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]. 21.68/22.87 198 $T # label(t3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 199 (all A all B all C all D k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) = k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D))) # label(t121_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 200 $T # label(t133_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 201 $T # label(t87_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 202 $T # label(t4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 203 (all A all B (k3_xboole_0(k1_tarski(A),B) = k1_tarski(A) | r1_xboole_0(k1_tarski(A),B))) # label(t58_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 204 (all A all B all C all D (r2_hidden(B,D) & C = A <-> r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 205 (all A k3_tarski(k1_tarski(A)) = A) # label(t31_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 206 (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]. 21.68/22.87 207 (all A all B all C all D (B = D & 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]. 21.68/22.87 208 (all A all B all C all D (k2_zfmisc_1(A,B) = k2_zfmisc_1(C,D) -> k1_xboole_0 = A | C = A & D = B | B = k1_xboole_0)) # label(t134_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 209 (all A all B all C (k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) = k2_zfmisc_1(C,k3_xboole_0(A,B)))) # label(t122_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 210 $T # label(t71_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 211 (all A all B all C (-r2_hidden(A,C) & -r2_hidden(B,C) <-> k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B))) # label(t72_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 212 (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]. 21.68/22.87 213 (all A r1_tarski(k1_tarski(A),k1_zfmisc_1(A))) # label(t80_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 214 (all A all B (k1_tarski(A) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) -> A = B)) # label(t13_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 215 (all A all B all C (r1_tarski(A,k2_tarski(B,C)) <-> -(k1_tarski(B) != A & k2_tarski(B,C) != A & k1_tarski(C) != A & A != k1_xboole_0))) # label(t42_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 216 (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]. 21.68/22.87 217 (all A all B -(A != k1_xboole_0 & k1_tarski(B) != A & k4_xboole_0(A,k1_tarski(B)) = k1_xboole_0)) # label(t66_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 218 (all A exists B ((all C all D (r2_hidden(C,B) & r1_tarski(D,C) -> r2_hidden(D,B))) & (all C -(-r2_hidden(C,B) & -r2_tarski(C,B) & r1_tarski(C,B))) & (all C (r2_hidden(C,B) -> r2_hidden(k1_zfmisc_1(C),B))) & r2_hidden(A,B))) # label(t136_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 219 $T # label(t85_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 220 (all A all B all C (k4_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k4_xboole_0(A,B),C) & k2_zfmisc_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)))) # label(t125_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 221 (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]. 21.68/22.87 222 (all A all B all C k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C)) # label(d3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 223 (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]. 21.68/22.87 224 (all A all B (k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) -> B = A)) # label(t115_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 225 (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]. 21.68/22.87 226 (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]. 21.68/22.87 227 (all A all B all C all D -(r1_tarski(k2_tarski(A,B),k2_tarski(C,D)) & A != D & A != C)) # label(t28_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 228 (all A all B all C (k1_tarski(A) = k2_tarski(B,C) -> B = C)) # label(t9_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 229 (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]. 21.68/22.87 230 (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]. 21.68/22.87 231 (all A r1_tarski(A,k1_zfmisc_1(k3_tarski(A)))) # label(t100_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 232 (all A all B (A != B -> r1_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t17_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 233 (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]. 21.68/22.87 234 (all A all B k2_xboole_0(k1_tarski(A),B) != k1_xboole_0) # label(t49_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 235 (all A all B (k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A) -> k1_xboole_0 = A | B = k1_xboole_0 | B = A)) # label(t114_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 236 (all A all B (k1_xboole_0 != A -> k2_zfmisc_1(k1_tarski(B),A) != k1_xboole_0 & k1_xboole_0 != k2_zfmisc_1(A,k1_tarski(B)))) # label(t130_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 237 (all A A = k3_tarski(k1_zfmisc_1(A))) # label(t99_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 238 (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]. 21.68/22.87 239 (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]. 21.68/22.87 240 (all A all B (k1_tarski(A) = k4_xboole_0(k1_tarski(A),B) <-> -r2_hidden(A,B))) # label(t67_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 241 $T # label(t77_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 242 (all A all B (r1_tarski(k1_tarski(A),B) <-> r2_hidden(A,B))) # label(t37_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 243 (all A all B (B != A <-> k1_tarski(A) = k4_xboole_0(k1_tarski(A),k1_tarski(B)))) # label(t20_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 244 (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_zfmisc_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k4_tarski(A,C),k4_tarski(B,C)))) # label(t36_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 245 (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]. 21.68/22.87 246 $T # label(t15_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 247 (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]. 21.68/22.87 248 (all A all B all C -(k2_xboole_0(B,C) = k1_tarski(A) & k1_xboole_0 != C & k1_xboole_0 != B & B != C)) # label(t44_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 249 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(D,C)) | r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) -> r1_tarski(B,D))))) # label(t139_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 250 (all A all B ((all C (r1_tarski(C,A) <-> r2_hidden(C,B))) <-> B = k1_zfmisc_1(A))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 251 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> k2_zfmisc_1(A,C) = k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)))) # label(t124_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 252 (all A all B all C (k4_xboole_0(A,k2_tarski(B,C)) = k1_xboole_0 <-> -(A != k1_xboole_0 & k1_tarski(B) != A & k1_tarski(C) != A & A != k2_tarski(B,C)))) # label(t75_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 253 (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]. 21.68/22.87 254 (all A all B all C (k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) = k2_zfmisc_1(k2_xboole_0(A,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]. 21.68/22.87 255 (all A all B all C -(k4_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 & k4_xboole_0(k2_tarski(A,B),C) != k1_tarski(B) & k2_tarski(A,B) != k4_xboole_0(k2_tarski(A,B),C) & k1_tarski(A) != k4_xboole_0(k2_tarski(A,B),C))) # label(t74_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 256 (all A all B all C (r1_tarski(A,B) -> r1_tarski(A,k4_xboole_0(B,k1_tarski(C))) | r2_hidden(C,A))) # label(t40_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 257 $T # label(t76_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 258 (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]. 21.68/22.87 259 (all A all B ((all C -((all D all E k4_tarski(D,E) != C) & r2_hidden(C,A))) & (all C -(r2_hidden(C,B) & (all D all E k4_tarski(D,E) != C))) & (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A))) -> B = A)) # label(t112_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 260 (all A all B all C (C != A & r2_hidden(A,B) <-> r2_hidden(A,k4_xboole_0(B,k1_tarski(C))))) # label(t64_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 261 (all A all B k2_tarski(A,B) = k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B)))) # label(t32_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 262 $T # label(t89_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 263 (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]. 21.68/22.87 264 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 265 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t24_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 266 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(D,E)) & r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,D),k3_xboole_0(C,E))))) # label(t137_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 267 (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]. 21.68/22.87 268 (all A all B all C (r2_hidden(A,B) -> A != C & r2_hidden(C,B) | k1_tarski(A) = k3_xboole_0(k2_tarski(A,C),B))) # label(t60_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 269 (all A all B r1_tarski(k1_tarski(A),k2_tarski(A,B))) # label(t12_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 270 (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]. 21.68/22.87 271 (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]. 21.68/22.87 272 (all A all B (r2_hidden(A,B) -> k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B)) # label(t140_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 273 (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]. 21.68/22.87 274 (all A all B all C -(r1_xboole_0(k2_tarski(A,B),C) & r2_hidden(A,C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 275 (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]. 21.68/22.87 276 (all A (r1_tarski(A,k2_zfmisc_1(A,A)) -> A = k1_xboole_0)) # label(t116_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 277 (all A all B -(A != k1_tarski(B) & (all C -(r2_hidden(C,A) & C != B)) & k1_xboole_0 != A)) # label(t41_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 278 (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]. 21.68/22.87 279 (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]. 21.68/22.87 280 (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]. 21.68/22.87 281 (all A all B all C (k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) <-> (B = A | r2_hidden(B,C)) & -r2_hidden(A,C))) # label(t70_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 282 $T # label(t62_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 283 $T # label(t78_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 284 (all A all B (r2_hidden(A,B) -> r1_tarski(A,k3_tarski(B)))) # label(t92_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 285 (all A all B all C all D all E -((all F all G -(k4_tarski(F,G) = A & r2_hidden(F,k3_xboole_0(B,D)) & r2_hidden(G,k3_xboole_0(C,E)))) & 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]. 21.68/22.87 286 (all A all B all C all D -((all E all F -(r2_hidden(F,C) & k4_tarski(E,F) = D & r2_hidden(E,B))) & r2_hidden(D,A) & r1_tarski(A,k2_zfmisc_1(B,C)))) # label(t103_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 287 $T # label(t91_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 288 (all A all B k1_tarski(k4_tarski(A,B)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B))) # label(t35_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 289 (all A all B k1_xboole_0 = k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) # label(t22_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 290 $T # label(t7_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 291 (all A all B all C all D k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) = k2_xboole_0(k2_zfmisc_1(k4_xboole_0(A,C),B),k2_zfmisc_1(A,k4_xboole_0(B,D)))) # label(t126_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 292 (all A all B all C (k2_zfmisc_1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E exists F (r2_hidden(F,B) & D = k4_tarski(E,F) & r2_hidden(E,A))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 293 $T # label(dt_k4_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 294 (all A all B all C -(-(k1_tarski(A) = C & k1_xboole_0 = B) & -(k1_tarski(A) = B & C = k1_xboole_0) & -(k1_tarski(A) = B & C = k1_tarski(A)) & k1_tarski(A) = k2_xboole_0(B,C))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 295 (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]. 21.68/22.87 296 (all A all B (r1_tarski(k1_tarski(A),k1_tarski(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 297 (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]. 21.68/22.87 298 (all A all B all C -(k1_tarski(A) = k3_xboole_0(k2_tarski(A,B),C) & A != B & r2_hidden(B,C))) # label(t59_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 299 (all A all B k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B))) # label(t83_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 300 (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]. 21.68/22.87 301 (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]. 21.68/22.87 302 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k2_tarski(A,C) = k3_xboole_0(k2_tarski(A,C),B))) # label(t53_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 303 (all A all B -v1_xboole_0(k4_tarski(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 304 $T # label(t88_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 305 (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]. 21.68/22.87 306 (all A all B (k1_xboole_0 = B | A = k1_xboole_0 <-> k2_zfmisc_1(A,B) = k1_xboole_0)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 307 (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]. 21.68/22.87 308 $T # label(dt_k3_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 309 (all A all B ((all C all D (r2_hidden(C,k2_xboole_0(A,B)) & r2_hidden(D,k2_xboole_0(A,B)) -> C = D | r1_xboole_0(C,D))) -> k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)))) # label(t101_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 310 (all A all B all C all D k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D))) # label(t123_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 311 (all A all B all C all D (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))) # label(t119_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 312 (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) & D = B)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 313 (all A all B (r2_hidden(A,B) -> k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A))) # label(t52_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 314 (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]. 21.68/22.87 315 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> k2_xboole_0(k2_tarski(A,C),B) = B)) # label(t48_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 316 (all A all B (A != B -> k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A))) # label(t23_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 317 $T # label(t90_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 318 (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]. 21.68/22.87 319 (all A all B all C -(k1_xboole_0 != A & -r1_tarski(B,C) & (r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(A,C)) | r1_tarski(k2_zfmisc_1(B,A),k2_zfmisc_1(C,A))))) # label(t117_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 320 (all A all B all C all D (A != B -> r1_xboole_0(k2_zfmisc_1(k1_tarski(A),C),k2_zfmisc_1(k1_tarski(B),D)) & r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))))) # label(t131_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 321 (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]. 21.68/22.87 322 (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]. 21.68/22.87 323 $T # label(t11_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 324 (all A all B all C all D (k4_tarski(A,B) = k4_tarski(C,D) -> A = C & D = B)) # label(t33_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 325 (all A all B all C all D all E all F ((all G all H (r2_hidden(k4_tarski(G,H),D) <-> r2_hidden(k4_tarski(G,H),A))) & r1_tarski(D,k2_zfmisc_1(E,F)) & r1_tarski(A,k2_zfmisc_1(B,C)) -> D = A)) # label(t110_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 326 (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]. 21.68/22.87 327 (all A all B all C (r2_hidden(A,C) & r2_hidden(B,C) <-> k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0)) # label(t73_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 328 (all A all B (A = k1_tarski(B) | A = k1_xboole_0 <-> r1_tarski(A,k1_tarski(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 329 (all A all B all C -(A != B & C != A & r1_tarski(k1_tarski(A),k2_tarski(B,C)))) # label(t25_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 330 (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]. 21.68/22.87 331 $T # label(t14_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 332 (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]. 21.68/22.87 333 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k4_subset_1(A,B,k2_subset_1(A)) = k2_subset_1(A))) # label(t28_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 334 (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]. 21.68/22.87 335 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_subset_1(A,C,B) = k5_subset_1(A,B,C))) # label(commutativity_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 336 (all A (m1_subset_1(A,f1_s4_subset_1) -> (r2_hidden(A,f2_s4_subset_1) <-> p1_s4_subset_1(A)))) & (all A (m1_subset_1(A,f1_s4_subset_1) -> (p1_s4_subset_1(A) <-> r2_hidden(A,f3_s4_subset_1)))) -> f3_s4_subset_1 = f2_s4_subset_1 # label(s4_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 337 (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]. 21.68/22.87 338 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,B)) <-> k1_subset_1(A) = B))) # label(t38_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 339 $T # label(t19_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 340 (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]. 21.68/22.87 341 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k6_subset_1(A,B,C)) = k4_subset_1(A,k3_subset_1(A,B),C))))) # label(t33_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 342 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(C) -> -v1_xboole_0(k4_zfmisc_1(A,B,C,D)))) # label(fc6_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 343 (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]. 21.68/22.87 344 $T # label(t20_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 345 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k4_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)) = k3_subset_1(A,k5_subset_1(A,B,C)))))) # label(t30_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 346 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (k1_xboole_0 != A -> m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A))))))) # label(t56_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 347 (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)))) -> C = B))))) # label(t8_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 348 $T # label(t1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 349 (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]. 21.68/22.87 350 (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]. 21.68/22.87 351 (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]. 21.68/22.87 352 $T # label(t11_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 353 (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]. 21.68/22.87 354 (all A (k1_xboole_0 != A -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,A) -> (-r2_hidden(C,B) -> r2_hidden(C,k3_subset_1(A,B))))))))) # label(t50_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 355 $T # label(t23_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 356 $T # label(d1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 357 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> -(r2_hidden(E,C) <-> r2_hidden(E,D))))) -> k7_subset_1(A,C,D) = B))))))) # label(t18_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 358 $T # label(t9_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 359 (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]. 21.68/22.87 360 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k6_subset_1(A,B,C) = k4_xboole_0(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 361 (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]. 21.68/22.87 362 (all A all B (m1_subset_1(B,A) -> (A != k1_xboole_0 -> m1_subset_1(k1_tarski(B),k1_zfmisc_1(A))))) # label(t55_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.87 363 (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]. 21.68/22.87 364 (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]. 21.68/22.87 365 (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]. 21.68/22.87 366 (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]. 21.68/22.87 367 (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]. 21.68/22.88 368 (all A k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A))) # label(t22_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 369 (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]. 21.68/22.88 370 $T # label(t27_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 371 $T # label(t3_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 372 (all A A = k2_subset_1(A)) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 373 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (-r2_hidden(E,D) & r2_hidden(E,C) <-> r2_hidden(E,B)))) -> k6_subset_1(A,C,D) = B))))))) # label(t17_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 374 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (r2_hidden(E,B) <-> r2_hidden(E,C) & r2_hidden(E,D)))) -> B = k5_subset_1(A,C,D)))))))) # label(t16_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 375 (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]. 21.68/22.88 376 (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]. 21.68/22.88 377 (all A all B -v1_xboole_0(k2_tarski(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 378 (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]. 21.68/22.88 379 (all A all B all C (-v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k3_zfmisc_1(A,B,C)))) # label(fc5_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 380 (exists A (m1_subset_1(A,k1_zfmisc_1(f1_s1_subset_1)) & (all B (r2_hidden(B,A) <-> r2_hidden(B,f1_s1_subset_1) & p1_s1_subset_1(B))))) # label(s1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 381 $T # label(t13_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 382 $T # label(t45_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 383 $T # label(t5_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 384 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,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]. 21.68/22.88 385 (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]. 21.68/22.88 386 (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) -> (k1_xboole_0 != A -> m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A))))))))))))))) # label(t60_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 387 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> B = k5_subset_1(A,B,B))) # label(idempotence_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 388 (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]. 21.68/22.88 389 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,B) -> r2_hidden(D,C)))) -> r1_tarski(B,C)))))) # label(t7_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 390 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(B,k3_subset_1(A,C)) & r1_tarski(B,C) -> B = k1_xboole_0))) # label(t40_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 391 $T # label(t24_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 392 (all A all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,A) -> (A != k1_xboole_0 -> m1_subset_1(k5_enumset1(B,C,D,E,F,G,H),k1_zfmisc_1(A))))))))))))))))) # label(t61_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 393 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> -(r2_hidden(B,k3_subset_1(A,C)) & r2_hidden(B,C)))) # label(t54_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 394 $T # label(t6_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 395 (all A exists B (m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 396 (all A all B ((v1_xboole_0(A) -> (v1_xboole_0(B) <-> m1_subset_1(B,A))) & (-v1_xboole_0(A) -> (r2_hidden(B,A) <-> m1_subset_1(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 397 (all A k1_subset_1(A) = k3_subset_1(A,k2_subset_1(A))) # label(t21_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 398 (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]. 21.68/22.88 399 (all A (m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) & v1_xboole_0(k1_subset_1(A)))) # label(dt_k1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 400 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -r1_subset_1(A,A))) # label(irreflexivity_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 401 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,B) <-> m2_subset_1(C,A,B))))) # label(redefinition_m2_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 402 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_xboole_0(B,C) & r1_xboole_0(k3_subset_1(A,B),k3_subset_1(A,C)) -> B = k3_subset_1(A,C)))))) # label(t46_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 403 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) <-> r1_tarski(B,C)))))) # label(t31_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 404 $T # label(t37_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 405 (all A m1_subset_1(k8_subset_1(A),A)) # label(dt_k8_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 406 (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]. 21.68/22.88 407 (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) = k4_subset_1(A,C,B))) # label(commutativity_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 408 (all A m1_subset_1(k1_xboole_0,k1_zfmisc_1(A))) # label(t4_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 409 (all A m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 410 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (-r2_hidden(D,C) <-> r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t51_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 411 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 412 (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]. 21.68/22.88 413 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k7_subset_1(A,C,B) = k7_subset_1(A,B,C))) # label(commutativity_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 414 (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(k6_subset_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 415 (all A k1_subset_1(A) = k1_xboole_0) # label(d3_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 416 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,B) -> r2_hidden(D,C))) -> r1_tarski(B,C)))))) # label(t48_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 417 (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]. 21.68/22.88 418 (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]. 21.68/22.88 419 (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]. 21.68/22.88 420 (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]. 21.68/22.88 421 (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]. 21.68/22.88 422 (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]. 21.68/22.88 423 (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]. 21.68/22.88 424 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> k3_subset_1(A,k4_subset_1(A,B,C)) = k5_subset_1(A,k3_subset_1(A,B),k3_subset_1(A,C)))))) # label(t29_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 425 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) -> k5_xboole_0(B,C) = k7_subset_1(A,B,C))) # label(redefinition_k7_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 426 $T # label(t12_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 427 (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]. 21.68/22.88 428 (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) = k2_xboole_0(B,C))) # label(redefinition_k4_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 429 (all A -v1_xboole_0(k1_zfmisc_1(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 430 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(B,k1_zfmisc_1(A)) -> k3_xboole_0(B,C) = k5_subset_1(A,B,C))) # label(redefinition_k5_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 431 (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]. 21.68/22.88 432 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k3_subset_1(A,k3_subset_1(A,B)))) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 433 (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]. 21.68/22.88 434 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 435 (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) -> (k1_xboole_0 != A -> m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A))))))))))))) # label(t59_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 436 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,A) -> (r2_hidden(D,C) <-> -r2_hidden(D,B)))) -> B = k3_subset_1(A,C)))))) # label(t52_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 437 (all A -v1_xboole_0(k1_tarski(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 438 (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]. 21.68/22.88 439 (all A all B (-v1_xboole_0(A) & -v1_xboole_0(B) -> (r1_xboole_0(A,B) <-> r1_subset_1(A,B)))) # label(redefinition_r1_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 440 $T # label(t2_subset_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 441 (all A all B (v1_setfam_1(A) & v1_setfam_1(B) -> v1_setfam_1(k2_xboole_0(A,B)))) # label(fc4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 442 (all A all B (r2_setfam_1(A,B) <-> (all C -(r2_hidden(C,B) & (all D -(r1_tarski(D,C) & r2_hidden(D,A))))))) # label(d3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 443 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 444 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_xboole_0(B) -> v1_xboole_0(k7_setfam_1(A,B)))) # label(fc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 445 (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]. 21.68/22.88 446 $T # label(t22_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 447 (all A all B -(A != k1_xboole_0 & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) & k1_xboole_0 != B)) # label(t10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 448 (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]. 21.68/22.88 449 (all A (r1_setfam_1(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t21_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 450 (all A r1_setfam_1(k3_setfam_1(A,A),A)) # label(t30_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 451 $T # label(d7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 452 $T # label(t16_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 453 (all A all B all C (r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) & (all D (r2_hidden(D,B) -> r1_xboole_0(D,C))) -> r1_tarski(C,k3_tarski(A)))) # label(t57_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 454 (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]. 21.68/22.88 455 $T # label(t43_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 456 (all A all B (r1_tarski(A,B) -> r1_setfam_1(A,B))) # label(t17_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 457 (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]. 21.68/22.88 458 (all A (v1_setfam_1(A) <-> -r2_hidden(k1_xboole_0,A))) # label(d9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 459 (all A all B all 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))))) <-> k3_setfam_1(A,B) = C)) # label(d5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 460 (all A all B all C (r2_hidden(A,B) & r1_xboole_0(A,C) -> r1_xboole_0(k1_setfam_1(B),C))) # label(t9_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 461 (all A all B (k1_xboole_0 != B -> k3_tarski(k4_setfam_1(k1_tarski(A),B)) = k4_xboole_0(A,k1_setfam_1(B)))) # label(t38_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 462 (all A A = k1_setfam_1(k1_tarski(A))) # label(t11_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 463 $T # label(t15_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 464 (all A r1_setfam_1(A,k2_setfam_1(A,A))) # label(t29_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 465 $T # label(dt_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 466 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> -(B != k1_xboole_0 & k1_xboole_0 = k7_setfam_1(A,B)))) # label(t46_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 467 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B != k1_xboole_0 -> k8_setfam_1(A,B) = k6_setfam_1(A,B)) & (B = k1_xboole_0 -> k8_setfam_1(A,B) = A))) # label(d10_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 468 (all A (v1_setfam_1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> -v1_xboole_0(B))))) # label(cc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 469 (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]. 21.68/22.88 470 $T # label(t13_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 471 $T # label(t42_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 472 $T # label(t26_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 473 (all A all B (B != k1_xboole_0 -> k4_xboole_0(A,k3_tarski(B)) = k1_setfam_1(k4_setfam_1(k1_tarski(A),B)))) # label(t37_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 474 (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]. 21.68/22.88 475 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> 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]. 21.68/22.88 476 (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]. 21.68/22.88 477 (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]. 21.68/22.88 478 (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]. 21.68/22.88 479 (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]. 21.68/22.88 480 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k7_setfam_1(A,k7_setfam_1(A,B)) = B)) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 481 (all A all B k3_xboole_0(A,k3_tarski(B)) = k3_tarski(k3_setfam_1(k1_tarski(A),B))) # label(t36_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 482 (all A r1_setfam_1(k1_xboole_0,A)) # label(t20_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 483 (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))) -> k4_subset_1(k1_zfmisc_1(A),k7_setfam_1(A,B),k7_setfam_1(A,C)) = k7_setfam_1(A,k4_subset_1(k1_zfmisc_1(A),B,C)))))) # label(t54_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 484 (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(k3_subset_1(A,C),k7_setfam_1(A,B)) <-> r2_hidden(C,B)))))) # label(t49_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 485 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k1_xboole_0 != B -> k6_subset_1(A,k2_subset_1(A),k6_setfam_1(A,B)) = k5_setfam_1(A,k7_setfam_1(A,B))))) # label(t48_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 486 (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]. 21.68/22.88 487 (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]. 21.68/22.88 488 $T # label(dt_k3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 489 (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]. 21.68/22.88 490 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (B = k1_tarski(A) -> k7_setfam_1(A,B) = k1_tarski(k1_xboole_0)))) # label(t55_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 491 (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]. 21.68/22.88 492 (all A (-v1_xboole_0(A) -> v1_setfam_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 493 (all A all B r1_setfam_1(A,A)) # label(reflexivity_r1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 494 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (r2_hidden(B,A) -> ((all D (r2_hidden(D,C) -> r2_hidden(B,D))) <-> r2_hidden(B,k8_setfam_1(A,C)))))) # label(t58_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 495 (all A r1_setfam_1(k4_setfam_1(A,A),A)) # label(t31_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 496 (all A (-v2_setfam_1(A) -> -v1_xboole_0(A))) # label(cc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 497 (all A all B all C (C = k2_setfam_1(A,B) <-> (all D ((exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & k2_xboole_0(E,F) = D)) <-> r2_hidden(D,C))))) # label(d4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 498 $T # label(t50_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 499 $T # label(dt_k4_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 500 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k5_setfam_1(A,B) = k3_tarski(B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 501 $T # label(t33_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 502 $T # label(t1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 503 (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]. 21.68/22.88 504 (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]. 21.68/22.88 505 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)))) # label(fc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 506 (all A all B (B != k1_xboole_0 -> k1_setfam_1(k2_setfam_1(k1_tarski(A),B)) = k2_xboole_0(A,k1_setfam_1(B)))) # label(t35_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 507 (exists A -v2_setfam_1(A)) # label(rc2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 508 (all A all B -(-r1_tarski(k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B)),k1_setfam_1(k2_setfam_1(A,B))) & k1_xboole_0 != B & A != k1_xboole_0)) # label(t40_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 509 (all A all B all C (r2_hidden(A,B) & r1_tarski(A,C) -> r1_tarski(k1_setfam_1(B),C))) # label(t8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 510 (all A (-v2_setfam_1(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 511 $T # label(t45_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 512 $T # label(t32_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 513 (all A all B ((all C -((all D -(r2_hidden(D,B) & r1_tarski(C,D))) & r2_hidden(C,A))) <-> r1_setfam_1(A,B))) # label(d2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 514 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> r2_hidden(D,B)))) -> C = B))))) # label(t44_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 515 (all A all B all C ((all D ((exists E exists F (r2_hidden(E,A) & r2_hidden(F,B) & k4_xboole_0(E,F) = D)) <-> r2_hidden(D,C))) <-> C = k4_setfam_1(A,B))) # label(d6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 516 $T # label(t27_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 517 (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]. 21.68/22.88 518 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k7_setfam_1(A,C) = k7_setfam_1(A,B) -> B = C))))) # label(t53_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 519 (all A all B r2_setfam_1(B,B)) # label(reflexivity_r2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 520 (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]. 21.68/22.88 521 (all A all B all C (r1_setfam_1(B,C) & r1_setfam_1(A,B) -> r1_setfam_1(A,C))) # label(t23_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 522 (all A all B k2_setfam_1(B,A) = k2_setfam_1(A,B)) # label(commutativity_k2_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 523 (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]. 21.68/22.88 524 (all A all B (r1_tarski(A,B) -> r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) | k1_xboole_0 = A)) # label(t7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 525 (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]. 21.68/22.88 526 (all A r1_tarski(k1_setfam_1(A),k3_tarski(A))) # label(t3_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 527 (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(k3_subset_1(A,D),B) <-> r2_hidden(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 528 $T # label(t28_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 529 (all A all B ((k1_xboole_0 = A -> (B = k1_setfam_1(A) <-> k1_xboole_0 = 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]. 21.68/22.88 530 (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]. 21.68/22.88 531 $T # label(t14_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 532 (exists A (-v1_xboole_0(A) & v1_setfam_1(A))) # label(rc1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 533 (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]. 21.68/22.88 534 (all A all B (m1_subset_1(A,k1_zfmisc_1(B)) <-> r1_tarski(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 535 (all A all B all C -(r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 536 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(C)) & r2_hidden(A,B) -> m1_subset_1(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 537 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 538 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 539 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k1_relat_1(k7_relat_1(C,B))) <-> r2_hidden(A,B) & r2_hidden(A,k1_relat_1(C))))) # label(t86_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 540 (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]. 21.68/22.88 541 (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]. 21.68/22.88 542 (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]. 21.68/22.88 543 (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]. 21.68/22.88 544 (all A all B all C (v1_relat_1(C) -> k9_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)))) # label(t153_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 545 (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]. 21.68/22.88 546 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k1_relat_1(B)) -> A = k1_relat_1(k7_relat_1(B,A))))) # label(t91_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 547 (all A (v1_relat_1(A) -> k1_xboole_0 = k9_relat_1(A,k1_xboole_0))) # label(t149_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 548 (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]. 21.68/22.88 549 (exists A (v1_relat_1(A) & -v1_xboole_0(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 550 (all A (v1_relat_1(A) -> k8_relat_1(k2_relat_1(A),A) = A)) # label(t126_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 551 (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]. 21.68/22.88 552 $T # label(t83_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 553 (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]. 21.68/22.88 554 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 555 (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]. 21.68/22.88 556 (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]. 21.68/22.88 557 (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]. 21.68/22.88 558 (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]. 21.68/22.88 559 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> k8_relat_1(A,B) = B))) # label(t125_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 560 (all A (v1_relat_1(A) -> (all B all C ((all D (r2_hidden(D,C) <-> (exists E (r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B))))) <-> C = k10_relat_1(A,B))))) # label(d14_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 561 (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]. 21.68/22.88 562 (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]. 21.68/22.88 563 (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]. 21.68/22.88 564 (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]. 21.68/22.88 565 (all A (v1_relat_1(A) -> k1_xboole_0 = k10_relat_1(A,k1_xboole_0))) # label(t171_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 566 (all A (v1_relat_1(A) -> k1_xboole_0 = k8_relat_1(k1_xboole_0,A))) # label(t137_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 567 (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]. 21.68/22.88 568 (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]. 21.68/22.88 569 (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]. 21.68/22.88 570 $T # label(t165_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 571 (all A v1_relat_1(k6_relat_1(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 572 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(C,B) -> r1_tarski(C,k7_relat_1(B,A))))))) # label(t186_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 573 (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]. 21.68/22.88 574 (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_tarski(A,C) = k1_relat_1(E) & k2_relat_1(E) = k2_tarski(B,D)))) # label(t24_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 575 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> ((all D all E (r2_hidden(k4_tarski(D,E),C) <-> r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B))) <-> k8_relat_1(A,B) = C))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 576 (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]. 21.68/22.88 577 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k9_relat_1(B,k2_relat_1(A)) = k2_relat_1(k5_relat_1(A,B)))))) # label(t160_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 578 (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]. 21.68/22.88 579 $T # label(t12_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 580 (all A (A = k1_relat_1(k6_relat_1(A)) & k2_relat_1(k6_relat_1(A)) = A)) # label(t71_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.88 581 (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]. 21.68/22.88 582 (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]. 21.68/22.88 583 (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]. 21.68/22.89 584 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B))) # label(t128_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 585 (all A all B all C (v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C))))) # label(t30_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 586 (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]. 21.68/22.89 587 $T # label(t142_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 588 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_relat_1(A),k3_relat_1(B))))))) # label(t31_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 589 $T # label(t58_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 590 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_xboole_0(k5_relat_1(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 591 (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]. 21.68/22.89 592 (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]. 21.68/22.89 593 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))))) # label(t13_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 594 (all A (v1_relat_1(A) -> k1_xboole_0 = k5_relat_1(A,k1_xboole_0) & k1_xboole_0 = k5_relat_1(k1_xboole_0,A))) # label(t62_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 595 (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]. 21.68/22.89 596 $T # label(t69_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 597 (all A k7_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t111_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 598 (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]. 21.68/22.89 599 (all A (v1_relat_1(A) -> (all B all C ((all D (r2_hidden(D,C) <-> (exists E (r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B))))) <-> C = k9_relat_1(A,B))))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 600 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k3_xboole_0(A,B)) = k7_relat_1(k7_relat_1(C,A),B))) # label(t100_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 601 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 602 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,A),B)))) # label(t102_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 603 (all A all B (v1_relat_1(B) -> k3_xboole_0(B,k2_zfmisc_1(k1_relat_1(B),A)) = k8_relat_1(A,B))) # label(t124_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 604 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(A,C)))) # label(t130_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 605 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (B = k4_relat_1(A) <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(D,C),A)))))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 606 $T # label(t57_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 607 $T # label(t164_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 608 (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]. 21.68/22.89 609 (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]. 21.68/22.89 610 $T # label(t61_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 611 (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]. 21.68/22.89 612 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k2_relat_1(B)) & (all C -r2_hidden(C,k1_relat_1(B)))))) # label(t19_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 613 (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]. 21.68/22.89 614 (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]. 21.68/22.89 615 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (A = B <-> (all C all D (r2_hidden(k4_tarski(C,D),B) <-> r2_hidden(k4_tarski(C,D),A)))))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 616 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 617 $T # label(t16_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 618 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k2_tarski(A,B) = k3_relat_1(C)))) # label(t32_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 619 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & k1_xboole_0 = k9_relat_1(B,A) & r1_tarski(A,k1_relat_1(B))))) # label(t152_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 620 (all A all B (v1_relat_1(B) -> k9_relat_1(B,A) = k9_relat_1(B,k3_xboole_0(k1_relat_1(B),A)))) # label(t145_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 621 (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]. 21.68/22.89 622 (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]. 21.68/22.89 623 (all A (-v1_xboole_0(A) & v1_relat_1(A) -> -v1_xboole_0(k2_relat_1(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 624 (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]. 21.68/22.89 625 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k2_xboole_0(k5_relat_1(A,B),k5_relat_1(A,C)) = k5_relat_1(A,k2_xboole_0(B,C)))))))) # label(t51_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 626 (all A (v1_relat_1(A) <-> (all B -((all C all D B != k4_tarski(C,D)) & r2_hidden(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 627 $T # label(t42_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 628 (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]. 21.68/22.89 629 (all A all B (v1_relat_1(B) -> (k7_relat_1(B,A) = k1_xboole_0 <-> r1_xboole_0(k1_relat_1(B),A)))) # label(t95_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 630 (all A all B (v1_relat_1(A) & v1_relat_1(B) -> v1_relat_1(k2_xboole_0(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 631 (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]. 21.68/22.89 632 (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]. 21.68/22.89 633 $T # label(t35_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 634 (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]. 21.68/22.89 635 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(A,D) = k7_relat_1(B,D) & k7_relat_1(B,C) = k7_relat_1(A,C) -> k7_relat_1(B,k2_xboole_0(C,D)) = k7_relat_1(A,k2_xboole_0(C,D)))))))) # label(t185_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 636 (all A all B all C (v1_relat_1(C) -> ((exists D (r2_hidden(D,k1_relat_1(C)) & r2_hidden(k4_tarski(D,A),C) & r2_hidden(D,B))) <-> r2_hidden(A,k9_relat_1(C,B))))) # label(t143_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 637 (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]. 21.68/22.89 638 $T # label(t113_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 639 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> k2_relat_1(k8_relat_1(A,B)) = A))) # label(t120_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 640 (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]. 21.68/22.89 641 (all A (v1_relat_1(A) -> k2_relat_1(A) = k1_relat_1(k4_relat_1(A)) & k2_relat_1(k4_relat_1(A)) = k1_relat_1(A))) # label(t37_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 642 (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]. 21.68/22.89 643 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 644 $T # label(t2_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 645 (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]. 21.68/22.89 646 (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]. 21.68/22.89 647 (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]. 21.68/22.89 648 $T # label(t1_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 649 $T # label(t141_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 650 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k10_relat_1(C,A),k10_relat_1(D,B))))))) # label(t180_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 651 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k5_relat_1(k7_relat_1(B,A),C) = k7_relat_1(k5_relat_1(B,C),A))))) # label(t112_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 652 (all A (v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A)) # label(t78_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 653 (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]. 21.68/22.89 654 (all A (v1_xboole_0(A) -> v1_relat_1(k1_relat_1(A)) & v1_xboole_0(k1_relat_1(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 655 (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]. 21.68/22.89 656 (all A (v1_relat_1(A) -> k10_relat_1(A,k2_relat_1(A)) = k1_relat_1(A))) # label(t169_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 657 (all A k4_relat_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t72_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 658 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k1_relat_1(k5_relat_1(A,B)) = k10_relat_1(A,k1_relat_1(B)))))) # label(t182_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 659 $T # label(t114_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 660 (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]. 21.68/22.89 661 (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]. 21.68/22.89 662 (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]. 21.68/22.89 663 (all A all B all C (v1_relat_1(C) -> k7_relat_1(C,k4_xboole_0(A,B)) = k4_xboole_0(k7_relat_1(C,A),k7_relat_1(C,B)))) # label(t109_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 664 (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]. 21.68/22.89 665 (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]. 21.68/22.89 666 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k2_relat_1(B))))) # label(t96_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 667 (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]. 21.68/22.89 668 (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]. 21.68/22.89 669 (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]. 21.68/22.89 670 (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]. 21.68/22.89 671 (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]. 21.68/22.89 672 (all A all B (v1_relat_1(B) -> (r1_xboole_0(k1_relat_1(B),A) <-> k9_relat_1(B,A) = k1_xboole_0))) # label(t151_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 673 $T # label(t8_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 674 $T # label(t43_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 675 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k10_relat_1(B,k10_relat_1(C,A)) = k10_relat_1(k5_relat_1(B,C),A))))) # label(t181_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 676 (all A (v1_relat_1(A) & -v1_xboole_0(A) -> -v1_xboole_0(k1_relat_1(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 677 (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]. 21.68/22.89 678 $T # label(t85_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 679 (all A (v1_relat_1(A) -> (all B (r1_xboole_0(B,k1_relat_1(A)) -> k1_xboole_0 = k7_relat_1(A,B))))) # label(t187_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 680 (all A k10_relat_1(k1_xboole_0,A) = k1_xboole_0) # label(t172_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 681 (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]. 21.68/22.89 682 $T # label(t162_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 683 (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]. 21.68/22.89 684 (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]. 21.68/22.89 685 $T # label(t36_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 686 (all A (v1_relat_1(A) -> k5_relat_1(A,k6_relat_1(k2_relat_1(A))) = A)) # label(t80_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 687 (all A all B (v1_relat_1(B) & v1_xboole_0(A) -> v1_relat_1(k5_relat_1(A,B)) & v1_xboole_0(k5_relat_1(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 688 (all A k1_xboole_0 = k9_relat_1(k1_xboole_0,A)) # label(t150_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 689 $T # label(t17_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 690 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k7_relat_1(k7_relat_1(C,B),A) = k7_relat_1(C,A)))) # label(t103_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 691 (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(D,B) & r2_hidden(k4_tarski(A,D),C)))))) # label(t166_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 692 (all A (v1_relat_1(A) -> (k1_xboole_0 = k1_relat_1(A) | k1_xboole_0 = k2_relat_1(A) -> A = k1_xboole_0))) # label(t64_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 693 (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]. 21.68/22.89 694 (exists A (v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 695 (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]. 21.68/22.89 696 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> k5_relat_1(k4_relat_1(B),k4_relat_1(A)) = k4_relat_1(k5_relat_1(A,B)))))) # label(t54_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 697 (all A (v1_relat_1(A) -> (all B (B = k2_relat_1(A) <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 698 (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]. 21.68/22.89 699 $T # label(t59_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 700 $T # label(t70_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 701 (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]. 21.68/22.89 702 $T # label(t7_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 703 (all A (v1_relat_1(A) -> r1_tarski(k2_relat_1(A),k3_relat_1(A)) & r1_tarski(k1_relat_1(A),k3_relat_1(A)))) # label(t29_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 704 (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]. 21.68/22.89 705 (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]. 21.68/22.89 706 (all A all B all C (v1_relat_1(C) -> k8_relat_1(k4_xboole_0(A,B),C) = k4_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)))) # label(t136_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 707 (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]. 21.68/22.89 708 (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]. 21.68/22.89 709 $T # label(t84_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 710 (all A (v1_relat_1(A) -> v1_relat_1(k4_relat_1(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 711 (all A all B (v1_relat_1(B) -> k8_relat_1(A,B) = k5_relat_1(B,k6_relat_1(A)))) # label(t123_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 712 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 713 (all A all B (v1_relat_1(B) -> r1_tarski(k5_relat_1(k6_relat_1(A),B),B) & r1_tarski(k5_relat_1(B,k6_relat_1(A)),B))) # label(t76_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 714 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k8_relat_1(B,k8_relat_1(A,C)) = k8_relat_1(A,C)))) # label(t129_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 715 (all A all B (v1_relat_1(B) -> (r1_tarski(k1_relat_1(B),A) -> k5_relat_1(k6_relat_1(A),B) = B))) # label(t77_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 716 (exists A (v1_relat_1(A) & v3_relat_1(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 717 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k5_relat_1(k6_relat_1(A),B))) # label(t94_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 718 (all A (v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_xboole_0 = A))) # label(t56_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 719 (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]. 21.68/22.89 720 (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]. 21.68/22.89 721 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C all D (k7_relat_1(B,D) = k7_relat_1(A,D) & r1_tarski(C,D) -> k7_relat_1(A,C) = k7_relat_1(B,C))))))) # label(t188_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 722 (all A k8_relat_1(A,k1_xboole_0) = k1_xboole_0) # label(t138_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 723 (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]. 21.68/22.89 724 (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]. 21.68/22.89 725 (all A all B (v1_relat_1(B) -> -(A != k1_xboole_0 & k10_relat_1(B,A) = k1_xboole_0 & r1_tarski(A,k2_relat_1(B))))) # label(t174_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 726 (all A all B (v1_relat_1(B) -> -(r2_hidden(A,k1_relat_1(B)) & (all C -r2_hidden(C,k2_relat_1(B)))))) # label(t18_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 727 (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]. 21.68/22.89 728 (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]. 21.68/22.89 729 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> k9_relat_1(k5_relat_1(B,C),A) = k9_relat_1(C,k9_relat_1(B,A)))))) # label(t159_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 730 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 731 (all A all B v1_relat_1(k2_zfmisc_1(A,B))) # label(t6_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 732 (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]. 21.68/22.89 733 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_tarski(A,B) -> r1_tarski(k1_relat_1(A),k1_relat_1(B)) & r1_tarski(k2_relat_1(A),k2_relat_1(B))))))) # label(t25_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 734 (all A all B v1_relat_1(k1_tarski(k4_tarski(A,B)))) # label(t4_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 735 (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]. 21.68/22.89 736 (all A (v1_relat_1(A) -> (k1_relat_1(A) = k1_xboole_0 <-> k2_relat_1(A) = k1_xboole_0))) # label(t65_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 737 (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]. 21.68/22.89 738 $T # label(t68_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 739 (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]. 21.68/22.89 740 (all A (v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k2_relat_1(A)) -> k1_xboole_0 = B))))) # label(t184_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 741 (all A all B all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k8_relat_1(A,C),k8_relat_1(B,D))))))) # label(t133_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 742 (all A all B (v1_relat_1(B) -> k2_relat_1(k7_relat_1(B,A)) = k9_relat_1(B,A))) # label(t148_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 743 (all A (v1_relat_1(A) -> k1_xboole_0 = k7_relat_1(A,k1_xboole_0))) # label(t110_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 744 (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]. 21.68/22.89 745 (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]. 21.68/22.89 746 (all A all B (v1_relat_1(B) -> k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A))) # label(t90_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 747 (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]. 21.68/22.89 748 (exists A (v1_relat_1(A) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_relat_1) & r2_hidden(C,f2_s1_relat_1) & p1_s1_relat_1(B,C))))) # label(s1_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 749 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r1_xboole_0(k2_relat_1(A),k1_relat_1(B)) -> k5_relat_1(A,B) = k1_xboole_0))))) # label(t67_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 750 (all A all B all C (v1_relat_1(C) -> (k1_tarski(k4_tarski(A,B)) = C -> k1_tarski(B) = k2_relat_1(C) & k1_relat_1(C) = k1_tarski(A)))) # label(t23_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 751 (all A (v1_relat_1(A) -> k3_relat_1(A) = k3_relat_1(k4_relat_1(A)))) # label(t38_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.68/22.89 752 (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]. 21.68/22.89 753 (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]. 21.68/22.89 754 (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]. 21.68/22.89 755 (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]. 21.68/22.89 756 (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(D,B) & r2_hidden(k4_tarski(D,E),A))) <-> k7_relat_1(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 757 (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]. 21.72/22.89 758 (all A all B (v1_relat_1(B) -> k7_relat_1(B,A) = k7_relat_1(k7_relat_1(B,A),A))) # label(t101_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 759 $T # label(t63_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 760 $T # label(t11_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 761 (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]. 21.72/22.89 762 (all A (v1_xboole_0(A) -> v1_relat_1(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 763 (all A all B (v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) -> B = k5_relat_1(B,k6_relat_1(A))))) # label(t79_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 764 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (k5_relat_1(A,B) = C <-> (all D all E ((exists F (r2_hidden(k4_tarski(F,E),B) & r2_hidden(k4_tarski(D,F),A))) <-> r2_hidden(k4_tarski(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 765 (all A all B all C (v1_relat_1(C) -> k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) = k8_relat_1(k2_xboole_0(A,B),C))) # label(t134_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 766 (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]. 21.72/22.89 767 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_relat_1(D) -> (r1_tarski(k2_relat_1(C),A) & k5_relat_1(C,B) = k6_relat_1(k1_relat_1(D)) & k6_relat_1(A) = k5_relat_1(B,D) & k1_relat_1(B) = A -> D = C))))))) # label(t82_relat_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 768 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (B = k2_relat_1(A) <-> (all C ((exists D (r2_hidden(D,k1_relat_1(A)) & k1_funct_1(A,D) = C)) <-> r2_hidden(C,B))))))) # label(d5_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 769 $T # label(t75_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 770 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(C) & v2_funct_1(B) & B = k5_relat_1(C,B) & r1_tarski(k2_relat_1(C),A) & A = k1_relat_1(B) -> k6_relat_1(A) = C))))) # label(t50_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 771 $T # label(t74_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 772 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B r1_tarski(k10_relat_1(A,k9_relat_1(A,B)),B)) -> v2_funct_1(A)))) # label(t153_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 773 $T # label(t100_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 774 $T # label(t106_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 775 (exists A (v1_funct_1(A) & v2_relat_1(A) & v1_relat_1(A))) # label(rc5_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 776 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,B) -> k7_relat_1(C,A) = k7_relat_1(k7_relat_1(C,B),A) & k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,A)))) # label(t82_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 777 $T # label(t24_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 778 $T # label(t116_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 779 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> v2_funct_1(k5_relat_1(A,B))))))) # label(t46_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 780 (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) & k6_relat_1(k2_relat_1(A)) = k5_relat_1(B,A) -> B = k2_funct_1(A)))))) # label(t64_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 781 (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]. 21.72/22.89 782 $T # label(t133_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 783 (all A (v1_relat_1(A) & v1_funct_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)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) -> B = A))))) # label(t9_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 784 (all A (v1_funct_1(A) & v1_relat_1(A) -> k5_relat_1(k6_relat_1(k1_relat_1(A)),A) = A & A = k5_relat_1(A,k6_relat_1(k2_relat_1(A))))) # label(t42_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 785 $T # label(t41_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 786 $T # label(t29_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 787 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(A) = k2_relat_1(B) & v2_funct_1(k5_relat_1(B,A)) -> v2_funct_1(A) & v2_funct_1(B)))))) # label(t48_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 788 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) <-> r2_hidden(k1_funct_1(C,B),A) & r2_hidden(B,k1_relat_1(C))))) # label(t86_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 789 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_relat_1(A)) & k1_relat_1(C) = k1_relat_1(B) & k5_relat_1(B,A) = k5_relat_1(C,A) & r1_tarski(k2_relat_1(B),k1_relat_1(A)) -> C = B)))))))) # label(t49_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 790 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> v2_funct_1(k2_funct_1(A))))) # label(t62_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 791 (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]. 21.72/22.89 792 $T # label(d2_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 793 $T # label(t102_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 794 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) & v2_funct_1(A) -> k2_funct_1(k5_relat_1(A,B)) = k5_relat_1(k2_funct_1(B),k2_funct_1(A))))))) # label(t66_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 795 $T # label(t5_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 796 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_relat_1(k5_relat_1(k6_relat_1(A),B)) = k3_xboole_0(k1_relat_1(B),A))) # label(t37_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 797 $T # label(d11_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 798 $T # label(t115_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 799 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s4_funct_1) -> f2_s4_funct_1(B) = k1_funct_1(A,B))) & k1_relat_1(A) = f1_s4_funct_1 & v1_relat_1(A))) # label(s4_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 800 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k3_xboole_0(k1_relat_1(C),A)) -> k1_funct_1(k5_relat_1(k6_relat_1(A),C),B) = k1_funct_1(C,B)))) # label(t38_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 801 $T # label(t101_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 802 $T # label(t69_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 803 $T # label(t88_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 804 $T # label(t114_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 805 $T # label(t131_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 806 $T # label(t31_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 807 $T # label(t96_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.89 808 $T # label(t128_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 809 $T # label(t93_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 810 (all A (v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) -> v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 811 (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]. 21.72/22.90 812 $T # label(t6_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 813 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(A,k9_relat_1(C,B)) = k9_relat_1(k8_relat_1(A,C),B))) # label(t126_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 814 (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]. 21.72/22.90 815 $T # label(t90_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 816 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k4_relat_1(A) = k2_funct_1(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 817 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 21.72/22.90 818 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k9_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t121_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 819 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,A) -> k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t72_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 820 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C -((all D -(k1_funct_1(B,D) = C & r2_hidden(D,k1_relat_1(B)))) & r2_hidden(C,A))) -> r1_tarski(A,k2_relat_1(B))))) # label(t19_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 821 $T # label(t105_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 822 $T # label(t39_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 823 (exists A ((all B (r2_hidden(B,f1_s3_funct_1) -> k1_funct_1(A,B) = f2_s3_funct_1(B))) & f1_s3_funct_1 = k1_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s3_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 824 (exists A (v1_relat_1(A) & v2_funct_1(A) & v1_funct_1(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 825 $T # label(t129_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 826 $T # label(t7_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 827 (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(k7_relat_1(C,A),B) = k1_funct_1(C,B)))) # label(t70_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 828 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(A) = k1_relat_1(k5_relat_1(k2_funct_1(A),A)) & k2_relat_1(A) = k2_relat_1(k5_relat_1(k2_funct_1(A),A))))) # label(t59_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 829 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(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]. 21.72/22.90 830 $T # label(t3_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 831 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(k5_relat_1(B,A)) -> r1_tarski(k2_relat_1(B),k1_relat_1(A))))))) # label(t27_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 832 (all A all B (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 833 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) -> k4_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B)) = k9_relat_1(C,k4_xboole_0(A,B))))) # label(t123_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 834 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_relat_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_xboole_0(k1_funct_1(A,B))))))) # label(d14_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 835 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C ((all D (r2_hidden(k1_funct_1(A,D),B) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,C))) <-> k10_relat_1(A,B) = C)))) # label(d13_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 836 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k9_relat_1(A,k4_xboole_0(B,C)) = k4_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C))) -> v2_funct_1(A)))) # label(t124_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 837 (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]. 21.72/22.90 838 (all A all B (v1_relat_1(B) & v1_funct_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]. 21.72/22.90 839 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k1_relat_1(k7_relat_1(B,A)),k1_relat_1(B)) & r1_tarski(k2_relat_1(k7_relat_1(B,A)),k2_relat_1(B)))) # label(t76_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 840 $T # label(t95_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 841 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k2_relat_1(k2_funct_1(A)) = k1_relat_1(A) & k2_relat_1(A) = k1_relat_1(k2_funct_1(A))))) # label(t55_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 842 (all A (v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) -> v1_setfam_1(k2_relat_1(A)))) # label(fc6_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 843 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_relat_1(A) <-> (all B -(r2_hidden(B,k1_relat_1(A)) & v1_xboole_0(k1_funct_1(A,B))))))) # label(d15_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 844 $T # label(d10_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 845 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (k6_relat_1(A) = B <-> (all C (r2_hidden(C,A) -> k1_funct_1(B,C) = C)) & k1_relat_1(B) = A))) # label(t34_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 846 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_funct_1(A) = B <-> k2_relat_1(A) = k1_relat_1(B) & (all C all D ((D = k1_funct_1(B,C) & r2_hidden(C,k2_relat_1(A)) -> r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D)) & (C = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(B,C) = D & r2_hidden(C,k2_relat_1(A))))))))))) # label(t54_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 847 $T # label(t45_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 848 $T # label(t104_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 849 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_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]. 21.72/22.90 850 $T # label(t108_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 851 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k9_relat_1(B,k10_relat_1(B,A)),A))) # label(t145_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 852 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(A) & k1_relat_1(A) = k2_relat_1(B) & (all C all D (r2_hidden(C,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(B)) -> (k1_funct_1(B,D) = C <-> D = k1_funct_1(A,C)))) & k1_relat_1(B) = k2_relat_1(A) -> k2_funct_1(A) = B))))) # label(t60_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 853 (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]. 21.72/22.90 854 $T # label(t110_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 855 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k5_relat_1(B,C) = k5_relat_1(B,D) & A = k1_relat_1(D) & A = k1_relat_1(C) & k2_relat_1(B) = A -> D = C))))))) # label(t156_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 856 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v2_funct_1(C) & r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) -> r1_tarski(A,B)))) # label(t157_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 857 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),C) <-> r2_hidden(A,k1_relat_1(C)) & B = k1_funct_1(C,A)))) # label(t8_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 858 (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)) & k6_relat_1(k2_relat_1(A)) = k5_relat_1(k2_funct_1(A),A)))) # label(t61_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 859 (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)) & k1_relat_1(B) = k2_relat_1(A) -> B = k2_funct_1(A)))))) # label(t63_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 860 $T # label(t103_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 861 (exists A (v1_xboole_0(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 862 $T # label(t94_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 863 (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]. 21.72/22.90 864 $T # label(t13_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 865 $T # label(t78_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 866 $T # label(t11_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 867 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 868 (all A all B k6_relat_1(k3_xboole_0(A,B)) = k5_relat_1(k6_relat_1(B),k6_relat_1(A))) # label(t43_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 869 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k2_relat_1(B)) & v2_funct_1(B) -> 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) = A))) # label(t57_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 870 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B exists C r1_tarski(k10_relat_1(A,k1_tarski(B)),k1_tarski(C))) <-> v2_funct_1(A)))) # label(t159_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 871 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_tarski(A) -> k2_relat_1(B) = k1_tarski(k1_funct_1(B,A))))) # label(t14_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 872 $T # label(t112_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 873 (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]. 21.72/22.90 874 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> C = D)) & (all B -(r2_hidden(B,A) & (all C all D B != k4_tarski(C,D)))) -> v1_relat_1(A) & v1_funct_1(A))) # label(t2_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 875 (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]. 21.72/22.90 876 (all A all B all C (p1_s1_funct_1(A,C) & p1_s1_funct_1(A,B) -> C = B)) -> (exists A ((all B all C (r2_hidden(k4_tarski(B,C),A) <-> r2_hidden(B,f1_s1_funct_1) & p1_s1_funct_1(B,C))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 877 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(k8_relat_1(A,C))) -> k1_funct_1(k8_relat_1(A,C),B) = k1_funct_1(C,B)))) # label(t87_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 878 $T # label(t10_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 879 (all A ((all B all C all D (r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(B,C),A) -> C = D)) <-> v1_funct_1(A))) # label(d1_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 880 $T # label(t140_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 881 $T # label(t91_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 882 $T # label(t132_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 883 (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)) & D = k1_funct_1(A,E) & r2_hidden(E,B))))))))) # label(d12_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 884 (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]. 21.72/22.90 885 (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]. 21.72/22.90 886 $T # label(t113_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 887 $T # label(d6_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 888 $T # label(t92_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 889 $T # label(t81_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 890 $T # label(t83_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 891 $T # label(t141_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 892 (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 (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) & r2_hidden(D,k1_relat_1(A)) <-> r2_hidden(D,k1_relat_1(C)))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k1_funct_1(A,D)) = k1_funct_1(C,D))) -> k5_relat_1(A,B) = C))))))) # label(t20_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 893 $T # label(t134_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 894 $T # label(t28_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 895 $T # label(t1_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 896 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) & r2_hidden(k1_funct_1(C,A),k1_relat_1(B)) <-> r2_hidden(A,k1_relat_1(k5_relat_1(C,B)))))))) # label(t21_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 897 (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]. 21.72/22.90 898 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k9_relat_1(B,k10_relat_1(B,A)) = k3_xboole_0(A,k9_relat_1(B,k1_relat_1(B))))) # label(t148_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 899 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) -> A = k2_funct_1(k2_funct_1(A))))) # label(t65_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 900 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> k9_relat_1(C,k2_tarski(A,B)) = k2_tarski(k1_funct_1(C,A),k1_funct_1(C,B))))) # label(t118_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 901 (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]. 21.72/22.90 902 $T # label(t36_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 903 (all A (k1_xboole_0 != A -> (all B exists C (v1_relat_1(C) & v1_funct_1(C) & k1_tarski(B) = k2_relat_1(C) & A = k1_relat_1(C))))) # label(t15_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 904 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_funct_1(A) <-> (all B all C (r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) & r2_hidden(B,k1_relat_1(A)) -> B = C))))) # label(d8_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 905 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(k1_funct_1(C,D),A) & r2_hidden(D,k1_relat_1(C)) <-> r2_hidden(D,k1_relat_1(B)))) & (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) <-> B = k8_relat_1(A,C)))))) # label(t85_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 906 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k2_relat_1(B),A) & (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (A = k1_relat_1(C) & A = k1_relat_1(D) & k5_relat_1(B,C) = k5_relat_1(B,D) -> D = C))))) -> A = k2_relat_1(B)))) # label(t33_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 907 $T # label(t135_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 908 (all A (v1_xboole_0(A) -> v1_funct_1(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 909 (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]. 21.72/22.90 910 (all A all B (v1_relat_1(B) -> (k10_relat_1(B,k1_tarski(A)) != k1_xboole_0 <-> r2_hidden(A,k2_relat_1(B))))) # label(t142_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 911 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 912 (all A all B (v1_relat_1(B) -> ((all C -(r2_hidden(C,A) & k1_xboole_0 = k10_relat_1(B,k1_tarski(C)))) -> r1_tarski(A,k2_relat_1(B))))) # label(t143_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 913 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(A,k2_relat_1(k5_relat_1(C,B))) -> r2_hidden(A,k2_relat_1(B))))))) # label(t25_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 914 (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]. 21.72/22.90 915 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v2_funct_1(A) -> k1_relat_1(A) = k2_relat_1(k5_relat_1(A,k2_funct_1(A))) & k1_relat_1(A) = k1_relat_1(k5_relat_1(A,k2_funct_1(A)))))) # label(t58_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 916 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) & v2_funct_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]. 21.72/22.90 917 $T # label(t79_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 918 $T # label(t119_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 919 $T # label(t26_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 920 (all A all B (v1_funct_1(B) & v1_relat_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]. 21.72/22.90 921 $T # label(d7_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 922 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_tarski(k1_funct_1(B,A)) = k9_relat_1(B,k1_tarski(A))))) # label(t117_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 923 (all A all B -((all C (v1_relat_1(C) & v1_funct_1(C) -> -(B = k1_relat_1(C) & r1_tarski(k2_relat_1(C),A)))) & -(k1_xboole_0 = A & k1_xboole_0 != B))) # label(t18_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 924 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(k2_relat_1(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]. 21.72/22.90 925 (all A ((all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (A = k1_relat_1(C) & A = k1_relat_1(B) -> B = C))))) -> A = k1_xboole_0)) # label(t16_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 926 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(B,k2_relat_1(C)) & r1_tarski(A,k2_relat_1(C)) & k10_relat_1(C,B) = k10_relat_1(C,A) -> A = B))) # label(t161_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 927 (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]. 21.72/22.90 928 $T # label(t130_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 929 (exists A (v1_relat_1(A) & v1_funct_1(A) & v3_relat_1(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 930 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C ((r2_hidden(B,k1_relat_1(A)) -> (r2_hidden(k4_tarski(B,C),A) <-> C = k1_funct_1(A,B))) & (-r2_hidden(B,k1_relat_1(A)) -> (C = k1_funct_1(A,B) <-> C = k1_xboole_0)))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 931 $T # label(d3_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 932 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k3_xboole_0(A,B)))) # label(t137_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 933 $T # label(t32_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 934 (all A (v1_relat_1(A) & v1_funct_1(A) -> ((all B -(r2_hidden(B,k2_relat_1(A)) & (all C k1_tarski(C) != k10_relat_1(A,k1_tarski(B))))) <-> v2_funct_1(A)))) # label(t144_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 935 (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]. 21.72/22.90 936 $T # label(t136_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 937 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k2_relat_1(B)) -> A = k9_relat_1(B,k10_relat_1(B,A))))) # label(t147_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 938 (all A k2_funct_1(k6_relat_1(A)) = k6_relat_1(A)) # label(t67_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 939 (exists A (v1_funct_1(A) & v1_relat_1(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 940 $T # label(t127_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 941 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> k4_xboole_0(k10_relat_1(C,A),k10_relat_1(C,B)) = k10_relat_1(C,k4_xboole_0(A,B)))) # label(t138_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 942 $T # label(t77_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 943 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(B,A) = k10_relat_1(k2_funct_1(B),A)))) # label(t154_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 944 $T # label(t109_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 945 (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]. 21.72/22.90 946 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(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]. 21.72/22.90 947 $T # label(t98_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 948 $T # label(t80_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 949 (all A -((all B -p1_s2_funct_1(A,B)) & r2_hidden(A,f1_s2_funct_1))) & (all A all B all C (r2_hidden(A,f1_s2_funct_1) & p1_s2_funct_1(A,B) & p1_s2_funct_1(A,C) -> C = B)) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (r2_hidden(B,f1_s2_funct_1) -> p1_s2_funct_1(B,k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s2_funct_1)) # label(s2_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 950 (all A v2_funct_1(k6_relat_1(A))) # label(t52_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 951 $T # label(t111_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 952 $T # label(t107_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 953 (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]. 21.72/22.90 954 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(A) = k1_relat_1(B) & k5_relat_1(A,B) = A -> k6_relat_1(k1_relat_1(B)) = B))))) # label(t44_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 955 $T # label(t4_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 956 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (B = k7_relat_1(C,A) <-> (all D (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D))) & k3_xboole_0(k1_relat_1(C),A) = k1_relat_1(B)))))) # label(t68_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 957 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_tarski(A) = k2_relat_1(B) & k2_relat_1(C) = k1_tarski(A) & k1_relat_1(B) = k1_relat_1(C) -> B = C))))) # label(t17_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 958 $T # label(t30_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 959 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) & r1_xboole_0(A,B) -> r1_xboole_0(k9_relat_1(C,A),k9_relat_1(C,B))))) # label(t125_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 960 (all A all B all C (v1_funct_1(C) & v1_relat_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]. 21.72/22.90 961 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 962 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C k3_xboole_0(k9_relat_1(A,B),k9_relat_1(A,C)) = k9_relat_1(A,k3_xboole_0(B,C))) -> v2_funct_1(A)))) # label(t122_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 963 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k2_relat_1(A) = k2_relat_1(k5_relat_1(B,A)) & v2_funct_1(A) -> r1_tarski(k1_relat_1(A),k2_relat_1(B))))))) # label(t51_funct_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 964 (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]. 21.72/22.90 965 $T # label(t15_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 966 $T # label(t8_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 967 (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]. 21.72/22.90 968 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(D,B) & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B))) <-> r7_relat_2(A,B))))) # label(d7_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 969 (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]. 21.72/22.90 970 (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]. 21.72/22.90 971 (all A (v1_relat_1(A) -> (v1_relat_2(A) -> k2_relat_1(A) = k2_relat_1(k4_relat_1(A)) & k1_relat_1(A) = k1_relat_1(k4_relat_1(A))))) # label(t29_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 972 (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]. 21.72/22.90 973 $T # label(t9_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 974 (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) -> D = C)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 975 $T # label(t7_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 976 (all A (v1_relat_1(A) -> (all B ((all C all D (r2_hidden(k4_tarski(C,D),A) & r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_tarski(D,C),A))) <-> r3_relat_2(A,B))))) # label(d3_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 977 $T # label(t1_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 978 (all A (v1_relat_1(A) -> (k4_relat_1(A) = A <-> v3_relat_2(A)))) # label(t30_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 979 (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]. 21.72/22.90 980 (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]. 21.72/22.90 981 $T # label(t21_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 982 (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]. 21.72/22.90 983 (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]. 21.72/22.90 984 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r2_relat_2(A,k3_relat_1(A))))) # label(d10_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 985 (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]. 21.72/22.90 986 $T # label(t11_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 987 $T # label(t14_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 988 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v3_relat_2(B) & v3_relat_2(A) -> v3_relat_2(k4_xboole_0(A,B)) & v3_relat_2(k3_xboole_0(A,B)) & v3_relat_2(k2_xboole_0(A,B))))))) # label(t35_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 989 (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]. 21.72/22.90 990 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v3_relat_2(A) -> v1_relat_2(A)))) # label(t22_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 991 (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]. 21.72/22.90 992 (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]. 21.72/22.90 993 (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]. 21.72/22.90 994 (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]. 21.72/22.90 995 (all A (v1_relat_1(A) -> (v2_relat_2(A) <-> r1_xboole_0(k6_relat_1(k3_relat_1(A)),A)))) # label(t18_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 996 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v2_relat_2(A) -> v5_relat_2(A)))) # label(t25_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 997 (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]. 21.72/22.90 998 $T # label(t6_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 999 $T # label(t4_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1000 $T # label(t10_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1001 (all A (v1_relat_1(A) -> (all B (r8_relat_2(A,B) <-> (all C all D all E (r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) & r2_hidden(D,B) & r2_hidden(C,B) -> r2_hidden(k4_tarski(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1002 $T # label(t5_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1003 $T # label(t16_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1004 (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]. 21.72/22.90 1005 $T # label(t3_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1006 (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]. 21.72/22.90 1007 (all A (v1_relat_1(A) -> (r6_relat_2(A,k3_relat_1(A)) <-> v6_relat_2(A)))) # label(d14_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1008 $T # label(t12_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1009 (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]. 21.72/22.90 1010 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v8_relat_2(B) & v8_relat_2(A) -> v8_relat_2(k3_xboole_0(A,B))))))) # label(t43_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1011 (all A (v1_relat_1(A) -> (v5_relat_2(A) -> v2_relat_2(A) & v4_relat_2(A)))) # label(t26_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1012 $T # label(t2_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1013 (all A (v1_relat_1(A) -> (r1_tarski(k5_relat_1(A,A),A) <-> v8_relat_2(A)))) # label(t44_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1014 $T # label(t13_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1015 (all A (v1_relat_1(A) -> (all B ((all C all D -(r2_hidden(C,B) & r2_hidden(D,B) & -r2_hidden(k4_tarski(D,C),A) & -r2_hidden(k4_tarski(C,D),A) & D != C)) <-> r6_relat_2(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1016 (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]. 21.72/22.90 1017 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v1_relat_2(A) & v1_relat_2(B) -> v1_relat_2(k3_xboole_0(A,B)) & v1_relat_2(k2_xboole_0(A,B))))))) # label(t31_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1018 (all A (v3_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)))) # label(t23_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.90 1019 (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]. 21.72/22.91 1020 (all A (v1_relat_1(A) -> (v4_relat_2(A) <-> r4_relat_2(A,k3_relat_1(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1021 (all A (v1_relat_1(A) -> (v1_relat_2(A) <-> r1_tarski(k6_relat_1(k3_relat_1(A)),A)))) # label(t17_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1022 (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]. 21.72/22.91 1023 (all A (v1_relat_1(A) -> (all B ((all C -(r2_hidden(C,B) & r2_hidden(k4_tarski(C,C),A))) <-> r2_relat_2(A,B))))) # label(d2_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1024 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v5_relat_2(B) & v5_relat_2(A) -> v5_relat_2(k3_xboole_0(A,B))))))) # label(t37_relat_2) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1025 (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]. 21.72/22.91 1026 (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]. 21.72/22.91 1027 (all A all B (k1_ordinal1(A) = k1_ordinal1(B) -> A = B)) # label(t12_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1028 (all A exists B m1_ordinal1(B,A)) # label(existence_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1029 $T # label(t11_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1030 (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]. 21.72/22.91 1031 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(B,A) | r1_ordinal1(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1032 (all A (v4_ordinal1(A) <-> A = k3_tarski(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1033 (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]. 21.72/22.91 1034 $T # label(t17_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1035 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_ordinal1(k1_ordinal1(A),B) <-> r2_hidden(A,B)))))) # label(t33_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1036 $T # label(t44_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1037 $T # label(t8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1038 $T # label(t43_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1039 (exists A (v2_ordinal1(A) & v3_ordinal1(A) & v1_ordinal1(A) & -v1_xboole_0(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1040 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k1_relat_1(A)) & v2_ordinal1(k1_relat_1(A)) & v1_ordinal1(k1_relat_1(A)))) # label(fc5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1041 (all A all B (v3_ordinal1(B) & v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k7_relat_1(A,B) = k2_ordinal1(A,B))) # label(redefinition_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1042 (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]. 21.72/22.91 1043 (exists A (v1_funct_1(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_xboole_0(A) & v2_funct_1(A) & v1_relat_1(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1044 $T # label(t18_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1045 (all A all B (r2_hidden(A,k1_ordinal1(B)) <-> r2_hidden(A,B) | B = A)) # label(t13_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1046 (all A all B all C all D -(r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(D,A))) # label(t4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1047 (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]. 21.72/22.91 1048 (all A all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (m1_ordinal1(B,A) <-> r1_tarski(k2_relat_1(B),A)))) # label(d8_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1049 $T # label(t40_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1050 (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]. 21.72/22.91 1051 (all A (v3_ordinal1(A) -> v3_ordinal1(k3_tarski(A)))) # label(t30_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1052 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v3_ordinal1(k1_relat_1(A)) -> m1_ordinal1(A,k2_relat_1(A))))) # label(t46_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1053 k1_relat_1(f4_s3_ordinal1) = f1_s3_ordinal1 & (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) -> (r2_hidden(A,f1_s3_ordinal1) & k2_ordinal1(f4_s3_ordinal1,A) = B -> k1_funct_1(f4_s3_ordinal1,A) = f2_s3_ordinal1(B)))))) & (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_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)))))) & f1_s3_ordinal1 = k1_relat_1(f3_s3_ordinal1) -> f4_s3_ordinal1 = f3_s3_ordinal1 # label(s3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1054 $T # label(t20_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1055 (all A k2_xboole_0(A,k1_tarski(A)) = k1_ordinal1(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1056 (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]. 21.72/22.91 1057 (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]. 21.72/22.91 1058 (all A -v1_xboole_0(k1_ordinal1(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1059 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (v3_ordinal1(B) -> (all C (v1_funct_1(C) & v5_ordinal1(C) & v1_relat_1(C) -> (k2_ordinal1(A,B) = C & r2_hidden(B,f1_s4_ordinal1) -> f2_s4_ordinal1(C) = k1_funct_1(A,B)))))) & k1_relat_1(A) = f1_s4_ordinal1 & v5_ordinal1(A))) # label(s4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1060 (all A all B (v3_ordinal1(B) -> (r2_hidden(A,B) -> v3_ordinal1(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1061 (all A (v3_ordinal1(A) -> -v1_xboole_0(k1_ordinal1(A)) & v2_ordinal1(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) & v1_ordinal1(k1_ordinal1(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1062 $T # label(t28_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1063 (exists A (p1_s1_ordinal1(A) & v3_ordinal1(A))) -> (exists A (v3_ordinal1(A) & p1_s1_ordinal1(A) & (all B (v3_ordinal1(B) -> (p1_s1_ordinal1(B) -> r1_ordinal1(A,B)))))) # label(s1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1064 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> r3_xboole_0(A,B))))) # label(t25_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1065 (all A all B all C all D all E -(r2_hidden(B,C) & r2_hidden(D,E) & r2_hidden(E,A) & r2_hidden(C,D) & r2_hidden(A,B))) # label(t5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1066 (all A k1_ordinal1(A) != A) # label(t14_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1067 (all A (v3_ordinal1(A) <-> v2_ordinal1(A) & v1_ordinal1(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1068 (all A all B (v3_ordinal1(B) -> -((all C (v3_ordinal1(C) -> -((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> r1_ordinal1(C,D)))) & r2_hidden(C,A)))) & A != k1_xboole_0 & r1_tarski(A,B)))) # label(t32_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1069 (all A ((all B (r2_hidden(B,A) -> v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B))) & v6_ordinal1(A) -> v5_ordinal1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) & v1_relat_1(k3_tarski(A)))) # label(t49_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1070 (all A all B (v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal1(B) & v1_relat_1(A) -> m1_ordinal1(k2_ordinal1(A,B),k2_relat_1(A)))) # label(dt_k2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1071 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) <-> (all B (v3_ordinal1(B) -> (r2_hidden(B,A) -> r2_hidden(k1_ordinal1(B),A))))))) # label(t41_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1072 (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]. 21.72/22.91 1073 $T # label(t16_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1074 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1075 $T # label(t9_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1076 (all A -(all B (r2_hidden(B,A) <-> v3_ordinal1(B)))) # label(t37_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1077 (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]. 21.72/22.91 1078 (all A r2_hidden(A,k1_ordinal1(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1079 $T # label(t15_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1080 (all A (v1_xboole_0(A) -> v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1081 (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]. 21.72/22.91 1082 (all A (v3_ordinal1(A) -> v1_ordinal1(A) & v2_ordinal1(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1083 (all A (v1_ordinal1(A) & v2_ordinal1(A) -> v3_ordinal1(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1084 (all A (v3_ordinal1(A) -> v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)) & v1_ordinal1(k3_tarski(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1085 (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]. 21.72/22.91 1086 (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]. 21.72/22.91 1087 (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]. 21.72/22.91 1088 (all A (v3_ordinal1(A) -> -((all B (v3_ordinal1(B) -> A != k1_ordinal1(B))) & -v4_ordinal1(A)) & -(v4_ordinal1(A) & (exists B (v3_ordinal1(B) & k1_ordinal1(B) = A))))) # label(t42_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1089 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> r1_ordinal1(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1090 (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]. 21.72/22.91 1091 $T # label(d5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1092 (all A (v1_ordinal1(A) <-> (all B (r2_hidden(B,A) -> r1_tarski(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1093 (all A m1_ordinal1(k1_xboole_0,A)) # label(t45_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1094 (exists A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A))) # label(rc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1095 (all A all B -(r2_hidden(A,B) & r1_tarski(B,A))) # label(t7_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1096 (all A -(all B (v3_ordinal1(B) -> r2_hidden(B,A)))) # label(t38_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1097 (exists A (v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1098 (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]. 21.72/22.91 1099 (all A (v3_ordinal1(A) -> v3_ordinal1(k1_ordinal1(A)))) # label(t29_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1100 (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) -> (all B ((exists C (v1_funct_1(C) & v5_ordinal1(C) & f3_s5_ordinal1(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = f3_s5_ordinal1(k2_ordinal1(C,D))))) & k1_relat_1(C) = A & v1_relat_1(C))) <-> B = f2_s5_ordinal1(A))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s5_ordinal1)) -> f3_s5_ordinal1(k2_ordinal1(f1_s5_ordinal1,A)) = k1_funct_1(f1_s5_ordinal1,A)))) # label(s5_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1101 (all A all B all C -(r2_hidden(B,C) & r2_hidden(C,A) & r2_hidden(A,B))) # label(t3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1102 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -(-r2_hidden(B,A) & A != B & -r2_hidden(A,B)))))) # label(t24_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1103 $T # label(t2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1104 $T # label(t1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1105 (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]. 21.72/22.91 1106 (all A all B (m1_ordinal1(B,A) -> v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) # label(dt_m1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1107 (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]. 21.72/22.91 1108 (all A (v2_ordinal1(A) <-> (all B all C -(r2_hidden(C,A) & B != C & -r2_hidden(C,B) & -r2_hidden(B,C) & r2_hidden(B,A))))) # label(d3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1109 (all A all B all C (v1_relat_1(C) -> (r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C)) & v2_wellord1(C) -> (r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)) <-> A = B | r2_hidden(A,k1_wellord1(C,B)))))) # label(t38_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1110 (all A all B all C (v1_relat_1(C) -> r1_tarski(k1_wellord1(k2_wellord1(C,A),B),k1_wellord1(C,B)))) # label(t21_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1111 $T # label(t44_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1112 (all A all B all C (v1_relat_1(C) -> -(v2_wellord1(C) & r4_wellord1(k2_wellord1(C,k1_wellord1(C,A)),k2_wellord1(C,k1_wellord1(C,B))) & A != B & r2_hidden(B,k3_relat_1(C)) & r2_hidden(A,k3_relat_1(C))))) # label(t58_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1113 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r3_wellord1(A,B,C) <-> (all D all E (r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) & r2_hidden(E,k3_relat_1(A)) & r2_hidden(D,k3_relat_1(A)) <-> r2_hidden(k4_tarski(D,E),A))) & v2_funct_1(C) & k3_relat_1(B) = k2_relat_1(C) & k3_relat_1(A) = k1_relat_1(C)))))))) # label(d7_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1114 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((exists C (v1_funct_1(C) & r3_wellord1(A,B,C) & v1_relat_1(C))) <-> r4_wellord1(A,B)))))) # label(d8_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1115 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k2_wellord1(C,B)) <-> r2_hidden(A,C) & r2_hidden(A,k2_zfmisc_1(B,B))))) # label(t16_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1116 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> r3_wellord1(B,A,k2_funct_1(C))))))))) # label(t49_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1117 (all A all B all C (v1_relat_1(C) -> k2_wellord1(C,k3_xboole_0(A,B)) = k2_wellord1(k2_wellord1(C,A),B))) # label(t26_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1118 (all A (v1_relat_1(A) -> (all B ((all C -((all D -(r2_hidden(D,C) & r1_xboole_0(k1_wellord1(A,D),C))) & k1_xboole_0 != C & r1_tarski(C,B))) <-> r1_wellord1(A,B))))) # label(d3_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1119 (all A all B (v1_relat_1(B) -> r2_hidden(A,k3_relat_1(B)) | k1_wellord1(B,A) = k1_xboole_0)) # label(t2_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1120 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B ((all C (r2_hidden(C,k3_relat_1(A)) & r1_tarski(k1_wellord1(A,C),B) -> r2_hidden(C,B))) -> r1_tarski(k3_relat_1(A),B)))))) # label(t41_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1121 (all A all B (v1_relat_1(B) -> (v1_relat_2(B) -> v1_relat_2(k2_wellord1(B,A))))) # label(t22_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1122 (all A all B (v1_relat_1(A) -> v1_relat_1(k2_wellord1(A,B)))) # label(dt_k2_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1123 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) & v2_wellord1(A) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k3_wellord1(A,B) = C <-> r3_wellord1(A,B,C))))))))) # label(d9_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1124 $T # label(t4_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1125 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1126 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> (r3_wellord1(A,B,D) & r3_wellord1(B,C,E) -> r3_wellord1(A,C,k5_relat_1(D,E))))))))))))) # label(t51_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1127 (all A all B (v1_relat_1(B) -> k8_relat_1(A,k7_relat_1(B,A)) = k2_wellord1(B,A))) # label(t18_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1128 $T # label(t46_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1129 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (v8_relat_2(A) -> v8_relat_2(B)) & (v6_relat_2(A) -> v6_relat_2(B)) & (v1_wellord1(A) -> v1_wellord1(B)) & (v4_relat_2(A) -> v4_relat_2(B)) & (v1_relat_2(A) -> v1_relat_2(B))))))))) # label(t53_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1130 $T # label(t1_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1131 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> k1_xboole_0 = k3_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) & (all D -(-r2_hidden(k4_tarski(C,D),A) & B != D & r2_hidden(k4_tarski(B,D),A) & r2_hidden(D,k3_relat_1(A)))))) & (exists C (r2_hidden(C,k3_relat_1(A)) & -r2_hidden(k4_tarski(C,B),A)))))))) # label(t12_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1132 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> r2_wellord1(A,k3_relat_1(A))))) # label(t8_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1133 (all A all B (v1_relat_1(B) -> k7_relat_1(k8_relat_1(A,B),A) = k2_wellord1(B,A))) # label(t17_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1134 (all A all B (v1_relat_1(B) -> k2_wellord1(k2_wellord1(B,A),A) = k2_wellord1(B,A))) # label(t28_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1135 (all A all B (v1_relat_1(B) -> -(v2_wellord1(B) & -r4_wellord1(B,k2_wellord1(B,A)) & (all C -(r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)) & r2_hidden(C,k3_relat_1(B)))) & r1_tarski(A,k3_relat_1(B))))) # label(t64_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1136 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A)))) # label(t40_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1137 (all A (v1_relat_1(A) -> (all B k3_xboole_0(A,k2_zfmisc_1(B,B)) = k2_wellord1(A,B)))) # label(d6_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1138 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> -((all C -(r2_hidden(C,k3_relat_1(A)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B))) & (all C -(r2_hidden(C,k3_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))))) & -r4_wellord1(A,B) & v2_wellord1(B) & v2_wellord1(A)))))) # label(t63_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1139 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(B,k1_wellord1(C,A)) & r2_hidden(A,k3_relat_1(C)) -> k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B) = k1_wellord1(C,B)))) # label(t35_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1140 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> v2_wellord1(B)))))))) # label(t54_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1141 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) -> ((all C (r2_hidden(C,A) -> (all D (r2_hidden(k4_tarski(D,C),B) -> r2_hidden(D,A))))) <-> -((all C -(r2_hidden(C,k3_relat_1(B)) & A = k1_wellord1(B,C))) & k3_relat_1(B) != A))))) # label(t36_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1142 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(k2_wellord1(C,B))) -> r2_hidden(A,k3_relat_1(C)) & r2_hidden(A,B)))) # label(t19_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1143 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> (all C -(C != k1_xboole_0 & (all D -(r2_hidden(D,C) & (all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),B))))) & r1_tarski(C,A)))))) # label(t9_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1144 (all A all B (v1_relat_1(B) -> (v2_wellord1(B) -> v2_wellord1(k2_wellord1(B,A))))) # label(t32_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1145 (all A (v1_relat_1(A) -> r3_wellord1(A,A,k6_relat_1(k3_relat_1(A))))) # label(t47_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1146 $T # label(t56_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1147 $T # label(t7_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1148 $T # label(t14_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1149 (all A all B (v1_relat_1(B) -> r1_tarski(k1_wellord1(B,A),k3_relat_1(B)))) # label(t13_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1150 (all A (v1_relat_1(A) -> (r1_wellord1(A,k3_relat_1(A)) <-> v1_wellord1(A)))) # label(t5_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1151 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (r4_wellord1(A,B) -> r4_wellord1(B,A)))))) # label(t50_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1152 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) -> (all D all E (r2_hidden(k4_tarski(D,E),A) -> k1_funct_1(C,D) != k1_funct_1(C,E) & r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) | E = D))))))))) # label(t45_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1153 (all A all B (v1_relat_1(B) -> r1_tarski(k2_wellord1(B,A),B) & r1_tarski(k2_wellord1(B,A),k2_zfmisc_1(A,A)))) # label(t15_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1154 (all A all B all C (v1_relat_1(C) -> k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(k2_wellord1(C,B),A))) # label(t27_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1155 $T # label(t3_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1156 (all A (v1_relat_1(A) -> r4_wellord1(A,A))) # label(t48_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1157 (all A all B (v1_relat_1(B) -> (v4_relat_2(B) -> v4_relat_2(k2_wellord1(B,A))))) # label(t25_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1158 (all A all B (v1_relat_1(B) -> (v6_relat_2(B) -> v6_relat_2(k2_wellord1(B,A))))) # label(t23_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1159 (all A (v1_relat_1(A) -> (all B all C ((all D (r2_hidden(D,C) <-> r2_hidden(k4_tarski(D,B),A) & B != D)) <-> k1_wellord1(A,B) = C)))) # label(d1_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1160 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (r4_wellord1(A,B) & r4_wellord1(B,C) -> r4_wellord1(A,C)))))))) # label(t52_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1161 (all A (v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_wellord1(A) & r1_tarski(k2_relat_1(B),k3_relat_1(A)) & (all C all D (r2_hidden(k4_tarski(C,D),A) -> k1_funct_1(B,C) != k1_funct_1(B,D) & r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D)),A) | C = D)) & k1_relat_1(B) = k3_relat_1(A) -> (all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(C,k1_funct_1(B,C)),A)))))))) # label(t43_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1162 (all A (v1_relat_1(A) -> k2_wellord1(A,k3_relat_1(A)) = A)) # label(t30_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1163 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) -> r3_xboole_0(k1_wellord1(C,A),k1_wellord1(C,B))))) # label(t33_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1164 (all A all B (v1_relat_1(B) -> (r1_tarski(A,k3_relat_1(B)) & v2_wellord1(B) -> k3_relat_1(k2_wellord1(B,A)) = A))) # label(t39_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1165 (all A (v1_relat_1(A) -> (all B (r1_relat_2(A,B) & r4_relat_2(A,B) & r6_relat_2(A,B) & r1_wellord1(A,B) & r8_relat_2(A,B) <-> r2_wellord1(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1166 (all A (v1_relat_1(A) -> (v2_wellord1(A) <-> v1_relat_2(A) & v4_relat_2(A) & v1_wellord1(A) & v6_relat_2(A) & v8_relat_2(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1167 (all A all B all C (v1_relat_1(C) -> (v2_wellord1(C) & r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C)) -> (r2_hidden(k4_tarski(A,B),C) <-> r1_tarski(k1_wellord1(C,A),k1_wellord1(C,B)))))) # label(t37_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1168 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r3_wellord1(A,B,C) & v2_wellord1(A) -> (all D -((all E -(r2_hidden(E,k3_relat_1(B)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t61_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1169 (all A all B (v1_relat_1(B) -> r1_tarski(k3_relat_1(k2_wellord1(B,A)),k3_relat_1(B)) & r1_tarski(k3_relat_1(k2_wellord1(B,A)),A))) # label(t20_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1170 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & (all B -((all C (r2_hidden(C,k3_relat_1(A)) -> r2_hidden(k4_tarski(B,C),A))) & r2_hidden(B,k3_relat_1(A)))) & k1_xboole_0 != k3_relat_1(A)))) # label(t11_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1171 (all A all B (v1_relat_1(B) -> (v8_relat_2(B) -> v8_relat_2(k2_wellord1(B,A))))) # label(t24_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1172 $T # label(t34_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1173 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (v2_wellord1(A) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r3_wellord1(A,B,D) & r3_wellord1(A,B,C) -> C = D)))))))))) # label(t55_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1174 (all A all B all C (v1_relat_1(C) -> (r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C)) & (all D (r2_hidden(D,k1_wellord1(C,A)) -> D != B & r2_hidden(k4_tarski(D,B),C))) & v2_wellord1(C) -> r2_hidden(k4_tarski(A,B),C)))) # label(t42_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1175 (all A all B (v1_relat_1(B) -> (all C (v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (v2_wellord1(B) & r1_tarski(A,k3_relat_1(B)) & r3_wellord1(B,C,D) -> r4_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A))) & r3_wellord1(k2_wellord1(B,A),k2_wellord1(C,k9_relat_1(D,A)),k7_relat_1(D,A))))))))) # label(t59_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1176 $T # label(t6_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1177 (all A all B (v1_relat_1(B) -> (v1_wellord1(B) -> v1_wellord1(k2_wellord1(B,A))))) # label(t31_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1178 (all A (v1_relat_1(A) -> ((all B -(r1_tarski(B,k3_relat_1(A)) & (all C -(r2_hidden(C,B) & r1_xboole_0(k1_wellord1(A,C),B))) & k1_xboole_0 != B)) <-> v1_wellord1(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1179 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_wellord1(A) & r3_wellord1(A,B,C) -> (all D -((all E -(k9_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E) & r2_hidden(E,k3_relat_1(B)))) & r2_hidden(D,k3_relat_1(A))))))))))) # label(t60_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1180 (all A all B (v1_relat_1(B) & v1_relat_1(A) -> v1_funct_1(k3_wellord1(A,B)) & v1_relat_1(k3_wellord1(A,B)))) # label(dt_k3_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1181 (all A all B all C all D (v1_relat_1(D) -> (all E (v1_relat_1(E) -> (r2_hidden(A,k3_relat_1(D)) & r2_hidden(C,k3_relat_1(E)) & r4_wellord1(D,k2_wellord1(E,k1_wellord1(E,B))) & r4_wellord1(k2_wellord1(D,k1_wellord1(D,A)),k2_wellord1(E,k1_wellord1(E,C))) & r2_hidden(B,k3_relat_1(E)) & v2_wellord1(E) & v2_wellord1(D) -> r2_hidden(k4_tarski(C,B),E) & r1_tarski(k1_wellord1(E,C),k1_wellord1(E,B))))))) # label(t62_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1182 (all A all B all C (v1_relat_1(C) -> (r1_tarski(A,B) -> k2_wellord1(k2_wellord1(C,B),A) = k2_wellord1(C,A)))) # label(t29_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1183 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B))) & r2_hidden(B,k3_relat_1(A))))))) # label(t57_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1184 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> (all B -(r1_tarski(B,k3_relat_1(A)) & k1_xboole_0 != B & (all C -((all D (r2_hidden(D,B) -> r2_hidden(k4_tarski(C,D),A))) & r2_hidden(C,B)))))))) # label(t10_wellord1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1185 (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,D,C) = k2_relset_1(A,B,C,D))) # label(commutativity_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1186 (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]. 21.72/22.91 1187 $T # label(t5_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1188 (all A all B all C all D (m2_relset_1(D,A,B) -> (r1_tarski(B,C) -> D = k9_relset_1(A,B,C,D)))) # label(t36_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1189 (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]. 21.72/22.91 1190 (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]. 21.72/22.91 1191 (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]. 21.72/22.91 1192 (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]. 21.72/22.91 1193 (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]. 21.72/22.91 1194 (all A all B all C all D all E all F (m1_relset_1(F,C,D) & m1_relset_1(E,A,B) -> k5_relat_1(E,F) = k7_relset_1(A,B,C,D,E,F))) # label(redefinition_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1195 (all A all B all C all D all E (m2_relset_1(E,A,C) -> (r1_tarski(A,B) & r1_tarski(C,D) -> m2_relset_1(E,B,D)))) # label(t17_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1196 (all A m2_relset_1(k6_relat_1(A),A,A)) # label(t29_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1197 $T # label(t7_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.91 1198 (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]. 21.72/22.91 1199 (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 (r2_hidden(k4_tarski(F,E),D) & r2_hidden(F,B) & m1_subset_1(F,C))) <-> r2_hidden(E,k10_relset_1(C,A,D,B))))))))))))) # label(t52_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1200 (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]. 21.72/22.92 1201 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> m2_relset_1(k3_relset_1(A,B,C,D),A,B))) # label(dt_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1202 (all A all B all C (m2_relset_1(C,B,A) -> k4_relset_1(B,A,C) = k11_relset_1(B,A,C,k10_relset_1(B,A,C,B)) & k10_relset_1(B,A,C,k11_relset_1(B,A,C,A)) = k5_relset_1(B,A,C))) # label(t39_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1203 $T # label(t41_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1204 (all A all B all C (m2_relset_1(C,A,B) -> k11_relset_1(A,B,C,B) = k4_relset_1(A,B,C) & k10_relset_1(A,B,C,A) = k5_relset_1(A,B,C))) # label(t38_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1205 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1206 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,B,A) -> (all D (m1_subset_1(D,A) -> (r2_hidden(D,k5_relset_1(B,A,C)) <-> (exists E (m1_subset_1(E,B) & r2_hidden(k4_tarski(E,D),C)))))))))))) # label(t48_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1207 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> -(r2_hidden(D,k4_relset_1(A,B,C)) & (all E (m1_subset_1(E,B) -> -r2_hidden(E,k5_relset_1(A,B,C))))))))))))) # label(t49_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1208 (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) -> -((all E (m1_subset_1(E,B) -> -r2_hidden(E,k4_relset_1(B,A,C)))) & r2_hidden(D,k5_relset_1(B,A,C))))))))))) # label(t50_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1209 (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]. 21.72/22.92 1210 (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]. 21.72/22.92 1211 $T # label(t3_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1212 $T # label(t18_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1213 (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]. 21.72/22.92 1214 $T # label(t2_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1215 (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,D) = k3_xboole_0(C,D))) # label(redefinition_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1216 (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]. 21.72/22.92 1217 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k3_relset_1(A,B,C,D) = k4_xboole_0(C,D))) # label(redefinition_k3_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1218 (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]. 21.72/22.92 1219 (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]. 21.72/22.92 1220 (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]. 21.72/22.92 1221 (all A all B all C (m1_relset_1(C,A,B) -> k6_relset_1(A,B,k6_relset_1(A,B,C)) = C)) # label(involutiveness_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1222 (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]. 21.72/22.92 1223 (all A all B m2_relset_1(k1_xboole_0,A,B)) # label(t25_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1224 (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]. 21.72/22.92 1225 (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]. 21.72/22.92 1226 (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]. 21.72/22.92 1227 (all A all B exists C m2_relset_1(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1228 (all A all B all C all D (m1_relset_1(C,A,B) -> k10_relset_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k10_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1229 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,D) = k2_xboole_0(C,D))) # label(redefinition_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1230 (exists A (m2_relset_1(A,f1_s1_relset_1,f2_s1_relset_1) & (all B all C (p1_s1_relset_1(B,C) & r2_hidden(C,f2_s1_relset_1) & r2_hidden(B,f1_s1_relset_1) <-> r2_hidden(k4_tarski(B,C),A))))) # label(s1_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1231 (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]. 21.72/22.92 1232 (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]. 21.72/22.92 1233 (all A all B all C all D all E all F (m1_relset_1(E,A,B) & m1_relset_1(F,C,D) -> m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D))) # label(dt_k7_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1234 (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]. 21.72/22.92 1235 (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 (r2_hidden(k4_tarski(H,G),E) & r2_hidden(k4_tarski(F,H),D) & m1_subset_1(H,B))) <-> 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]. 21.72/22.92 1236 (all A (-v1_xboole_0(A) -> k1_xboole_0 != k6_relat_1(A))) # label(t46_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1237 $T # label(t37_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1238 (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]. 21.72/22.92 1239 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k2_relset_1(A,B,C,C) = C)) # label(idempotence_k2_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1240 $T # label(t40_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1241 (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]. 21.72/22.92 1242 (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]. 21.72/22.92 1243 (all A all B all C all D (m1_relset_1(D,A,B) & m1_relset_1(C,A,B) -> k1_relset_1(A,B,C,D) = k1_relset_1(A,B,D,C))) # label(commutativity_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1244 (all A all B all C (m2_relset_1(C,B,A) -> (k4_relset_1(B,A,C) = B <-> (all D -((all E -r2_hidden(k4_tarski(D,E),C)) & r2_hidden(D,B)))))) # label(t22_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1245 (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]. 21.72/22.92 1246 $T # label(t20_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1247 (all A all B all C (m2_relset_1(C,B,A) -> (m2_relset_1(C,B,k1_xboole_0) -> k1_xboole_0 = C))) # label(t27_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1248 (all A all B all C all D (m1_relset_1(C,A,B) & m1_relset_1(D,A,B) -> k1_relset_1(A,B,C,C) = C)) # label(idempotence_k1_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1249 (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]. 21.72/22.92 1250 $T # label(t42_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1251 (all A all B all C (m2_relset_1(C,A,B) -> (B = k5_relset_1(A,B,C) <-> (all D -((all E -r2_hidden(k4_tarski(E,D),C)) & r2_hidden(D,B)))))) # label(t23_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1252 (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]. 21.72/22.92 1253 $T # label(t21_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1254 (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]. 21.72/22.92 1255 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,C) -> (all E (m1_subset_1(E,A) -> (r2_hidden(E,k11_relset_1(A,C,D,B)) <-> (exists F (m1_subset_1(F,C) & r2_hidden(F,B) & r2_hidden(k4_tarski(E,F),D)))))))))))))) # label(t53_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1256 (all A all B all C (m1_relset_1(C,A,B) -> k4_relat_1(C) = k6_relset_1(A,B,C))) # label(redefinition_k6_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1257 $T # label(t1_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1258 $T # label(t43_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1259 (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]. 21.72/22.92 1260 $T # label(t44_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1261 (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]. 21.72/22.92 1262 (all A all B (m2_relset_1(B,A,A) -> B = k5_relat_1(B,k6_relat_1(A)) & B = k5_relat_1(k6_relat_1(A),B))) # label(t45_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1263 (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)) & k5_relset_1(B,A,k6_relset_1(A,B,C)) = k4_relset_1(A,B,C))) # label(t24_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1264 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) -> m2_relset_1(k1_tarski(k4_tarski(C,D)),A,B))) # label(t8_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1265 (all A r1_tarski(k6_relat_1(A),k2_zfmisc_1(A,A))) # label(t28_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1266 (all A all B all C (m1_relset_1(C,A,B) -> k2_relat_1(C) = k5_relset_1(A,B,C))) # label(redefinition_k5_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1267 (all A all B all C all D (m2_relset_1(D,A,B) -> -(r2_hidden(C,D) & (all E all F -(C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B)))))) # label(t6_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1268 (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]. 21.72/22.92 1269 (all A all B exists C m1_relset_1(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1270 (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]. 21.72/22.92 1271 (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]. 21.72/22.92 1272 (all A all B all C (m2_relset_1(C,B,A) -> (r1_tarski(k6_relat_1(B),C) -> B = k4_relset_1(B,A,C) & r1_tarski(B,k5_relset_1(B,A,C))))) # label(t31_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1273 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m1_subset_1(D,A) -> ((exists E (r2_hidden(k4_tarski(D,E),C) & m1_subset_1(E,B))) <-> r2_hidden(D,k4_relset_1(A,B,C))))))))))) # label(t47_relset_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1274 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k4_relset_1(A,B,C) = k10_relat_1(C,B))) # label(t53_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1275 $T # label(t103_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1276 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> m2_relset_1(k9_relset_1(A,B,C,D),A,B) & v1_funct_1(k9_relset_1(A,B,C,D)))) # label(t46_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1277 (all A all B all C (k4_partfun1(A,B) = C <-> (all D (r2_hidden(D,C) <-> (exists E (v1_relat_1(E) & v1_funct_1(E) & E = D & r1_tarski(k1_relat_1(E),A) & r1_tarski(k2_relat_1(E),B))))))) # label(d5_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1278 $T # label(t170_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1279 $T # label(t159_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1280 (all A all B all C (m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k10_relat_1(C,B))) # label(t61_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1281 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_xboole_0 = k2_relat_1(C) -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t63_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1282 (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]. 21.72/22.92 1283 (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]. 21.72/22.92 1284 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> C = k3_partfun1(C,A,B))) # label(t87_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1285 $T # label(t183_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1286 (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(C,A,B) & r1_partfun1(C,D) & v1_partfun1(D,A,B) -> D = C))))) # label(t148_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1287 (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]. 21.72/22.92 1288 (all A all B (m2_relset_1(B,k1_xboole_0,A) & v1_funct_1(B) -> k2_relat_1(B) = k1_xboole_0 & k1_xboole_0 = k4_relset_1(k1_xboole_0,A,B))) # label(t54_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1289 $T # label(t15_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1290 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (r1_tarski(k3_xboole_0(k2_relat_1(D),k1_relat_1(E)),A) -> 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]. 21.72/22.92 1291 $T # label(t184_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1292 $T # label(t105_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1293 $T # label(t110_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1294 (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]. 21.72/22.92 1295 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_partfun1(k7_relat_1(k8_relat_1(A,C),B),C))) # label(t146_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1296 (all A all B all C (m2_relset_1(C,A,B) -> C = k5_relat_1(C,k6_relat_1(B)))) # label(t37_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1297 (all A all B all C all D all E all F (v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) -> v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D))) # label(dt_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1298 (all A k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t122_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1299 (all A all B (p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> r2_hidden(B,f2_s2_partfun1))) & (all A all B all C (p1_s2_partfun1(A,C) & p1_s2_partfun1(A,B) & r2_hidden(A,f1_s2_partfun1) -> B = C)) -> (exists A (v1_funct_1(A) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) -> p1_s2_partfun1(B,k1_funct_1(A,B)))) & (all B (r2_hidden(B,k4_relset_1(f1_s2_partfun1,f2_s2_partfun1,A)) <-> r2_hidden(B,f1_s2_partfun1) & (exists C p1_s2_partfun1(B,C)))) & m2_relset_1(A,f1_s2_partfun1,f2_s2_partfun1))) # label(s2_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1300 $T # label(t102_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1301 (exists A (v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_relat_1(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1302 (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]. 21.72/22.92 1303 $T # label(t157_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1304 $T # label(t17_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1305 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r2_hidden(C,k2_relat_1(D)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C)))))) # label(t26_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1306 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,B) -> (r1_partfun1(C,E) & v1_partfun1(E,A,B) & r1_partfun1(D,E) -> r1_partfun1(C,D)))))))) # label(t158_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1307 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,A,C),k3_partfun1(D,B,C))))) # label(t82_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1308 (all A all B (v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) & v1_relat_1(A) -> r1_partfun1(A,A))) # label(reflexivity_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1309 $T # label(t4_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1310 (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_funct_1(E) & v1_relat_1(E) -> (r1_partfun1(C,E) & r1_tarski(D,C) -> r1_partfun1(D,E)))))))) # label(t140_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1311 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (v1_partfun1(k3_partfun1(C,A,B),A,B) -> r1_tarski(A,k1_relat_1(C))))) # label(t113_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1312 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k9_relat_1(C,A),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t117_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1313 $T # label(t165_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1314 $T # label(t22_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1315 (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]. 21.72/22.92 1316 (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]. 21.72/22.92 1317 (exists A ((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) -> k1_funct_1(A,B) = f3_s1_partfun1(B)))) & f1_s1_partfun1 = k1_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1318 $T # label(t88_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1319 $T # label(t18_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1320 $T # label(t182_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1321 (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]. 21.72/22.92 1322 $T # label(t124_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1323 $T # label(t42_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1324 $T # label(t134_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1325 (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) -> (C = k2_xboole_0(A,B) -> (all D (r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,D) = k1_funct_1(B,D)))))))))) # label(t3_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1326 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k3_partfun1(C,A,B),C))) # label(t76_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1327 (all A exists B (m1_relset_1(B,A,A) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) & v1_relat_1(B))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1328 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> (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]. 21.72/22.92 1329 (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]. 21.72/22.92 1330 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(A,B) -> r1_tarski(k3_partfun1(D,C,A),k3_partfun1(D,C,B))))) # label(t83_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1331 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_tarski(A) = k1_relat_1(D) & r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) -> m2_relset_1(D,B,C) & v1_funct_1(D)))) # label(t72_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1332 $T # label(t180_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1333 $T # label(t23_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1334 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> (exists C (v1_funct_1(C) & k2_xboole_0(A,B) = C & v1_relat_1(C)))))))) # label(t130_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1335 (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]. 21.72/22.92 1336 (all A all B -v1_xboole_0(k4_partfun1(A,B))) # label(fc1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1337 (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]. 21.72/22.92 1338 $T # label(t177_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1339 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(C)) & r1_tarski(k2_relat_1(C),B) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t115_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1340 (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]. 21.72/22.92 1341 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t67_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1342 (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]. 21.72/22.92 1343 $T # label(t153_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1344 $T # label(t20_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1345 (all A k6_partfun1(A) = k6_relat_1(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1346 (all A all B all C (m2_relset_1(C,A,B) -> k5_relat_1(k6_relat_1(A),C) = C)) # label(t36_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1347 (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]. 21.72/22.92 1348 $T # label(t7_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1349 $T # label(t14_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1350 $T # label(t16_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1351 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> (all D (m2_relset_1(D,B,k1_xboole_0) & v1_funct_1(D) -> D = C)))) # label(t65_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1352 (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]. 21.72/22.92 1353 $T # label(t133_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1354 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -(r2_hidden(C,k9_relat_1(D,A)) & (all E (m1_subset_1(E,A) -> -(r2_hidden(E,k4_relset_1(A,B,D)) & k1_funct_1(D,E) = C)))))) # label(t49_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1355 (all A all B all C (r2_hidden(C,k4_partfun1(A,B)) -> m2_relset_1(C,A,B) & v1_funct_1(C))) # label(t120_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1356 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C))) # label(t142_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1357 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_partfun1(k7_relat_1(B,A),B))) # label(t144_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1358 (all A all B all C all D all E all F (r1_tarski(A,k2_zfmisc_1(B,C)) & r1_tarski(D,k2_zfmisc_1(E,F)) -> r1_tarski(k2_xboole_0(A,D),k2_zfmisc_1(k2_xboole_0(B,E),k2_xboole_0(C,F))))) # label(t1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1359 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(B,C) -> v1_funct_1(D) & m2_relset_1(D,A,C)))) # label(t31_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1360 $T # label(t154_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1361 $T # label(t40_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1362 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(A,B) & r2_hidden(k1_funct_1(D,A),C) & r2_hidden(A,k1_relat_1(D)) -> k1_funct_1(D,A) = k1_funct_1(k3_partfun1(D,B,C),A)))) # label(t79_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1363 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,k1_tarski(B)) -> (r2_hidden(C,k4_relset_1(A,k1_tarski(B),D)) -> k1_funct_1(D,C) = B))) # label(t73_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1364 $T # label(t149_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1365 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> m2_relset_1(k8_relset_1(A,B,D,C),A,B) & v1_funct_1(k8_relset_1(A,B,D,C)))) # label(t44_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1366 (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]. 21.72/22.92 1367 $T # label(t8_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1368 $T # label(t164_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1369 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> r2_hidden(C,k4_partfun1(A,B)))) # label(t119_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1370 $T # label(t156_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1371 (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]. 21.72/22.92 1372 (all A (v1_relat_1(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) & v4_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]. 21.72/22.92 1373 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,k1_tarski(B)) -> (all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> (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]. 21.72/22.92 1374 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> m2_relset_1(D,A,B) & v1_funct_1(D))))) # label(t168_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1375 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (k1_xboole_0 = B & v1_partfun1(C,A,B) -> k1_xboole_0 = A))) # label(t99_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1376 (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)) -> r1_partfun1(C,D))))) # label(t143_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1377 (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]. 21.72/22.92 1378 $T # label(t108_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1379 $T # label(dt_k5_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1380 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> -((all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(B,C) = k1_funct_1(A,C))) & (all C (v1_relat_1(C) & v1_funct_1(C) -> k2_xboole_0(A,B) != C))))))) # label(t2_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1381 $T # label(t151_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1382 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> -(r1_partfun1(C,D) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t186_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1383 (all A k4_partfun1(A,k1_xboole_0) = k1_tarski(k1_xboole_0)) # label(t123_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1384 (all A all B all C (m2_relset_1(C,A,k1_xboole_0) & v1_funct_1(C) -> k10_relat_1(C,B) = k1_xboole_0)) # label(t68_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1385 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> B = k1_xboole_0)) # label(t64_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1386 (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]. 21.72/22.92 1387 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (v2_funct_1(C) -> v2_funct_1(k3_partfun1(C,A,B))))) # label(t94_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1388 $T # label(t13_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1389 (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]. 21.72/22.92 1390 (all A all B all C all D (v1_relat_1(D) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_relat_1(E) -> r1_tarski(k1_partfun1(C,A,A,B,k3_partfun1(D,C,A),k3_partfun1(E,A,B)),k3_partfun1(k5_relat_1(D,E),C,B)))))) # label(t92_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1391 $T # label(t90_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1392 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (k4_relset_1(A,B,D) = k4_relset_1(A,B,C) & (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)))) -> D = C))))) # label(t34_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1393 (all A (p1_s3_partfun1(A) -> r2_hidden(f3_s3_partfun1(A),f2_s3_partfun1))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s3_partfun1,f2_s3_partfun1) & (all B (r2_hidden(B,f1_s3_partfun1) & p1_s3_partfun1(B) <-> r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)))) & (all B (r2_hidden(B,k4_relset_1(f1_s3_partfun1,f2_s3_partfun1,A)) -> f3_s3_partfun1(B) = k1_funct_1(A,B))))) # label(s3_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1394 $T # label(dt_k4_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1395 (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]. 21.72/22.92 1396 $T # label(t109_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1397 $T # label(t166_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1398 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> (all C (r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) -> k1_funct_1(A,C) = k1_funct_1(B,C)))))))) # label(d6_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1399 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,k1_xboole_0) -> (A != k1_xboole_0 -> k1_xboole_0 = k5_partfun1(A,k1_xboole_0,B)))) # label(t172_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1400 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_tarski(A),B) -> v2_funct_1(C))) # label(t70_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1401 $T # label(d1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1402 $T # label(t89_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1403 (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]. 21.72/22.92 1404 $T # label(t161_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1405 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> r1_partfun1(C,D)))))) # label(t171_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1406 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_partfun1(D,A,B)))))) # label(t169_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1407 (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]. 21.72/22.92 1408 $T # label(t179_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1409 $T # label(t155_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1410 (all A all B all C (v1_relat_1(C) & v1_funct_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]. 21.72/22.92 1411 $T # label(t5_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.92 1412 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> r1_tarski(k2_relat_1(C),k1_tarski(k1_funct_1(C,A))))) # label(t69_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1413 (all A all B (v1_funct_1(k1_xboole_0) & m2_relset_1(k1_xboole_0,A,B))) # label(t56_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1414 $T # label(t101_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1415 (all A all B k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0) # label(t91_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1416 $T # label(t11_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1417 (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) -> ((all F all G (r2_hidden(k4_tarski(F,G),k4_relset_1(k2_zfmisc_1(A,B),C,D)) -> k1_funct_1(D,k4_tarski(F,G)) = k1_funct_1(E,k4_tarski(F,G)))) & k4_relset_1(k2_zfmisc_1(A,B),C,D) = k4_relset_1(k2_zfmisc_1(A,B),C,E) -> D = E))))) # label(t35_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1418 (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]. 21.72/22.93 1419 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) -> k3_partfun1(C,A,B) = C))) # label(t85_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1420 (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]. 21.72/22.93 1421 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> k1_xboole_0 = k4_relset_1(A,k1_xboole_0,B) & k1_xboole_0 = k2_relat_1(B))) # label(t62_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1422 (all A all B exists C (m1_relset_1(C,A,B) & v1_funct_1(C) & v1_relat_1(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1423 $T # label(t181_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1424 $T # label(t160_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1425 $T # label(t98_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1426 $T # label(t150_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1427 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_partfun1(k1_xboole_0,A))) # label(t141_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1428 $T # label(t118_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1429 $T # label(t6_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1430 $T # label(t152_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1431 $T # label(t173_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1432 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(k1_relat_1(A),k1_relat_1(B)) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C))) <-> r1_partfun1(A,B))))))) # label(t132_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1433 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> (-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]. 21.72/22.93 1434 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (k5_partfun1(A,B,C) = D <-> (all E ((exists F (v1_funct_1(F) & m2_relset_1(F,A,B) & E = F & r1_partfun1(C,F) & v1_partfun1(F,A,B))) <-> r2_hidden(E,D))))))) # label(d7_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1435 (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) -> k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F))) # label(redefinition_k1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1436 (all A all B (v1_funct_1(B) & m2_relset_1(B,k1_xboole_0,A) -> k1_tarski(B) = k5_partfun1(k1_xboole_0,A,B))) # label(t175_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1437 $T # label(t129_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1438 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> k9_relat_1(C,A) = k2_relat_1(C))) # label(t51_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1439 $T # label(t106_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1440 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,k1_xboole_0,A) -> k1_xboole_0 = k9_relat_1(C,B))) # label(t60_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1441 $T # label(t41_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1442 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k1_xboole_0 -> m2_relset_1(C,A,B) & v1_funct_1(C)))) # label(t55_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1443 $T # label(t137_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1444 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_1(E) -> (r1_tarski(B,D) & r1_tarski(A,C) -> v1_funct_1(E) & m2_relset_1(E,C,D)))) # label(t32_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1445 $T # label(t100_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1446 $T # label(t52_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1447 $T # label(t107_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1448 $T # label(t12_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1449 (all A all B (m2_relset_1(B,A,k1_xboole_0) & v1_funct_1(B) -> v2_funct_1(B))) # label(t66_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1450 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),C) -> m2_relset_1(D,C,B) & v1_funct_1(D)))) # label(t28_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1451 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> (r1_partfun1(A,B) -> r1_partfun1(B,A)))) # label(symmetry_r1_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1452 $T # label(t21_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1453 (all A all B (p1_s5_partfun1(A,B) -> r2_hidden(f4_s5_partfun1(A,B),f3_s5_partfun1))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s5_partfun1(B,C))) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s5_partfun1,f2_s5_partfun1),f3_s5_partfun1,A)) <-> r2_hidden(C,f2_s5_partfun1) & p1_s5_partfun1(B,C) & r2_hidden(B,f1_s5_partfun1))) & v1_funct_1(A))) # label(s5_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1454 (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]. 21.72/22.93 1455 $T # label(t50_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1456 (all A all B all C all D (r1_tarski(A,B) & r1_tarski(C,D) -> r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)))) # label(t128_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1457 (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(A,B) & r2_hidden(k1_funct_1(D,A),C) <-> r2_hidden(A,k4_relset_1(B,C,k3_partfun1(D,B,C)))))) # label(t78_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1458 $T # label(t9_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1459 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & (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)))) & r1_partfun1(C,D)))))) # label(t162_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1460 (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]. 21.72/22.93 1461 $T # label(t75_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1462 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,A,B) -> k2_partfun1(A,B,C,D) = k7_relat_1(C,D))) # label(redefinition_k2_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1463 $T # label(t19_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1464 $T # label(t167_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1465 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k1_tarski(A),B) -> r1_tarski(k9_relat_1(D,C),k1_tarski(k1_funct_1(D,A))))) # label(t71_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1466 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k3_partfun1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t86_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1467 $T # label(t111_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1468 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_partfun1(C,A,B) <-> k1_tarski(C) = k5_partfun1(A,B,C)))) # label(t174_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1469 (all A all B all C all D (r2_hidden(A,f1_s4_partfun1) & p1_s4_partfun1(A,B,D) & p1_s4_partfun1(A,B,C) & r2_hidden(B,f2_s4_partfun1) -> D = C)) & (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))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1) & (all B all C (r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)) -> p1_s4_partfun1(B,C,k1_funct_1(A,k4_tarski(B,C))))) & (all B all C (r2_hidden(B,f1_s4_partfun1) & (exists D p1_s4_partfun1(B,C,D)) & r2_hidden(C,f2_s4_partfun1) <-> r2_hidden(k4_tarski(B,C),k4_relset_1(k2_zfmisc_1(f1_s4_partfun1,f2_s4_partfun1),f3_s4_partfun1,A)))))) # label(s4_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1470 $T # label(t163_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1471 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k2_relat_1(k3_partfun1(C,A,B)),k2_relat_1(C)) & r1_tarski(k4_relset_1(A,B,k3_partfun1(C,A,B)),k1_relat_1(C)))) # label(t77_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1472 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v2_funct_1(C) -> m2_relset_1(k2_funct_1(C),B,A) & v1_funct_1(k2_funct_1(C))))) # label(t39_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1473 (all A all B all C (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k3_partfun1(A,B,C)) & m2_relset_1(k3_partfun1(A,B,C),B,C))) # label(dt_k3_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1474 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & r1_tarski(B,C) & r1_tarski(A,C)))))))) # label(t131_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1475 (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]. 21.72/22.93 1476 $T # label(t104_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1477 (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_partfun1(A,B)))))) # label(t138_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1478 $T # label(t178_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1479 $T # label(t48_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1480 (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,E) = k1_funct_1(C,D) -> D = E))))) -> v2_funct_1(C)))) # label(t38_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1481 (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]. 21.72/22.93 1482 (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]. 21.72/22.93 1483 (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) -> A = B))))) # label(t136_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1484 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) -> 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]. 21.72/22.93 1485 $T # label(d2_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1486 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(A) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)))) # label(t24_partfun1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1487 (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]. 21.72/22.93 1488 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C))) -> C = k2_mcart_1(A) & B = k1_mcart_1(A))) # label(t14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1489 (all A all B all C all D all E all F all G all H (m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) & m1_subset_1(F,k1_zfmisc_1(B)) -> m1_subset_1(k14_mcart_1(A,B,C,D,E,F,G,H),k1_zfmisc_1(k4_zfmisc_1(A,B,C,D))))) # label(dt_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1490 (all A all B all C all D -(C != k1_xboole_0 & k1_xboole_0 != D & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k8_mcart_1(A,B,C,D,E) != E & E != k10_mcart_1(A,B,C,D,E) & E != k11_mcart_1(A,B,C,D,E) & k9_mcart_1(A,B,C,D,E) != E)) & B != k1_xboole_0 & A != k1_xboole_0)) # label(t62_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1491 (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 A != k4_tarski(D,E)))) # label(t11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1492 $T # label(dt_k17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1493 (all A -(k1_xboole_0 != A & (all B -((all C all D all E all F -((r2_hidden(C,A) | r2_hidden(D,A)) & k4_mcart_1(C,D,E,F) = B)) & r2_hidden(B,A))))) # label(t34_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1494 (all A k20_mcart_1(A) = k2_mcart_1(k2_mcart_1(A))) # label(d17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1495 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> B = k1_xboole_0 | C = F & B = E & A = D | k1_xboole_0 = C | A = k1_xboole_0)) # label(t36_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1496 (all A ((exists B exists C k4_tarski(B,C) = A) -> A != k1_mcart_1(A) & k2_mcart_1(A) != A)) # label(t20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1497 (all A k17_mcart_1(A) = k1_mcart_1(k1_mcart_1(A))) # label(d14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1498 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = I))))))))) -> k1_xboole_0 = A | B = k1_xboole_0 | k1_xboole_0 = C | E = k10_mcart_1(A,B,C,D,F) | D = k1_xboole_0))) # label(t81_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1499 (all A all B all C k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C)) = k1_tarski(k3_mcart_1(A,B,C))) # label(t39_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1500 (all A all B all C all D all E -(r2_hidden(A,k4_zfmisc_1(B,C,D,E)) & (all F all G all H all I -(r2_hidden(F,B) & r2_hidden(G,C) & r2_hidden(H,D) & A = k4_mcart_1(F,G,H,I) & r2_hidden(I,E))))) # label(t83_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1501 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k1_tarski(D))) -> (k1_mcart_1(A) = C | B = k1_mcart_1(A)) & D = k2_mcart_1(A))) # label(t17_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1502 (all A ((exists B exists C A = k4_tarski(B,C)) -> (all B (k1_mcart_1(A) = B <-> (all C all D (k4_tarski(C,D) = A -> B = C)))))) # label(d1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1503 $T # label(dt_k3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1504 (all A -(k1_xboole_0 != A & (all B -((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))) & r2_hidden(B,A))))) # label(t6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1505 $T # label(dt_k1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1506 (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]. 21.72/22.93 1507 (all A all B all C (r2_hidden(A,k2_zfmisc_1(k1_tarski(B),C)) -> B = k1_mcart_1(A) & r2_hidden(k2_mcart_1(A),C))) # label(t12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1508 (all A -((all B -(r1_xboole_0(B,A) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t1_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1509 $T # label(dt_k4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1510 (all A all B all C all D k2_tarski(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D)) = k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k1_tarski(D))) # label(t41_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1511 (all A all B all C -(k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,A) -> ((all F all G all H (D = k3_mcart_1(F,G,H) -> E = F)) <-> E = k5_mcart_1(A,B,C,D)))))) & k1_xboole_0 != B & A != k1_xboole_0)) # label(d5_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1512 $T # label(dt_k19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1513 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> D = H))))))) -> B = k1_xboole_0 | D = k7_mcart_1(A,B,C,E) | C = k1_xboole_0 | A = k1_xboole_0))) # label(t71_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1514 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> A != k2_mcart_1(A) & A != k1_mcart_1(A))) # label(t67_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1515 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (k4_mcart_1(G,H,I,J) = F -> E = G))))))))) -> k1_xboole_0 = A | B = k1_xboole_0 | k8_mcart_1(A,B,C,D,F) = E | k1_xboole_0 = D | C = k1_xboole_0))) # label(t79_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1516 (all A -(A != k1_xboole_0 & (all B -((all C all D all E -(B = k3_mcart_1(C,D,E) & (r2_hidden(C,A) | r2_hidden(D,A)))) & r2_hidden(B,A))))) # label(t29_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1517 (all A -(A != k1_xboole_0 & (all B -((all C (r2_hidden(C,B) -> r1_xboole_0(C,A))) & r2_hidden(B,A))))) # label(t2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1518 (all A all B -(A != k1_xboole_0 & B != k1_xboole_0 & -(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> k4_tarski(k1_mcart_1(C),k2_mcart_1(C)) = C)))) # label(t24_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1519 (all A all B all C -(k1_xboole_0 != A & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,B) -> ((all F all G all H (D = k3_mcart_1(F,G,H) -> E = G)) <-> k6_mcart_1(A,B,C,D) = E))))) & k1_xboole_0 != B)) # label(d6_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1520 (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]. 21.72/22.93 1521 (all A all B (k4_zfmisc_1(B,B,B,B) = k4_zfmisc_1(A,A,A,A) -> B = A)) # label(t58_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1522 $T # label(dt_k2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1523 (all A all B all C all D all E all F all G all H -(k1_xboole_0 != A & B != k1_xboole_0 & k1_xboole_0 != D & k1_xboole_0 != F & G != k1_xboole_0 & (exists I ((exists J (-(k8_mcart_1(E,F,G,H,J) = k8_mcart_1(A,B,C,D,I) & k9_mcart_1(E,F,G,H,J) = k9_mcart_1(A,B,C,D,I) & k11_mcart_1(E,F,G,H,J) = k11_mcart_1(A,B,C,D,I) & k10_mcart_1(A,B,C,D,I) = k10_mcart_1(E,F,G,H,J)) & J = I & m1_subset_1(J,k4_zfmisc_1(E,F,G,H)))) & m1_subset_1(I,k4_zfmisc_1(A,B,C,D)))) & H != k1_xboole_0 & E != k1_xboole_0 & k1_xboole_0 != C)) # label(t86_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1524 (all A all B all C all D all E k3_zfmisc_1(k1_tarski(A),k2_tarski(B,C),k2_tarski(D,E)) = k2_enumset1(k3_mcart_1(A,B,D),k3_mcart_1(A,C,D),k3_mcart_1(A,B,E),k3_mcart_1(A,C,E))) # label(t45_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1525 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> r2_hidden(k2_mcart_1(A),C) & r2_hidden(k1_mcart_1(A),B))) # label(t10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1526 (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)) -> 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]. 21.72/22.93 1527 (all A -(A != k1_xboole_0 & (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))))))) # label(t4_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1528 (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)) -> k1_funct_1(B,C) = k1_mcart_1(k1_funct_1(A,C)))) & k1_relat_1(A) = k1_relat_1(B) <-> k15_mcart_1(A) = B))))) # label(d12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1529 (all A all B all C all D all E k3_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D),k1_tarski(E)) = k2_enumset1(k3_mcart_1(A,C,E),k3_mcart_1(B,C,E),k3_mcart_1(A,D,E),k3_mcart_1(B,D,E))) # label(t43_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1530 (all A all B all C all D all E all F (m1_subset_1(F,k4_zfmisc_1(A,B,C,D)) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> (all J (m1_subset_1(J,D) -> (F = k4_mcart_1(G,H,I,J) -> E = J))))))))) -> k11_mcart_1(A,B,C,D,F) = E | D = k1_xboole_0 | k1_xboole_0 = C | k1_xboole_0 = B | A = k1_xboole_0))) # label(t82_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1531 $T # label(t30_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1532 (all A all B all C all D k1_tarski(k4_mcart_1(A,B,C,D)) = k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D))) # label(t65_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1533 (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]. 21.72/22.93 1534 $T # label(dt_k18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1535 $T # label(t21_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1536 (all A all B all C all D -((all E all F all G -(r2_hidden(F,C) & r2_hidden(G,D) & A = k3_mcart_1(E,F,G) & r2_hidden(E,B))) & r2_hidden(A,k3_zfmisc_1(B,C,D)))) # label(t72_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1537 (all A all B all C all D all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(B)) -> (all G (m1_subset_1(G,k1_zfmisc_1(C)) -> (all H (m1_subset_1(H,k1_zfmisc_1(D)) -> (all I (m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) -> (r2_hidden(I,k4_zfmisc_1(E,F,G,H)) -> r2_hidden(k9_mcart_1(A,B,C,D,I),F) & r2_hidden(k11_mcart_1(A,B,C,D,I),H) & r2_hidden(k10_mcart_1(A,B,C,D,I),G) & r2_hidden(k8_mcart_1(A,B,C,D,I),E)))))))))))) # label(t87_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1538 (all A all B all C all D all E all F all G all H (m1_subset_1(E,k1_zfmisc_1(A)) & m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(H,k1_zfmisc_1(D)) & m1_subset_1(G,k1_zfmisc_1(C)) -> k4_zfmisc_1(E,F,G,H) = k14_mcart_1(A,B,C,D,E,F,G,H))) # label(redefinition_k14_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1539 (all A all B all C all D -(B != k1_xboole_0 & (exists E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & (exists F exists G exists H exists I (k4_mcart_1(F,G,H,I) = E & -(k9_mcart_1(A,B,C,D,E) = G & I = k11_mcart_1(A,B,C,D,E) & k10_mcart_1(A,B,C,D,E) = H & k8_mcart_1(A,B,C,D,E) = F))))) & k1_xboole_0 != D & k1_xboole_0 != C & A != k1_xboole_0)) # label(t59_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1540 (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]. 21.72/22.93 1541 (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(J,E) & k4_mcart_1(G,H,I,J) = F & r2_hidden(I,D) & r2_hidden(H,C))))) -> A = k4_zfmisc_1(B,C,D,E))) # label(t85_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1542 (all A (v1_funct_1(A) & v1_relat_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]. 21.72/22.93 1543 (all A all B all C all D all E all F all G all H (k4_mcart_1(A,B,C,D) = k4_mcart_1(E,F,G,H) -> A = E & G = C & D = H & F = B)) # label(t33_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1544 (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]. 21.72/22.93 1545 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,k1_tarski(C))) -> k2_mcart_1(A) = C & r2_hidden(k1_mcart_1(A),B))) # label(t13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1546 (all A all B all C all D -(k1_xboole_0 != B & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,B) -> (k9_mcart_1(A,B,C,D,E) = F <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> H = F))))))) & k1_xboole_0 != D & k1_xboole_0 != C & A != k1_xboole_0)) # label(d9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1547 (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]. 21.72/22.93 1548 (all A ((exists B exists C k4_tarski(B,C) = A) -> (all B (B = k2_mcart_1(A) <-> (all C all D (A = k4_tarski(C,D) -> D = B)))))) # label(d2_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1549 (all A all B all C (-(-r1_tarski(A,k3_zfmisc_1(C,A,B)) & -r1_tarski(A,k3_zfmisc_1(B,C,A)) & -r1_tarski(A,k3_zfmisc_1(A,B,C))) -> A = k1_xboole_0)) # label(t49_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1550 (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]. 21.72/22.93 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 = H))))))))) -> k1_xboole_0 = A | D = k1_xboole_0 | k9_mcart_1(A,B,C,D,F) = E | C = k1_xboole_0 | B = k1_xboole_0))) # label(t80_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1552 $T # label(t22_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.93 1553 (all A -(A != k1_xboole_0 & (all B -(r2_hidden(B,A) & (all C all D -((r2_hidden(C,A) | r2_hidden(D,A)) & k4_tarski(C,D) = B)))))) # label(t9_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1554 (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]. 21.72/22.94 1555 (all A all B all C all D -(k1_xboole_0 != B & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,D) -> (F = k11_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> J = F))))))) & D != k1_xboole_0 & k1_xboole_0 != C & A != k1_xboole_0)) # label(d11_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1556 (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]. 21.72/22.94 1557 (all A all B all C all D all E (m1_subset_1(E,k3_zfmisc_1(A,B,C)) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,C) -> (k3_mcart_1(F,G,H) = E -> G = D))))))) -> C = k1_xboole_0 | k6_mcart_1(A,B,C,E) = D | k1_xboole_0 = B | k1_xboole_0 = A))) # label(t70_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1558 (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]. 21.72/22.94 1559 (all A all B all C all D all E all F (m1_subset_1(D,k1_zfmisc_1(A)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) -> k3_zfmisc_1(D,E,F) = k13_mcart_1(A,B,C,D,E,F))) # label(redefinition_k13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1560 (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]. 21.72/22.94 1561 (all A all B all C -(A != k1_xboole_0 & k1_xboole_0 != C & (exists D ((exists E exists F exists G (-(k7_mcart_1(A,B,C,D) = G & F = k6_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = E) & k3_mcart_1(E,F,G) = D)) & m1_subset_1(D,k3_zfmisc_1(A,B,C)))) & B != k1_xboole_0)) # label(t47_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1562 (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)) -> k2_mcart_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(B) = k1_relat_1(A) <-> B = k16_mcart_1(A)))))) # label(d13_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1563 (all A all B all C (B != k1_xboole_0 & C != k1_xboole_0 & A != k1_xboole_0 <-> k3_zfmisc_1(A,B,C) != k1_xboole_0)) # label(t35_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1564 (all A all B all C all D all E (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),k2_tarski(D,E))) -> (C = k1_mcart_1(A) | B = k1_mcart_1(A)) & (k2_mcart_1(A) = D | E = k2_mcart_1(A)))) # label(t19_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1565 (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]. 21.72/22.94 1566 (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]. 21.72/22.94 1567 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_relat_1(k15_mcart_1(A)) & v1_funct_1(k15_mcart_1(A)))) # label(dt_k15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.72/22.94 1568 (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]. 21.72/22.94 1569 (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))))))) -> k5_mcart_1(A,B,C,E) = D | k1_xboole_0 = C | k1_xboole_0 = B | k1_xboole_0 = A))) # label(t69_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1570 (all A all B all C all D all E k2_enumset1(k3_mcart_1(A,C,D),k3_mcart_1(B,C,D),k3_mcart_1(A,C,E),k3_mcart_1(B,C,E)) = k3_zfmisc_1(k2_tarski(A,B),k1_tarski(C),k2_tarski(D,E))) # label(t44_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1571 (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]. 21.76/22.94 1572 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(C,k1_zfmisc_1(A)) -> m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))))) # label(dt_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1573 (all A all B all C -(k1_xboole_0 != A & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> (all E (m1_subset_1(E,C) -> (k7_mcart_1(A,B,C,D) = E <-> (all F all G all H (k3_mcart_1(F,G,H) = D -> H = E))))))) & C != k1_xboole_0 & k1_xboole_0 != B)) # label(d7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1574 (all A all B all C all D k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k2_tarski(C,D)) = k2_tarski(k3_mcart_1(A,B,C),k3_mcart_1(A,B,D))) # label(t42_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1575 (all A all B all C all D all E all F -(C != k1_xboole_0 & (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) & k7_mcart_1(A,B,C,G) = k7_mcart_1(D,E,F,H) & k6_mcart_1(A,B,C,G) = k6_mcart_1(D,E,F,H)) & m1_subset_1(H,k3_zfmisc_1(D,E,F)))))) & k1_xboole_0 != F & k1_xboole_0 != E & D != k1_xboole_0 & B != k1_xboole_0 & A != k1_xboole_0)) # label(t75_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1576 (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(C,F) & r2_hidden(B,E))) # label(t73_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1577 (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)) & B = k1_mcart_1(A))) # label(t18_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1578 (all A k1_mcart_1(k2_mcart_1(A)) = k19_mcart_1(A)) # label(d16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1579 (all A all B all C -(k1_xboole_0 != C & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> k1_mcart_1(k1_mcart_1(D)) = k5_mcart_1(A,B,C,D) & k2_mcart_1(k1_mcart_1(D)) = k6_mcart_1(A,B,C,D) & k7_mcart_1(A,B,C,D) = k2_mcart_1(D))) & B != k1_xboole_0 & k1_xboole_0 != A)) # label(t50_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1580 (all A all B all C all D all E all F (k3_mcart_1(A,B,C) = k3_mcart_1(D,E,F) -> E = B & F = C & A = D)) # label(t28_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1581 (all A all B all C all D all E all F all G all H (r1_tarski(A,B) & r1_tarski(C,D) & r1_tarski(G,H) & r1_tarski(E,F) -> r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)))) # label(t88_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1582 (all A all B all C all D (r2_hidden(A,k2_zfmisc_1(k2_tarski(B,C),D)) -> r2_hidden(k2_mcart_1(A),D) & (C = k1_mcart_1(A) | k1_mcart_1(A) = B))) # label(t15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1583 (all A all B all C all D (m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) -> k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D))) # label(redefinition_k12_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1584 (all A all B all C -(k1_xboole_0 != A & B != k1_xboole_0 & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D = k3_mcart_1(k5_mcart_1(A,B,C,D),k6_mcart_1(A,B,C,D),k7_mcart_1(A,B,C,D)))))) # label(t48_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1585 (all A all B all C all D -(B != k1_xboole_0 & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,C) -> (F = k10_mcart_1(A,B,C,D,E) <-> (all G all H all I all J (E = k4_mcart_1(G,H,I,J) -> I = F))))))) & D != k1_xboole_0 & k1_xboole_0 != A)) # label(d10_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1586 (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(C,G) & -r1_xboole_0(D,H) & -r1_xboole_0(A,E))) # label(t64_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1587 (all A all B all C all D -(A != k1_xboole_0 & k1_xboole_0 != B & C != k1_xboole_0 & D != k1_xboole_0 & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> (all F (m1_subset_1(F,A) -> (k8_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 = G))))))))) # label(d8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1588 (all A ((exists B exists C A = k4_tarski(B,C)) -> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)))) # label(t8_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1589 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> G = C & H = D & B = F & A = E | k4_zfmisc_1(A,B,C,D) = k1_xboole_0)) # label(t57_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1590 (all A all B all C all D all E all F all G all H (r2_hidden(A,E) & r2_hidden(B,F) & r2_hidden(C,G) & r2_hidden(D,H) <-> r2_hidden(k4_mcart_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)))) # label(t84_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1591 (all A all B -(-(all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k1_mcart_1(C) & k2_mcart_1(C) != C)) & B != k1_xboole_0 & A != k1_xboole_0)) # label(t26_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1592 $T # label(dt_k20_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1593 (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]. 21.76/22.94 1594 (all A all B all C all D (-(-r1_tarski(A,k4_zfmisc_1(A,B,C,D)) & -r1_tarski(A,k4_zfmisc_1(C,D,A,B)) & -r1_tarski(A,k4_zfmisc_1(D,A,B,C)) & -r1_tarski(A,k4_zfmisc_1(B,C,D,A))) -> A = k1_xboole_0)) # label(t63_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1595 (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) = D | C = k2_mcart_1(A)))) # label(t16_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1596 (all A all B all C all D -(k1_xboole_0 != A & k1_xboole_0 != B & k1_xboole_0 != C & -(all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> k8_mcart_1(A,B,C,D,E) = k1_mcart_1(k1_mcart_1(k1_mcart_1(E))) & k10_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(E)) & k11_mcart_1(A,B,C,D,E) = k2_mcart_1(E) & k9_mcart_1(A,B,C,D,E) = k2_mcart_1(k1_mcart_1(k1_mcart_1(E))))) & k1_xboole_0 != D)) # label(t61_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1597 (all A all B all C all D all E all F (k18_mcart_1(k4_tarski(k4_tarski(A,B),C)) = B & k19_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D & k20_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E & k17_mcart_1(k4_tarski(k4_tarski(A,B),C)) = A)) # label(t89_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1598 (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]. 21.76/22.94 1599 (all A all B all C all D all E all F (k3_zfmisc_1(A,B,C) = k3_zfmisc_1(D,E,F) -> A = D & B = E & C = F | k1_xboole_0 = k3_zfmisc_1(A,B,C))) # label(t37_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1600 (all A all B all C -(k1_xboole_0 != A & C != k1_xboole_0 & -(all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> D != k5_mcart_1(A,B,C,D) & k6_mcart_1(A,B,C,D) != D & D != k7_mcart_1(A,B,C,D))) & B != k1_xboole_0)) # label(t51_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1601 (all A all B (A = k1_mcart_1(k4_tarski(A,B)) & k2_mcart_1(k4_tarski(A,B)) = B)) # label(t7_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1602 (all A -(k1_xboole_0 != A & (all B -(r2_hidden(B,A) & (all C all D (r2_hidden(C,D) & r2_hidden(D,B) -> r1_xboole_0(C,A))))))) # label(t3_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1603 (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]. 21.76/22.94 1604 (all A all B all C all D (k1_xboole_0 != A & k1_xboole_0 != C & k1_xboole_0 != D & B != k1_xboole_0 <-> k4_zfmisc_1(A,B,C,D) != k1_xboole_0)) # label(t55_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1605 (all A all B all C (r2_hidden(A,k2_zfmisc_1(B,C)) -> k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) = A)) # label(t23_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1606 (all A k18_mcart_1(A) = k2_mcart_1(k1_mcart_1(A))) # label(d15_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1607 (all A all B all C all D all E all F (r1_tarski(E,F) & r1_tarski(C,D) & r1_tarski(A,B) -> r1_tarski(k3_zfmisc_1(A,C,E),k3_zfmisc_1(B,D,F)))) # label(t77_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1608 $T # label(t27_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1609 (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]. 21.76/22.94 1610 (all A all B all C all D -(k1_xboole_0 != B & -(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 & k1_xboole_0 != C & A != k1_xboole_0)) # label(t60_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1611 (all A all B all C all D all E all F all G all H (k4_zfmisc_1(E,F,G,H) = k4_zfmisc_1(A,B,C,D) -> A = k1_xboole_0 | k1_xboole_0 = C | F = B & H = D & G = C & A = E | D = k1_xboole_0 | k1_xboole_0 = B)) # label(t56_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1612 (all A all B (k2_zfmisc_1(A,B) != k1_xboole_0 -> (all C (m1_subset_1(C,k2_zfmisc_1(A,B)) -> C != k1_mcart_1(C) & C != k2_mcart_1(C))))) # label(t66_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1613 (all A all B all C all D ((all E (r2_hidden(E,A) <-> (exists F exists G exists H (r2_hidden(H,D) & k3_mcart_1(F,G,H) = E & r2_hidden(G,C) & r2_hidden(F,B))))) -> A = k3_zfmisc_1(B,C,D))) # label(t74_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1614 (all A all B (k3_zfmisc_1(B,B,B) = k3_zfmisc_1(A,A,A) -> B = A)) # label(t38_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1615 (all A all B all C all D all E (m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) -> -(B != k1_xboole_0 & (exists F exists G exists H exists I (k4_mcart_1(F,G,H,I) = E & -(F = k8_mcart_1(A,B,C,D,E) & k11_mcart_1(A,B,C,D,E) = I & k10_mcart_1(A,B,C,D,E) = H & G = k9_mcart_1(A,B,C,D,E)))) & D != k1_xboole_0 & C != k1_xboole_0 & A != k1_xboole_0))) # label(t78_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1616 (all A all B all C all D (m1_subset_1(D,k3_zfmisc_1(A,B,C)) -> -(k1_xboole_0 != B & (exists E exists F exists G (D = k3_mcart_1(E,F,G) & -(F = k6_mcart_1(A,B,C,D) & G = k7_mcart_1(A,B,C,D) & k5_mcart_1(A,B,C,D) = E))) & C != k1_xboole_0 & A != k1_xboole_0))) # label(t68_mcart_1) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1617 $T # label(t16_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1618 (all A v4_relat_2(k1_wellord2(A))) # label(t5_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1619 (all A (v1_relat_1(A) -> v3_ordinal1(k2_wellord2(A)))) # label(dt_k2_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1620 $T # label(t24_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1621 (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]. 21.76/22.94 1622 $T # label(t1_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.76/22.94 1623 (all A -(r2_hidden(A,f1_s2_wellord2) & (all B all C -(r2_hidden(B,f2_s2_wellord2) & r2_hidden(C,f3_s2_wellord2) & p1_s2_wellord2(A,B,C))))) -> (exists A (v1_funct_1(A) & (exists B (f1_s2_wellord2 = k1_relat_1(A) & f1_s2_wellord2 = k1_relat_1(B) & (all C (r2_hidden(C,f1_s2_wellord2) -> p1_s2_wellord2(C,k1_funct_1(A,C),k1_funct_1(B,C)))) & v1_funct_1(B) & v1_relat_1(B))) & v1_relat_1(A))) # label(s2_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1624 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) -> (A = k2_wellord2(B) <-> r1_wellord2(A,B)))))) # label(d3_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1625 (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]. 21.77/22.94 1626 (all A v8_relat_2(k1_wellord2(A))) # label(t3_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1627 (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]. 21.77/22.94 1628 (all A all B (r2_tarski(A,B) <-> r2_wellord2(A,B))) # label(redefinition_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1629 (all A (v1_relat_1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r4_wellord1(A,k1_wellord2(B)) & r4_wellord1(A,k1_wellord2(C)) -> B = C))))))) # label(t12_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1630 (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]. 21.77/22.94 1631 (all A all B (v1_relat_1(B) -> ((all C all D (r2_hidden(C,A) & r2_hidden(D,A) -> (r2_hidden(k4_tarski(C,D),B) <-> r1_tarski(C,D)))) & k3_relat_1(B) = A <-> k1_wellord2(A) = B))) # label(d1_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1632 (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]. 21.77/22.94 1633 (all A v1_relat_2(k1_wellord2(A))) # label(t2_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1634 (all A all B (v1_relat_1(B) -> (r2_wellord1(B,A) -> A = k3_relat_1(k2_wellord1(B,A)) & v2_wellord1(k2_wellord1(B,A))))) # label(t25_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1635 (all A (-v1_xboole_0(A) -> -((all B -(k1_xboole_0 = B & r2_hidden(B,A))) & (all B (v1_funct_1(B) & v1_relat_1(B) -> -((all C (r2_hidden(C,A) -> r2_hidden(k1_funct_1(B,C),C))) & k1_relat_1(B) = A)))))) # label(t28_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1636 (all A (v3_ordinal1(A) -> v1_wellord1(k1_wellord2(A)))) # label(t6_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1637 (all A v1_relat_1(k1_wellord2(A))) # label(dt_k1_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1638 $T # label(t18_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1639 (all A (v1_relat_1(A) -> -(v2_wellord1(A) & (all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B))))))) # label(t14_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1640 (all A all B ((exists C (v1_relat_1(C) & k1_relat_1(C) = A & k2_relat_1(C) = B & v2_funct_1(C) & v1_funct_1(C))) <-> r2_wellord2(A,B))) # label(d4_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1641 (all A -((all B -(p1_s1_wellord2(A,B) & r2_hidden(B,f2_s1_wellord2))) & r2_hidden(A,f1_s1_wellord2))) -> (exists A (r1_tarski(k2_relat_1(A),f2_s1_wellord2) & (all B (r2_hidden(B,f1_s1_wellord2) -> p1_s1_wellord2(B,k1_funct_1(A,B)))) & f1_s1_wellord2 = k1_relat_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1642 (all A (v1_relat_1(A) -> -((all B (v3_ordinal1(B) -> -r4_wellord1(A,k1_wellord2(B)))) & (all B -((all C (v3_ordinal1(C) -> -r4_wellord1(k2_wellord1(A,k1_wellord1(A,B)),k1_wellord2(C)))) & r2_hidden(B,k3_relat_1(A)))) & v2_wellord1(A)))) # label(t13_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1643 $T # label(t21_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1644 (all A all B r2_wellord2(A,A)) # label(reflexivity_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1645 (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]. 21.77/22.94 1646 (all A exists B (r2_wellord1(B,A) & v1_relat_1(B))) # label(t26_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1647 $T # label(t20_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1648 (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]. 21.77/22.94 1649 $T # label(t23_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1650 (all A all B (r2_wellord2(A,B) -> r2_wellord2(B,A))) # label(symmetry_r2_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1651 $T # label(t15_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1652 (all A (v3_ordinal1(A) -> v6_relat_2(k1_wellord2(A)))) # label(t4_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1653 (all A (v3_ordinal1(A) -> v2_wellord1(k1_wellord2(A)))) # label(t7_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1654 $T # label(t19_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1655 (all A (-v1_xboole_0(A) -> -((all B exists C (r2_hidden(C,A) & (all D k1_tarski(D) != k3_xboole_0(B,C)))) & (all B all C (r2_hidden(B,A) & r2_hidden(C,A) -> r1_xboole_0(B,C) | B = C)) & (all B -(r2_hidden(B,A) & k1_xboole_0 = B))))) # label(t27_wellord2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1656 $T # label(t135_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1657 $T # label(t15_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1658 $T # label(t91_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1659 $T # label(t2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1660 (all A all B all C all D (v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v1_funct_1(C) -> k9_relat_1(C,D) = k2_funct_2(A,B,C,D))) # label(redefinition_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1661 (all A all B all C all D (v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(A) -> m1_subset_1(k8_funct_2(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1662 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (r1_tarski(B,A) -> k3_funct_2(A,A,C,k2_funct_2(A,A,C,B)) = B & k2_funct_2(A,A,C,k3_funct_2(A,A,C,B)) = B))) # label(t92_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1663 (all A all B (m1_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> v3_funct_2(k6_funct_2(A,B),A,A) & m2_relset_1(k6_funct_2(A,B),A,A) & v1_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]. 21.77/22.94 1664 (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) & B = k2_relat_1(C) -> B = k1_xboole_0 | k6_partfun1(B) = k5_relat_1(k2_funct_1(C),C) & k6_partfun1(A) = k5_relat_1(C,k2_funct_1(C))))) # label(t35_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1665 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (v1_partfun1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B)))) # label(t131_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1666 $T # label(t123_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1667 $T # label(t139_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1668 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> (k2_relat_1(C) = B & v2_funct_1(C) -> v1_funct_1(k2_funct_1(C)) & m2_relset_1(k2_funct_1(C),B,A) & v1_funct_2(k2_funct_1(C),B,A)))) # label(t31_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1669 $T # label(t13_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1670 $T # label(t117_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1671 $T # label(t109_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1672 (all A all B (m2_relset_1(B,A,A) & v1_funct_1(B) -> (exists C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & r1_partfun1(B,C))))) # label(t149_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1673 (all A all B all C all D all E (v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) & v1_funct_1(D) & -v1_xboole_0(B) -> k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E))) # label(redefinition_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1674 (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(B,C) -> v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) | k1_xboole_0 = B & A != k1_xboole_0))) # label(t9_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1675 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> k1_tarski(B) = k5_partfun1(A,A,k3_partfun1(B,A,A)))) # label(t162_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1676 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> -((k1_xboole_0 = B -> k1_xboole_0 = A) & (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (exists E (k1_funct_1(D,E) != k1_funct_1(C,E) & r2_hidden(E,k4_relset_1(A,B,C))))))))) # label(t136_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1677 (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) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,A) & m2_relset_1(D,A,A) -> (r1_partfun1(C,D) & r1_partfun1(B,D) -> r1_partfun1(B,C)))))))) # label(t152_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1678 $T # label(t104_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1679 $T # label(t1_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1680 $T # label(t100_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1681 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_2(C,A,k1_tarski(B)) & v1_funct_1(C) -> (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]. 21.77/22.94 1682 (all A (m1_subset_1(A,f1_s12_funct_2) -> r2_hidden(f3_s12_funct_2(A),f2_s12_funct_2))) -> (exists A ((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) & v1_funct_2(A,f1_s12_funct_2,f2_s12_funct_2) & v1_funct_1(A))) # label(s12_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1683 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> (v2_funct_1(C) <-> (all D all E (r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) -> E = D)))))) # label(t25_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 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) -> (B != k1_xboole_0 -> (all E ((exists F (r2_hidden(F,C) & E = k1_funct_1(D,F) & r2_hidden(F,A))) -> r2_hidden(E,k9_relat_1(D,C))))))) # label(t43_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1685 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) & v2_funct_1(D) -> B = k1_xboole_0 | k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) = C))) # label(t32_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1686 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_partfun1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1687 (all A all B all C all D (v1_funct_2(C,A,B) & m1_subset_1(D,A) & m1_relset_1(C,A,B) & v1_funct_1(C) & -v1_xboole_0(A) -> k8_funct_2(A,B,C,D) = k1_funct_1(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1688 (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 (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> (v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(D) | B = k1_xboole_0 & k1_xboole_0 != A | B != k1_xboole_0 & C = k1_xboole_0))))) # label(t26_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1689 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (k2_relat_1(E) = C & B = k2_relat_1(D) -> k1_xboole_0 = B | C = k2_relat_1(k1_partfun1(A,B,B,C,D,E)) | C = k1_xboole_0))))) # label(t20_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1690 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,A,A) & v3_funct_2(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) & m1_relset_1(B,A,A) -> v1_funct_2(k5_funct_2(A,B,C),A,A) & m2_relset_1(k5_funct_2(A,B,C),A,A) & v3_funct_2(k5_funct_2(A,B,C),A,A) & v1_funct_1(k5_funct_2(A,B,C)))) # label(dt_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1691 (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_partfun1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1692 $T # label(t56_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1693 (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 -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,B)))) # label(t48_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1694 (all A all B all C ((all D ((exists E (v1_relat_1(E) & r1_tarski(k2_relat_1(E),B) & k1_relat_1(E) = A & D = E & v1_funct_1(E))) <-> r2_hidden(D,C))) <-> k1_funct_2(A,B) = C)) # label(d2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1695 (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]. 21.77/22.94 1696 $T # label(t63_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1697 (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]. 21.77/22.94 1698 (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]. 21.77/22.94 1699 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> r2_hidden(B,k1_funct_2(A,A)))) # label(t12_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1700 $T # label(t107_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1701 $T # label(t94_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1702 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> k1_tarski(C) = k5_partfun1(A,B,k3_partfun1(C,A,B))))) # label(t161_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1703 (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(E,k4_tarski(F,G)) = k1_funct_1(D,k4_tarski(F,G)))) -> E = D))))) # label(t118_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1704 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,A) & m2_relset_1(C,A,A) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r2_hidden(B,A) -> k1_funct_1(D,k1_funct_1(C,B)) = k1_funct_1(k5_relat_1(C,D),B)))))) # label(t70_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1705 (all A exists B (v2_funct_1(B) & v3_funct_2(B,A,A) & v2_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) & v1_relat_1(B) & m1_relset_1(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1706 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) -> r2_hidden(k1_funct_1(D,C),B) | B = k1_xboole_0))) # label(t7_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1707 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) -> (v2_funct_1(C) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D) & k2_relat_1(C) = B -> A = k1_xboole_0 | B = k1_xboole_0 | k2_funct_1(C) = D))))) # label(t36_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1708 (all A all B (v1_funct_1(B) & v1_relat_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]. 21.77/22.94 1709 $T # label(t147_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1710 $T # label(t138_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1711 (all A all B all C (v1_funct_2(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & m2_relset_1(k9_funct_2(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)) & v1_funct_1(k9_funct_2(A,B,C)))) # label(dt_k9_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1712 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_2(C,A,B) & v2_funct_2(C,A,B) & v2_funct_1(C) & v1_funct_1(C) -> 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]. 21.77/22.94 1713 $T # label(t68_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1714 $T # label(t127_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1715 (all A all B (v1_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (A = k2_relat_1(B) & k2_relat_1(C) = A -> k2_relat_1(k4_funct_2(A,B,C)) = A))))) # label(t73_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1716 (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) & v1_funct_2(A,k2_zfmisc_1(f1_s6_funct_2,f2_s6_funct_2),f3_s6_funct_2) & (all B all C (r2_hidden(C,f2_s6_funct_2) & r2_hidden(B,f1_s6_funct_2) -> f4_s6_funct_2(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & m2_relset_1(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]. 21.77/22.94 1717 (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]. 21.77/22.94 1718 (all A all B (m2_relset_1(B,A,A) -> k7_relset_1(A,A,A,A,k6_partfun1(A),B) = B & k7_relset_1(A,A,A,A,B,k6_partfun1(A)) = B)) # label(t74_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1719 (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) -> v1_partfun1(k3_partfun1(C,A,B),A,B)))) # label(t133_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1720 (all A all B all C (v1_funct_2(B,A,A) & m1_relset_1(B,A,A) & m1_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) & v1_funct_1(B) -> k5_relat_1(B,C) = k4_funct_2(A,B,C))) # label(redefinition_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1721 (all A all B all C (m2_relset_1(C,k1_tarski(A),B) & v1_funct_2(C,k1_tarski(A),B) & v1_funct_1(C) -> (k1_xboole_0 != B -> r2_hidden(k1_funct_1(C,A),B)))) # label(t61_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1722 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> r2_hidden(C,k1_funct_2(A,B))))) # label(t11_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1723 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_tarski(A,C) -> D = k2_partfun1(A,B,D,C)))) # label(t40_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1724 $T # label(dt_k1_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1725 (all A all B all C (r2_hidden(C,k1_funct_2(A,B)) -> v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B))) # label(t121_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.94 1726 $T # label(t69_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1727 (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]. 21.77/22.95 1728 (all A all B -(r2_hidden(A,f1_s5_funct_2) & (all C -(p1_s5_funct_2(A,B,C) & r2_hidden(C,f3_s5_funct_2))) & r2_hidden(B,f2_s5_funct_2))) -> (exists A (v1_funct_1(A) & (all B all C (r2_hidden(B,f1_s5_funct_2) & r2_hidden(C,f2_s5_funct_2) -> p1_s5_funct_2(B,C,k1_funct_1(A,k4_tarski(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s5_funct_2,f2_s5_funct_2),f3_s5_funct_2))) # label(s5_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1729 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (k4_relset_1(A,B,C) = A -> v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B)))) # label(t130_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1730 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) -> (all C (m2_relset_1(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (r1_partfun1(B,C) -> r2_hidden(C,k5_partfun1(A,A,B))))))) # label(t156_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1731 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (k2_relat_1(B) = A & v2_funct_1(B) -> v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_1(B)))) # label(t83_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1732 $T # label(t111_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1733 $T # label(t71_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1734 (all A all B all C (v1_funct_2(C,k1_tarski(A),B) & m2_relset_1(C,k1_tarski(A),B) & v1_funct_1(C) -> (k1_xboole_0 != B -> k1_tarski(k1_funct_1(C,A)) = k2_relat_1(C)))) # label(t62_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1735 (all A -v1_xboole_0(k1_funct_2(A,A))) # label(fc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1736 $T # label(t102_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1737 (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 -> (k2_relat_1(C) = B <-> (all D (k1_xboole_0 != D -> (all E (m2_relset_1(E,B,D) & v1_funct_2(E,B,D) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> (k1_partfun1(A,B,B,D,C,E) = k1_partfun1(A,B,B,D,C,F) -> E = F))))))))))) # label(t22_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1738 (all A all B (v3_funct_2(B,A,A) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> (all C (v1_funct_2(C,A,A) & v3_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (k5_funct_2(A,B,C) = k6_partfun1(A) -> k6_funct_2(A,B) = C))))) # label(t87_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1739 $T # label(t105_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1740 (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(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & (all E B != k1_tarski(E)) -> r1_tarski(D,C)))))) # label(t167_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1741 (exists A ((all B (m1_subset_1(B,f1_s8_funct_2) -> (all C (m1_subset_1(C,f2_s8_funct_2) -> k1_funct_1(A,k4_tarski(B,C)) = f4_s8_funct_2(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_2(A,k2_zfmisc_1(f1_s8_funct_2,f2_s8_funct_2),f3_s8_funct_2) & v1_funct_1(A))) # label(s8_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1742 $T # label(t33_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1743 $T # label(t39_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1744 $T # label(t157_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1745 (all A all B all C all D (m2_relset_1(D,A,k1_tarski(B)) & v1_funct_2(D,A,k1_tarski(B)) & v1_funct_1(D) -> (r2_hidden(C,A) -> k1_funct_1(D,C) = B))) # label(t65_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1746 f4_s11_funct_2 != f3_s11_funct_2 -> (exists A (v1_funct_2(A,f1_s11_funct_2,f2_s11_funct_2) & f6_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f4_s11_funct_2) & (all B (m1_subset_1(B,f1_s11_funct_2) -> -(f7_s11_funct_2(B) != k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,B) & B != f4_s11_funct_2 & B != f3_s11_funct_2))) & f5_s11_funct_2 = k8_funct_2(f1_s11_funct_2,f2_s11_funct_2,A,f3_s11_funct_2) & m2_relset_1(A,f1_s11_funct_2,f2_s11_funct_2) & v1_funct_1(A))) # label(s11_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1747 $T # label(t58_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1748 $T # label(t97_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1749 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (r2_hidden(D,k5_partfun1(A,B,C)) -> v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B))))) # label(t158_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1750 (all A (r2_hidden(A,f1_s2_funct_2) -> r2_hidden(f3_s2_funct_2(A),f2_s2_funct_2))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,f1_s2_funct_2,f2_s2_funct_2) & (all B (r2_hidden(B,f1_s2_funct_2) -> f3_s2_funct_2(B) = k1_funct_1(A,B))) & m2_relset_1(A,f1_s2_funct_2,f2_s2_funct_2))) # label(s2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1751 $T # label(t129_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1752 (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]. 21.77/22.95 1753 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(D,C) -> r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D))))))) # label(t165_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1754 (all A all B all C all D all E (v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & m1_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) & v1_funct_1(D) & -v1_xboole_0(B) -> m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & v1_funct_1(k7_funct_2(A,B,C,D,E)))) # label(dt_k7_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1755 (all A all B all C (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) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> ((all E (r2_hidden(E,k4_relset_1(A,B,C)) -> k1_funct_1(D,E) = k1_funct_1(C,E))) <-> r1_partfun1(C,D))))))) # label(t145_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1756 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (k1_xboole_0 != B -> (all E (r2_hidden(E,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]. 21.77/22.95 1757 (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 != A & k1_xboole_0 != B & -((all D all E (v1_funct_1(E) & v1_funct_2(E,D,A) & m2_relset_1(E,D,A) -> (all F (m2_relset_1(F,D,A) & v1_funct_2(F,D,A) & v1_funct_1(F) -> (k1_partfun1(D,A,A,B,F,C) = k1_partfun1(D,A,A,B,E,C) -> F = E))))) <-> v2_funct_1(C))))) # label(t27_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1758 (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_1(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))))))))) # label(s7_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1759 (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 & (exists D (v1_funct_1(D) & v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & k6_partfun1(A) = k1_partfun1(A,B,B,A,C,D))) & -v2_funct_1(C)))) # label(t37_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1760 (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) & k4_relset_1(A,A,B) = A)) # label(t67_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1761 $T # label(t10_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1762 $T # label(t80_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1763 (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]. 21.77/22.95 1764 (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(C,A) & k1_funct_1(B,C) = k1_funct_1(B,D) & r2_hidden(D,A) -> D = C))))) # label(t77_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1765 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> (k6_partfun1(B) = k1_partfun1(B,A,A,B,D,C) -> k2_relat_1(C) = B))))) # label(t24_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1766 (all A all B exists C (v1_relat_1(C) & v1_funct_2(C,A,B) & v1_funct_1(C) & m1_relset_1(C,A,B))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1767 $T # label(t89_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1768 (all A all B all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v3_funct_2(C,A,B) & v1_funct_2(C,A,B) -> v1_funct_1(C) & v2_funct_1(C) & v2_funct_2(C,A,B) & v1_funct_2(C,A,B)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1769 (all A (m1_subset_1(A,f1_s3_funct_2) -> (exists B (m1_subset_1(B,f2_s3_funct_2) & p1_s3_funct_2(A,B))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s3_funct_2,f2_s3_funct_2) & (all B (m1_subset_1(B,f1_s3_funct_2) -> p1_s3_funct_2(B,k8_funct_2(f1_s3_funct_2,f2_s3_funct_2,A,B)))) & v1_funct_2(A,f1_s3_funct_2,f2_s3_funct_2))) # label(s3_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1770 $T # label(t72_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1771 $T # label(t126_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1772 $T # label(t150_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1773 (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]. 21.77/22.95 1774 (all A all B (v1_funct_2(B,A,A) & v3_funct_2(B,A,A) & m1_relset_1(B,A,A) & v1_funct_1(B) -> k2_funct_1(B) = k6_funct_2(A,B))) # label(redefinition_k6_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1775 $T # label(t106_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1776 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,B,A) & v1_funct_2(D,B,A) -> ((all E all F ((r2_hidden(F,A) & E = k1_funct_1(C,F) -> r2_hidden(E,B) & F = k1_funct_1(D,E)) & (F = k1_funct_1(D,E) & r2_hidden(E,B) -> r2_hidden(F,A) & k1_funct_1(C,F) = E))) & v2_funct_1(C) & B = k2_relat_1(C) -> k1_xboole_0 = B | k2_funct_1(C) = D | A = k1_xboole_0))))) # label(t34_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1777 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_2(A,k1_relat_1(A),k2_relat_1(A)) & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) & v1_funct_1(A))) # label(t3_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1778 (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 (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> -(r1_partfun1(D,E) & r1_partfun1(C,E)))) & r1_partfun1(C,D) & (B = k1_xboole_0 -> A = k1_xboole_0)))))) # label(t154_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1779 (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) & m2_relset_1(C,A,A) & v1_funct_2(C,A,A) -> (r1_partfun1(B,C) -> C = B))))) # label(t143_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1780 $T # label(t57_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1781 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(C,k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(C),B) & k1_relat_1(C) = A))) # label(t169_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1782 $T # label(t108_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1783 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (v2_funct_1(B) & k4_funct_2(A,C,B) = B -> k6_partfun1(A) = C))))) # label(t76_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1784 (all A all B all C all D all E all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) -> (r2_hidden(E,B) & r2_hidden(D,A) -> C = k1_xboole_0 | r2_hidden(k1_funct_1(F,k4_tarski(D,E)),C)))) # label(t119_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1785 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((all E (m1_subset_1(E,A) -> k1_funct_1(D,E) = k1_funct_1(C,E))) -> D = C))))) # label(t113_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1786 (all A all B all C all D (v1_funct_2(D,k1_tarski(A),B) & m2_relset_1(D,k1_tarski(A),B) & v1_funct_1(D) -> (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]. 21.77/22.95 1787 $T # label(t144_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1788 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s4_funct_2) -> f3_s4_funct_2(B) = k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B))) & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2) & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2))) # label(s4_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1789 $T # label(t122_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1790 (all A (r2_hidden(A,f1_s9_funct_2) -> (-p1_s9_funct_2(A) -> r2_hidden(f4_s9_funct_2(A),f2_s9_funct_2)) & (p1_s9_funct_2(A) -> r2_hidden(f3_s9_funct_2(A),f2_s9_funct_2)))) -> (exists A (v1_funct_1(A) & (all B (r2_hidden(B,f1_s9_funct_2) -> (-p1_s9_funct_2(B) -> f4_s9_funct_2(B) = k1_funct_1(A,B)) & (p1_s9_funct_2(B) -> f3_s9_funct_2(B) = k1_funct_1(A,B)))) & m2_relset_1(A,f1_s9_funct_2,f2_s9_funct_2) & v1_funct_2(A,f1_s9_funct_2,f2_s9_funct_2))) # label(s9_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1791 (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) -> r1_tarski(C,k3_funct_2(A,B,D,k2_funct_2(A,B,D,C))) | k1_xboole_0 != A & k1_xboole_0 = B))) # label(t50_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1792 (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(k2_relat_1(D),C) -> v1_funct_1(D) & v1_funct_2(D,A,C) & m2_relset_1(D,A,C) | k1_xboole_0 = B & A != k1_xboole_0))) # label(t8_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1793 $T # label(t81_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1794 $T # label(t78_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1795 (exists A (v1_funct_2(A,f1_s10_funct_2,f2_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)))) & f4_s10_funct_2 = k8_funct_2(f1_s10_funct_2,f2_s10_funct_2,A,f3_s10_funct_2) & m2_relset_1(A,f1_s10_funct_2,f2_s10_funct_2) & v1_funct_1(A))) # label(s10_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1796 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (v3_funct_2(C,A,B) <-> v2_funct_2(C,A,B) & v2_funct_1(C)))) # label(d4_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1797 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,B,C) & m2_relset_1(E,B,C) -> (-(k1_xboole_0 != A & C != k1_xboole_0 & k1_xboole_0 = B) -> v1_funct_2(k1_partfun1(A,B,B,C,D,E),A,C) & m2_relset_1(k1_partfun1(A,B,B,C,D,E),A,C) & v1_funct_1(k1_partfun1(A,B,B,C,D,E))))))) # label(t19_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1798 (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) -> (k2_relat_1(B) = A & B = k4_funct_2(A,B,C) -> C = k6_partfun1(A)))))) # label(t75_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1799 (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,B,A) & m2_relset_1(D,B,A) -> (k1_partfun1(A,B,B,A,C,D) = k6_partfun1(A) -> v2_funct_1(C) & A = k2_relat_1(D) | k1_xboole_0 = B))))) # label(t29_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1800 $T # label(t95_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1801 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> ((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> 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]. 21.77/22.95 1802 $T # label(t128_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1803 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (r2_hidden(C,A) -> B = k1_xboole_0 | r2_hidden(k1_funct_1(D,C),k2_relat_1(D))))) # label(t6_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1804 $T # label(t90_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1805 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,C) & v1_funct_2(E,B,C) -> (B = k2_relat_1(D) & v2_funct_1(k1_partfun1(A,B,B,C,D,E)) -> v2_funct_1(E) & v2_funct_1(D) | B != k1_xboole_0 & k1_xboole_0 = C))))) # label(t30_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1806 (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_2(D,A,B) & v1_funct_1(D) -> -r1_partfun1(C,D))) & (k1_xboole_0 = B -> A = k1_xboole_0)))) # label(t148_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1807 (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 (r2_hidden(E,A) -> k1_funct_1(C,E) = k1_funct_1(D,E))) -> C = D))))) # label(t18_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1808 $T # label(t52_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1809 $T # label(t112_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1810 $T # label(t93_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1811 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(C,D),B))) & k1_relat_1(C) = A -> m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C)))) # label(t5_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1812 $T # label(t140_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1813 (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) -> (k5_partfun1(A,B,D) = k5_partfun1(A,B,C) & (all E k1_tarski(E) != B) -> D = C))))) # label(t168_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1814 (all A all B (m2_relset_1(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B) -> A = k3_funct_2(A,A,B,k2_funct_2(A,A,B,A)))) # label(t82_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1815 (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]. 21.77/22.95 1816 (all A all B all C (v1_funct_2(C,k1_xboole_0,A) & m2_relset_1(C,k1_xboole_0,A) & v1_funct_1(C) -> k1_xboole_0 = k2_funct_2(k1_xboole_0,A,C,B))) # label(t59_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1817 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> ((all D -((all E -(r2_hidden(E,A) & k1_funct_1(C,E) = D)) & r2_hidden(D,B))) -> B = k2_relat_1(C) | B = k1_xboole_0))) # label(t16_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1818 $T # label(t96_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1819 (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 (k1_funct_1(B,C) = k1_funct_1(B,D) & r2_hidden(D,A) & r2_hidden(C,A) -> C = D))))) # label(t85_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1820 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (v1_funct_1(C) & m2_relset_1(C,A,B) & v1_funct_2(C,A,B) -> k1_xboole_0 != A & k1_xboole_0 = B | v1_partfun1(C,A,B)))) # label(t132_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1821 (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) <-> (all D (r2_hidden(D,k4_relset_1(A,A,B)) -> k1_funct_1(C,D) = k1_funct_1(B,D)))))))) # label(t146_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1822 (all A all B all C (v1_funct_1(B) & v1_funct_2(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) & m1_relset_1(B,A,A) & v3_funct_2(B,A,A) -> k5_relat_1(B,C) = k5_funct_2(A,B,C))) # label(redefinition_k5_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1823 (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) -> (v2_funct_1(E) & k2_relat_1(k1_partfun1(A,B,B,C,D,E)) = C -> k2_relat_1(D) = B | k1_xboole_0 = C))))) # label(t28_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1824 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((all D -(k1_xboole_0 = k3_funct_2(A,B,C,k1_tarski(D)) & r2_hidden(D,B))) <-> B = k2_relat_1(C)))) # label(t49_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1825 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_1(D) -> (r1_tarski(k4_relset_1(A,B,D),k4_relset_1(A,B,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) -> r1_tarski(D,C)))))) # label(t166_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1826 (all A all B all C all D all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,B,C) & v1_funct_2(F,B,C) & v1_funct_1(F) -> -(-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 -> A = k1_xboole_0) & (C = k1_xboole_0 -> k1_xboole_0 = B)))))) # label(t53_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1827 (all A all B all C all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> -(B = k2_relat_1(D) & (all E -(r2_hidden(E,A) & k1_funct_1(D,E) = C)) & r2_hidden(C,B)))) # label(t17_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1828 (all A -(r2_hidden(A,f1_s1_funct_2) & (all B -(p1_s1_funct_2(A,B) & r2_hidden(B,f2_s1_funct_2))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,f1_s1_funct_2,f2_s1_funct_2) & (all B (r2_hidden(B,f1_s1_funct_2) -> p1_s1_funct_2(B,k1_funct_1(A,B)))) & v1_funct_2(A,f1_s1_funct_2,f2_s1_funct_2))) # label(s1_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1829 $T # label(t103_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1830 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> (v2_funct_2(C,A,B) <-> k2_relat_1(C) = B))) # label(d3_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1831 $T # label(t101_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1832 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E -((all F -(r2_hidden(F,C) & k1_funct_1(D,F) = E & r2_hidden(F,A))) & r2_hidden(E,k2_funct_2(A,B,D,C)))))) # label(t115_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1833 $T # label(t98_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1834 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> r1_tarski(k9_relat_1(D,C),B))) # label(t44_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1835 (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 (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (r1_partfun1(D,E) & r1_partfun1(C,E) -> B = k1_xboole_0 & A != k1_xboole_0 | r1_partfun1(C,D)))))))) # label(t151_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1836 (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]. 21.77/22.95 1837 $T # label(t99_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1838 (all A all B all C (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(B) -> v1_funct_1(k4_funct_2(A,B,C)) & v1_funct_2(k4_funct_2(A,B,C),A,A) & m2_relset_1(k4_funct_2(A,B,C),A,A))) # label(dt_k4_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1839 $T # label(t84_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1840 $T # label(t124_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1841 (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_relat_1(E) & v1_funct_1(E) -> (r2_hidden(C,A) -> B = k1_xboole_0 | k1_funct_1(E,k1_funct_1(D,C)) = k1_funct_1(k5_relat_1(D,E),C)))))) # label(t21_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1842 (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]. 21.77/22.95 1843 (all A all B all C (v1_funct_1(C) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (r1_partfun1(C,D) -> r2_hidden(D,k5_partfun1(A,B,C)) | B = k1_xboole_0 & k1_xboole_0 != A))))) # label(t155_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1844 $T # label(t163_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1845 $T # label(t137_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1846 (all A all B all C (m2_relset_1(C,A,k1_tarski(B)) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,k1_tarski(B)) & m2_relset_1(D,A,k1_tarski(B)) & v1_funct_1(D) -> k1_tarski(D) = k5_partfun1(A,k1_tarski(B),C))))) # label(t164_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1847 (all A all B all C (m2_relset_1(C,A,B) -> ((k1_xboole_0 = B -> k1_xboole_0 = A) -> (v1_funct_2(C,A,B) <-> A = k4_relset_1(A,B,C))) & (B = k1_xboole_0 -> k1_xboole_0 = A | (C = k1_xboole_0 <-> v1_funct_2(C,A,B))))) # label(d1_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1848 (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) -> -(E = k1_funct_1(D,F) & r2_hidden(F,C)))))))) # label(t116_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1849 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> ((B = k1_xboole_0 -> A = k1_xboole_0) -> A = k3_funct_2(A,B,C,k2_funct_2(A,B,C,A))))) # label(t51_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1850 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,A) & m2_relset_1(B,A,A) -> k2_relat_1(B) = k2_funct_2(A,A,B,A))) # label(t79_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1851 $T # label(t125_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1852 $T # label(t110_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1853 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) -> k5_funct_2(A,k6_funct_2(A,B),B) = k6_partfun1(A) & k6_partfun1(A) = k5_funct_2(A,B,k6_funct_2(A,B)))) # label(t88_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1854 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_1(C) -> k10_relat_1(C,D) = k3_funct_2(A,B,C,D))) # label(redefinition_k3_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1855 $T # label(t54_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1856 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> (all C (m1_relset_1(C,A,B) -> (v1_funct_1(C) & v1_funct_2(C,A,B) -> v1_partfun1(C,A,B) & v1_funct_2(C,A,B) & -v1_xboole_0(C) & v1_funct_1(C)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1857 (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]. 21.77/22.95 1858 (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 (m2_relset_1(C,A,A) & v3_funct_2(C,A,A) & v1_funct_2(C,A,A) & v1_funct_1(C) -> (C = k5_funct_2(A,B,C) -> k6_partfun1(A) = B))))) # label(t86_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1859 (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]. 21.77/22.95 1860 $T # label(t153_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1861 $T # label(t114_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1862 (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) & m2_relset_1(A,f1_s13_funct_2,f2_s13_funct_2) & (all B (m1_subset_1(B,f1_s13_funct_2) -> k8_funct_2(f1_s13_funct_2,f2_s13_funct_2,A,B) = f3_s13_funct_2(B))))) # label(s13_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1863 (all A all B all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (r1_partfun1(C,D) -> D = C | k1_xboole_0 != A & k1_xboole_0 = B))))) # label(t142_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1864 (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) -> (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) | B = k1_xboole_0))) # label(t41_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1865 (all A all B all C all D (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)))) # label(dt_k2_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1866 (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) -> k2_relat_1(C) = k2_funct_2(A,B,C,A)))) # label(t45_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1867 $T # label(t42_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1868 (all A all B (m1_relset_1(B,A,A) -> (v1_relat_2(B) & v1_funct_2(B,A,A) & v1_partfun1(B,A,A) & v1_funct_1(B) -> v2_funct_1(B) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) & v1_funct_2(B,A,A) & v1_funct_1(B)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1869 (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(C,A) -> B = k1_xboole_0 & k1_xboole_0 != 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))))) # label(t38_funct_2) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1870 (all A all B (k1_xboole_0 != A -> B = k2_relat_1(k8_funct_3(A,B)))) # label(t62_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1871 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funct_3(A)) & v1_funct_1(k1_funct_3(A)))) # label(dt_k1_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1872 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k7_funct_3(A,B) = C <-> k1_relat_1(C) = k2_zfmisc_1(A,B) & (all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> D = k1_funct_1(C,k4_tarski(D,E))))))) # label(d5_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.95 1873 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k3_xboole_0(k10_relat_1(C,A),k10_relat_1(D,B)) = k10_relat_1(k13_funct_3(C,D),k2_zfmisc_1(A,B)))))))) # label(t77_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1874 (all A all B (v1_relat_1(k8_funct_3(A,B)) & v1_funct_1(k8_funct_3(A,B)))) # label(dt_k8_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1875 $T # label(t41_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1876 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)) = k2_relat_1(k15_funct_3(A,B)))))) # label(t88_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1877 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k6_relat_1(B) = k6_funct_3(A,B))) # label(redefinition_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1878 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> -((C = k1_xboole_0 -> k1_xboole_0 = A) & -(E = k5_relat_1(k13_funct_3(D,E),k10_funct_3(B,C)) & k5_relat_1(k13_funct_3(D,E),k9_funct_3(B,C)) = D) & (k1_xboole_0 = B -> A = k1_xboole_0)))))) # label(t81_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1879 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k2_relat_1(k5_relat_1(B,C))) & v2_funct_1(C) -> r1_tarski(k10_relat_1(C,A),k2_relat_1(B))))))) # label(t4_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1880 $T # label(t23_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1881 (all A all B all C all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> k13_funct_3(D,E) = k5_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)))))) # label(t99_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1882 (all A all B k5_funct_3(A,B) = k4_funct_3(A,B)) # label(redefinition_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1883 $T # label(t52_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1884 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -((B = k1_xboole_0 -> A = k1_xboole_0) & -(v1_funct_1(k13_funct_3(D,E)) & v1_funct_2(k13_funct_3(D,E),A,k2_zfmisc_1(B,C)) & m2_relset_1(k13_funct_3(D,E),A,k2_zfmisc_1(B,C))) & (C = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t78_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1885 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) -> k3_tarski(k9_relat_1(k1_funct_3(B),A)) = k9_relat_1(B,k3_tarski(A))))) # label(t16_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1886 (all A (v1_funct_1(A) & v1_relat_1(A) -> m2_relset_1(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_2(k3_funct_3(A),k1_zfmisc_1(k2_relat_1(A)),k1_zfmisc_1(k1_relat_1(A))) & v1_funct_1(k3_funct_3(A)))) # label(t39_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1887 (all A all B (v1_relat_1(k7_funct_3(A,B)) & v1_funct_1(k7_funct_3(A,B)))) # label(dt_k7_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1888 $T # label(t64_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1889 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (B = k11_funct_3(A) <-> (all C (r2_hidden(C,A) -> k4_tarski(C,C) = k1_funct_1(B,C))) & k1_relat_1(B) = A))) # label(d7_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1890 $T # label(t46_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1891 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k1_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t15_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1892 (all A all B all C all D all E all F (v1_funct_2(E,A,C) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) & v1_funct_1(F) & m1_relset_1(E,A,C) & v1_funct_1(E) -> v1_funct_1(k16_funct_3(A,B,C,D,E,F)) & m2_relset_1(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k16_funct_3(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)))) # label(dt_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1893 (all A all B all C all D (p1_s1_funct_3(A,B,D) & p1_s1_funct_3(A,B,C) & r2_hidden(B,f2_s1_funct_3) & r2_hidden(A,f1_s1_funct_3) -> C = D)) & (all A all B -(r2_hidden(B,f2_s1_funct_3) & (all C -p1_s1_funct_3(A,B,C)) & r2_hidden(A,f1_s1_funct_3))) -> (exists A (v1_relat_1(A) & v1_funct_1(A) & k1_relat_1(A) = k2_zfmisc_1(f1_s1_funct_3,f2_s1_funct_3) & (all B all C (r2_hidden(B,f1_s1_funct_3) & r2_hidden(C,f2_s1_funct_3) -> p1_s1_funct_3(B,C,k1_funct_1(A,k4_tarski(B,C))))))) # label(s1_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1894 (all A r1_tarski(k2_relat_1(k11_funct_3(A)),k2_zfmisc_1(A,A))) # label(t66_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1895 (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) -> (C = k13_funct_3(A,B) <-> k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D)))))))))) # label(d8_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1896 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k10_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t28_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1897 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k10_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t13_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1898 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (v2_funct_1(B) -> k3_funct_3(k5_relat_1(A,B)) = k5_relat_1(k3_funct_3(B),k3_funct_3(A))))))) # label(t38_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1899 (all A all B (v1_funct_1(k4_funct_3(A,B)) & v1_relat_1(k4_funct_3(A,B)))) # label(dt_k4_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1900 (all A all B r1_tarski(k2_relat_1(k7_funct_3(A,B)),A)) # label(t59_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1901 (all A all B (v1_funct_2(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & m2_relset_1(k9_funct_3(A,B),k2_zfmisc_1(A,B),A) & v1_funct_1(k9_funct_3(A,B)))) # label(dt_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1902 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,C) & m2_relset_1(F,A,C) -> (all G (v1_funct_1(G) & v1_funct_2(G,A,C) & m2_relset_1(G,A,C) -> (k14_funct_3(A,B,C,E,G) = k14_funct_3(A,B,C,D,F) -> F = G & D = E))))))))))))) # label(t84_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1903 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_2(E,A,C) & m2_relset_1(E,A,C) & v1_funct_1(E) -> r1_tarski(k2_relat_1(k13_funct_3(D,E)),k2_zfmisc_1(B,C)))))) # label(t80_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1904 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k1_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t18_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1905 (all A all B all C (r2_hidden(A,k4_xboole_0(B,C)) -> k1_funct_1(k4_funct_3(C,B),A) = np__0)) # label(t43_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1906 (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) -> (k15_funct_3(A,B) = C <-> (all D all E (r2_hidden(D,k1_relat_1(A)) & r2_hidden(E,k1_relat_1(B)) -> k1_funct_1(C,k4_tarski(D,E)) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,E)))) & k1_relat_1(C) = k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))))))))) # label(d9_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1907 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k10_relat_1(k3_funct_3(B),A)),k9_relat_1(B,k3_tarski(A))))) # label(t31_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1908 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> (all F (m1_subset_1(F,A) -> k8_funct_2(A,k2_zfmisc_1(B,C),k14_funct_3(A,B,C,D,E),F) = k4_tarski(k8_funct_2(A,B,D,F),k8_funct_2(A,C,E,F)))))))))))))) # label(t79_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1909 (all A all B (v1_funct_2(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & m2_relset_1(k10_funct_3(A,B),k2_zfmisc_1(A,B),B) & v1_funct_1(k10_funct_3(A,B)))) # label(dt_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1910 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) -> r1_tarski(k10_relat_1(k3_funct_3(A),B),k9_relat_1(k1_funct_3(A),B)))))) # label(t35_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1911 (all A all B (m2_relset_1(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(np__0,np__1)) & v1_funct_1(k5_funct_3(A,B)))) # label(dt_k5_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1912 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k5_relat_1(k1_funct_3(A),k1_funct_3(B)) = k1_funct_3(k5_relat_1(A,B)))))) # label(t20_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1913 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_funct_1(k6_funct_3(A,B)) & v1_funct_2(k6_funct_3(A,B),B,A) & m2_relset_1(k6_funct_3(A,B),B,A))) # label(dt_k6_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1914 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> r1_tarski(k9_relat_1(k13_funct_3(B,C),A),k2_zfmisc_1(k9_relat_1(B,A),k9_relat_1(C,A))))))) # label(t76_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1915 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k15_funct_3(A,B)) & v1_relat_1(k15_funct_3(A,B)))) # label(dt_k15_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1916 $T # label(t65_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1917 $T # label(t58_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1918 (all A all B r1_tarski(k2_relat_1(k8_funct_3(A,B)),B)) # label(t61_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1919 (all A all B k7_funct_3(A,B) = k9_funct_3(A,B)) # label(redefinition_k9_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1920 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k10_relat_1(B,k3_tarski(A)) = k3_tarski(k9_relat_1(k3_funct_3(B),A))))) # label(t30_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1921 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k1_funct_3(B),A),k1_zfmisc_1(k2_relat_1(B))))) # label(t12_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1922 (all A all B all C all D all E (-v1_xboole_0(B) & -v1_xboole_0(C) & m1_relset_1(D,A,B) & m1_relset_1(E,A,C) & v1_funct_2(E,A,C) & v1_funct_1(E) & v1_funct_2(D,A,B) & v1_funct_1(D) -> m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & v1_funct_1(k14_funct_3(A,B,C,D,E)))) # label(dt_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1923 (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) -> v1_funct_1(k1_funct_3(C)) & m2_relset_1(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_2(k1_funct_3(C),k1_zfmisc_1(A),k1_zfmisc_1(B))))) # label(t22_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1924 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> ((all D (r2_hidden(D,B) -> (-r2_hidden(D,A) -> np__0 = k1_funct_1(C,D)) & (r2_hidden(D,A) -> k1_funct_1(C,D) = np__1))) & k1_relat_1(C) = B <-> k4_funct_3(A,B) = C))) # label(d3_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1925 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k13_funct_3(D,C) = k13_funct_3(A,B) & k1_relat_1(D) = k1_relat_1(C) & k1_relat_1(B) = k1_relat_1(A) -> C = B & A = D))))))))) # label(t74_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1926 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k3_funct_3(A)) & v1_relat_1(k3_funct_3(A)))) # label(dt_k3_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1927 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B all C (r2_hidden(C,f2_s2_funct_3) & r2_hidden(B,f1_s2_funct_3) -> k1_funct_1(A,k4_tarski(B,C)) = f3_s2_funct_3(B,C))) & k2_zfmisc_1(f1_s2_funct_3,f2_s2_funct_3) = k1_relat_1(A))) # label(s2_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1928 (all A all B all C all D all E (v1_funct_2(E,A,C) & m1_relset_1(E,A,C) & v1_funct_1(E) & m1_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) & -v1_xboole_0(C) & -v1_xboole_0(B) -> k14_funct_3(A,B,C,D,E) = k13_funct_3(D,E))) # label(redefinition_k14_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1929 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k15_funct_3(A,B) = k13_funct_3(k5_relat_1(k9_funct_3(k1_relat_1(A),k1_relat_1(B)),A),k5_relat_1(k10_funct_3(k1_relat_1(A),k1_relat_1(B)),B)))))) # label(t87_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1930 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v2_funct_1(A) -> r1_tarski(k9_relat_1(k1_funct_3(A),B),k10_relat_1(k3_funct_3(A),B)))))) # label(t36_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1931 (all A all B all C all D all E all F (m1_relset_1(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & v1_funct_2(E,A,C) & v1_funct_1(E) -> k15_funct_3(E,F) = k16_funct_3(A,B,C,D,E,F))) # label(redefinition_k16_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1932 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k13_funct_3(A,B)),k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B))))))) # label(t71_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1933 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> k7_relat_1(k6_relat_1(A),B) = k6_funct_3(A,B))) # label(t53_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1934 (all A all B all C (r1_tarski(A,B) & k4_funct_3(A,B) = k4_funct_3(C,B) & r1_tarski(C,B) -> C = A)) # label(t47_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1935 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k13_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)) = k5_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)))))))))) # label(t91_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1936 $T # label(t85_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1937 $T # label(t7_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1938 $T # label(t45_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1939 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k10_relat_1(k1_funct_3(B),A)))) # label(t33_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1940 (all A k12_funct_3(A) = k11_funct_3(A)) # label(redefinition_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1941 (all A all B all C (k1_funct_1(k4_funct_3(B,C),A) = np__1 -> r2_hidden(A,B))) # label(t42_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1942 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (v2_funct_1(B) -> k9_relat_1(k3_funct_3(B),A) = k10_relat_1(k1_funct_3(B),A)))) # label(t34_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1943 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k3_xboole_0(k1_relat_1(B),k1_relat_1(C))) -> k1_funct_1(k13_funct_3(B,C),A) = k4_tarski(k1_funct_1(B,A),k1_funct_1(C,A))))))) # label(t68_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1944 (all A all B r1_tarski(k2_relat_1(k4_funct_3(A,B)),k2_tarski(np__0,np__1))) # label(t48_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1945 $T # label(t51_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1946 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_xboole_0 = k1_funct_1(k1_funct_3(A),k1_xboole_0))) # label(t9_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1947 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) -> r1_tarski(k10_relat_1(k1_funct_3(D),B),k1_zfmisc_1(A)))))) # label(t14_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1948 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_relat_1(A) = k2_funct_2(k2_zfmisc_1(k1_relat_1(A),k2_relat_1(A)),k1_relat_1(A),k9_funct_3(k1_relat_1(A),k2_relat_1(A)),A))) # label(t100_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1949 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k1_relat_1(k5_relat_1(B,C))) -> r1_tarski(k9_relat_1(B,A),k1_relat_1(C))))))) # label(t2_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1950 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k3_tarski(k9_relat_1(k3_funct_3(B),A)),k10_relat_1(B,k3_tarski(A))))) # label(t29_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1951 $T # label(d4_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1952 (all A all B all C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> k2_funct_3(A,B,C) = k1_funct_3(C))) # label(redefinition_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1953 (all A all B all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> (all F (m2_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) -> k16_funct_3(A,B,C,D,E,F) = k13_funct_3(k5_relat_1(k9_funct_3(A,B),E),k5_relat_1(k10_funct_3(A,B),F)))))))))) # label(t98_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1954 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_zfmisc_1(k1_relat_1(B))) & v2_funct_1(B) -> k9_relat_1(B,k3_tarski(A)) = k3_tarski(k10_relat_1(k3_funct_3(B),A))))) # label(t32_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1955 (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) & v1_funct_2(F,C,D) & m2_relset_1(F,C,D) -> v1_funct_1(k15_funct_3(E,F)) & v1_funct_2(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) & m2_relset_1(k15_funct_3(E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))) # label(t95_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1956 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_tarski(A,k1_zfmisc_1(k2_relat_1(B))) -> k3_tarski(k10_relat_1(k1_funct_3(B),A)) = k10_relat_1(B,k3_tarski(A))))) # label(t19_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1957 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k10_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)) = k2_zfmisc_1(k10_relat_1(C,A),k10_relat_1(D,B)))))) # label(t94_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1958 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k3_funct_3(A)),k1_zfmisc_1(k1_relat_1(A))))) # label(t25_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1959 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (r1_tarski(B,k1_zfmisc_1(k1_relat_1(A))) & v2_funct_1(A) -> k9_relat_1(k1_funct_3(A),B) = k10_relat_1(k3_funct_3(A),B))))) # label(t37_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1960 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_funct_3(A)) & m2_relset_1(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))) & v1_funct_2(k1_funct_3(A),k1_zfmisc_1(k1_relat_1(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t21_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1961 (all A all B k6_relat_1(k2_zfmisc_1(A,B)) = k15_funct_3(k6_relat_1(A),k6_relat_1(B))) # label(t90_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1962 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k10_relat_1(C,A),k2_relat_1(B)) & r1_tarski(A,k2_relat_1(C)) -> r1_tarski(A,k2_relat_1(k5_relat_1(B,C)))))))) # label(t5_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1963 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & k1_relat_1(B) = A -> k13_funct_3(B,C) = k5_relat_1(k12_funct_3(A),k15_funct_3(B,C))))))) # label(t89_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1964 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(D),B) & r1_tarski(k2_relat_1(C),A) & k1_relat_1(C) = k1_relat_1(D) -> C = k5_relat_1(k13_funct_3(C,D),k9_funct_3(A,B)) & D = k5_relat_1(k13_funct_3(C,D),k10_funct_3(A,B))))))) # label(t72_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1965 (all A (v1_funct_1(k11_funct_3(A)) & v1_relat_1(k11_funct_3(A)))) # label(dt_k11_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1966 $T # label(t11_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1967 (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,A,B) & v1_funct_2(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,A,C) & m2_relset_1(F,A,C) -> (all G (v1_funct_1(G) & m2_relset_1(G,A,C) & v1_funct_2(G,A,C) -> (k13_funct_3(D,F) = k13_funct_3(E,G) -> k1_xboole_0 != A & k1_xboole_0 = C | G = F & E = D | k1_xboole_0 = B & k1_xboole_0 != A))))))))) # label(t83_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1968 $T # label(t55_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1969 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_funct_3(A) = B <-> k1_zfmisc_1(k1_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k1_relat_1(A)) -> k9_relat_1(A,C) = k1_funct_1(B,C)))))))) # label(d1_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1970 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k5_relat_1(k15_funct_3(B,D),k15_funct_3(A,C)) = k15_funct_3(k5_relat_1(B,A),k5_relat_1(D,C)))))))))) # label(t92_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1971 $T # label(t63_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1972 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> ((all D all E (r2_hidden(D,A) & r2_hidden(E,B) -> E = k1_funct_1(C,k4_tarski(D,E)))) & k2_zfmisc_1(A,B) = k1_relat_1(C) <-> k8_funct_3(A,B) = C))) # label(d6_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1973 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k2_relat_1(k1_funct_3(A)),k1_zfmisc_1(k2_relat_1(A))))) # label(t10_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1974 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_funct_1(k13_funct_3(A,B)) & v1_relat_1(k13_funct_3(A,B)))) # label(dt_k13_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1975 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(A,C) -> r2_hidden(k1_funct_1(k6_funct_3(B,C),A),B)))) # label(t56_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1976 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k1_funct_3(B))) -> k1_funct_1(k1_funct_3(B),A) = k9_relat_1(B,A)))) # label(t8_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1977 (all A all B k10_funct_3(A,B) = k8_funct_3(A,B)) # label(redefinition_k10_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1978 (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) -> k5_relat_1(C,k13_funct_3(A,B)) = k13_funct_3(k5_relat_1(C,A),k5_relat_1(C,B)))))))) # label(t75_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1979 (all A (v1_funct_1(k12_funct_3(A)) & v1_funct_2(k12_funct_3(A),A,k2_zfmisc_1(A,A)) & m2_relset_1(k12_funct_3(A),A,k2_zfmisc_1(A,A)))) # label(dt_k12_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1980 (all A all B all C (m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) & -v1_xboole_0(B) -> v1_funct_2(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & m2_relset_1(k2_funct_3(A,B,C),k1_zfmisc_1(A),k1_zfmisc_1(B)) & v1_funct_1(k2_funct_3(A,B,C)))) # label(dt_k2_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1981 (all A all B (v1_funct_1(B) & v1_funct_2(B,A,k2_tarski(np__0,np__1)) & m2_relset_1(B,A,k2_tarski(np__0,np__1)) -> B = k4_funct_3(k3_funct_2(A,k2_tarski(np__0,np__1),B,k1_tarski(np__1)),A))) # label(t49_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1982 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> (all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,C) -> k4_tarski(k8_funct_2(A,B,E,G),k8_funct_2(C,D,F,H)) = k1_funct_1(k16_funct_3(A,C,B,D,E,F),k4_tarski(G,H)))))))))))))))))) # label(t96_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1983 (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,C,D) & v1_funct_2(F,C,D) -> -(k13_funct_3(k5_relat_1(k9_funct_3(A,C),E),k5_relat_1(k10_funct_3(A,C),F)) != k16_funct_3(A,C,B,D,E,F) & (D = k1_xboole_0 -> C = k1_xboole_0) & (B = k1_xboole_0 -> k1_xboole_0 = A)))))) # label(t97_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1984 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> k9_relat_1(k15_funct_3(C,D),k2_zfmisc_1(A,B)) = k2_zfmisc_1(k9_relat_1(C,A),k9_relat_1(D,B)))))) # label(t93_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1985 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) & (all E all F (r2_hidden(F,B) & r2_hidden(E,A) -> k1_funct_1(D,k4_tarski(E,F)) = k1_funct_1(C,k4_tarski(E,F)))) & k2_zfmisc_1(A,B) = k1_relat_1(D) -> C = D))))) # label(t6_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1986 $T # label(t67_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1987 (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(k4_tarski(C,D),k2_zfmisc_1(k1_relat_1(A),k1_relat_1(B))) -> k4_tarski(k1_funct_1(A,C),k1_funct_1(B,D)) = k1_funct_1(k15_funct_3(A,B),k4_tarski(C,D)))))))) # label(t86_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1988 $T # label(t26_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1989 (all A all B (k1_xboole_0 != A -> B = k2_relat_1(k7_funct_3(B,A)))) # label(t60_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1990 (all A all B k13_funct_3(k9_funct_3(A,B),k10_funct_3(A,B)) = k6_relat_1(k2_zfmisc_1(A,B))) # label(t73_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1991 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,A,C) & v1_funct_2(E,A,C) -> D = k7_funct_2(A,k2_zfmisc_1(B,C),B,k14_funct_3(A,B,C,D,E),k9_funct_3(B,C)) & E = k7_funct_2(A,k2_zfmisc_1(B,C),C,k14_funct_3(A,B,C,D,E),k10_funct_3(B,C)))))))))) # label(t82_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1992 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k9_relat_1(k3_funct_3(B),A),k1_zfmisc_1(k1_relat_1(B))))) # label(t27_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1993 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_3(B))) -> k1_funct_1(k3_funct_3(B),A) = k10_relat_1(B,A)))) # label(t24_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1994 $T # label(t40_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1995 (all A all B all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,C) & v1_funct_2(D,A,C) -> (r1_tarski(B,k1_zfmisc_1(A)) -> k2_funct_2(A,C,D,k3_tarski(B)) = k3_tarski(k9_relat_1(k1_funct_3(D),B))))))) # label(t17_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1996 $T # label(t44_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1997 (all A all B (r1_tarski(A,B) -> k6_relat_1(A) = k7_relat_1(k6_relat_1(B),A))) # label(t1_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1998 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = A & A = k1_relat_1(B) -> A = k1_relat_1(k13_funct_3(B,C))))))) # label(t70_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 1999 $T # label(t50_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2000 $T # label(t57_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2001 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_zfmisc_1(k2_relat_1(A)) = k1_relat_1(B) & (all C (r1_tarski(C,k2_relat_1(A)) -> k10_relat_1(A,C) = k1_funct_1(B,C))) <-> B = k3_funct_3(A)))))) # label(d2_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2002 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(C) = B & r2_hidden(A,B) & k1_relat_1(D) = B -> k1_funct_1(k13_funct_3(C,D),A) = k4_tarski(k1_funct_1(C,A),k1_funct_1(D,A))))))) # label(t69_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2003 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(A,k1_relat_1(B)) & r1_tarski(k9_relat_1(B,A),k1_relat_1(C)) -> r1_tarski(A,k1_relat_1(k5_relat_1(B,C)))))))) # label(t3_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2004 $T # label(t54_funct_3) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2005 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r3_binop_1(A,C,B) <-> r2_binop_1(A,C,B))))))) # label(t15_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2006 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> m1_subset_1(k3_binop_1(A,B),A))) # label(dt_k3_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2007 $T # label(t22_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2008 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C) & k1_binop_1(B,C,D) = D)) <-> r3_binop_1(A,C,B)))))) # label(t11_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2009 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r6_binop_1(A,B,C) <-> r5_binop_1(A,B,C) & r4_binop_1(A,B,C)))))) # label(d11_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2010 (all A all B (m1_subset_1(B,A) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(C,D,B))) <-> r2_binop_1(A,B,C)))))) # label(d6_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2011 $T # label(t9_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2012 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)))))))) <-> r4_binop_1(A,B,C)))))) # label(d9_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2013 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r3_binop_1(A,C,B) & r3_binop_1(A,D,B) -> C = D))))))) # label(t18_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2014 (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) -> (v1_binop_1(C,A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,D,k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),k2_binop_1(A,A,A,C,D,F)))))))) <-> r6_binop_1(A,C,B))))))))) # label(t24_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2015 $T # label(t6_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2016 $T # label(t8_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2017 (all A (m1_relset_1(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) -> (v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v1_funct_1(A) -> v1_funct_1(A) & v1_xboole_0(A) & v1_funct_2(A,k2_zfmisc_1(k1_xboole_0,k1_xboole_0),k1_xboole_0) & v2_binop_1(A,k1_xboole_0) & v1_binop_1(A,k1_xboole_0)))) # label(cc1_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2018 (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) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,B,C,D),E) = k2_binop_1(A,A,A,B,C,k2_binop_1(A,A,A,B,D,E))))))))))))) # label(d14_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2019 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r5_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F)) = k1_binop_1(B,k1_binop_1(C,D,E),F)))))))))))) # label(d10_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2020 $T # label(dt_k1_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2021 $T # label(t4_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2022 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (r2_binop_1(A,D,B) & r1_binop_1(A,C,B) -> D = C))))))) # label(t17_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2023 $T # label(t5_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2024 $T # label(t7_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2025 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> ((exists C (m1_subset_1(C,A) & r3_binop_1(A,C,B))) -> (all C (m1_subset_1(C,A) -> (r3_binop_1(A,C,B) <-> k3_binop_1(A,B) = C)))))) # label(d8_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2026 (exists A ((all B (m1_subset_1(B,f1_s2_binop_1) -> (all C (m1_subset_1(C,f1_s2_binop_1) -> k2_binop_1(f1_s2_binop_1,f1_s2_binop_1,f1_s2_binop_1,A,B,C) = f2_s2_binop_1(B,C))))) & m2_relset_1(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & v1_funct_2(A,k2_zfmisc_1(f1_s2_binop_1,f1_s2_binop_1),f1_s2_binop_1) & v1_funct_1(A))) # label(s2_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2027 $T # label(t10_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2028 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> k1_binop_1(C,B,D) = D)) <-> r1_binop_1(A,B,C)))))) # label(d5_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2029 $T # label(t20_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.96 2030 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r1_binop_1(A,C,B) <-> r3_binop_1(A,C,B))))))) # label(t14_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2031 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r6_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k1_binop_1(C,k1_binop_1(B,D,E),k1_binop_1(B,D,F)) = k1_binop_1(B,D,k1_binop_1(C,E,F)) & k1_binop_1(B,k1_binop_1(C,D,E),F) = k1_binop_1(C,k1_binop_1(B,D,F),k1_binop_1(B,E,F))))))))))))) # label(t23_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2032 (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 (m1_subset_1(D,A) -> k2_binop_1(A,A,A,B,D,C) = k2_binop_1(A,A,A,B,C,D))))) <-> v1_binop_1(B,A)))))) # label(d13_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2033 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v2_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(B,C,k1_binop_1(B,D,E)) = k1_binop_1(B,k1_binop_1(B,C,D),E)))))))))) # label(d3_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2034 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r2_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> D = k2_binop_1(A,A,A,C,D,B)))))))))) # label(d17_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2035 (all A (m1_subset_1(A,f1_s1_binop_1) -> (all B (m1_subset_1(B,f1_s1_binop_1) -> (exists C (p1_s1_binop_1(A,B,C) & m1_subset_1(C,f1_s1_binop_1))))))) -> (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s1_binop_1) -> (all C (m1_subset_1(C,f1_s1_binop_1) -> p1_s1_binop_1(B,C,k2_binop_1(f1_s1_binop_1,f1_s1_binop_1,f1_s1_binop_1,A,B,C)))))) & m2_relset_1(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1) & v1_funct_2(A,k2_zfmisc_1(f1_s1_binop_1,f1_s1_binop_1),f1_s1_binop_1))) # label(s1_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2036 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (r1_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> k2_binop_1(A,A,A,C,B,D) = D))))))))) # label(d16_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2037 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,F),k2_binop_1(A,A,A,B,E,F)) = k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,E),F))))))) <-> r5_binop_1(A,B,C)))))))) # label(d19_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2038 $T # label(t19_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2039 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> (v3_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> C = k1_binop_1(B,C,C)))))) # label(d4_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2040 (all A (-v1_xboole_0(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) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_binop_1(A,A,A,C,k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E)) = k8_funct_2(A,A,B,k2_binop_1(A,A,A,C,D,E)))))) <-> r7_binop_1(A,B,C)))))))) # label(d20_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2041 (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) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t26_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2042 $T # label(t21_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2043 (all A all B (m1_subset_1(B,A) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (r3_binop_1(A,B,C) <-> r1_binop_1(A,B,C) & r2_binop_1(A,B,C)))))) # label(d7_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2044 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r5_binop_1(A,C,B) <-> r4_binop_1(A,C,B))))))))) # label(t28_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2045 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> r5_binop_1(A,C,B))))))))) # label(t27_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2046 (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) = C)) <-> v3_binop_1(B,A)))))) # label(d15_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2047 (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,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> ((all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k1_binop_1(C,k1_funct_1(B,D),k1_funct_1(B,E)) = k1_funct_1(B,k1_binop_1(C,D,E)))))) <-> r7_binop_1(A,B,C)))))) # label(d12_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2048 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,C,D))) <-> r3_binop_1(A,C,B))))))) # label(t12_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2049 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) -> (v1_binop_1(C,A) -> (r6_binop_1(A,C,B) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,k2_binop_1(A,A,A,C,D,F),k2_binop_1(A,A,A,C,E,F)) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),F))))))))))))))) # label(t25_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2050 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> (r2_binop_1(A,C,B) <-> r1_binop_1(A,C,B))))))) # label(t16_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2051 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (v1_binop_1(B,A) -> ((all D (m1_subset_1(D,A) -> D = k1_binop_1(B,D,C))) <-> r3_binop_1(A,C,B))))))) # label(t13_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2052 (all A all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (v1_binop_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_binop_1(B,D,C) = k1_binop_1(B,C,D)))))))) # label(d2_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2053 (all A all B all C all D all E all F (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(F,B) & m1_subset_1(E,A) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> k1_binop_1(D,E,F) = k2_binop_1(A,B,C,D,E,F))) # label(redefinition_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2054 $T # label(t1_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2055 (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 (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (r4_binop_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> k2_binop_1(A,A,A,B,D,k2_binop_1(A,A,A,C,E,F)) = k2_binop_1(A,A,A,C,k2_binop_1(A,A,A,B,D,E),k2_binop_1(A,A,A,B,D,F))))))))))))))) # label(d18_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2056 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & m1_subset_1(E,A) & m1_subset_1(F,B) & v1_funct_1(D) & -v1_xboole_0(A) -> m1_subset_1(k2_binop_1(A,B,C,D,E,F),C))) # label(dt_k2_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2057 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C))))) # label(d1_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2058 $T # label(t3_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2059 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (v1_funct_1(E) & 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) -> k2_binop_1(A,B,C,E,F,G) = k2_binop_1(A,B,C,D,F,G))))) -> E = D))))))))))) # label(t2_binop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2060 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,B) & v1_funct_2(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]. 21.77/22.97 2061 (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) -> k9_funcop_1(A,C,B,k10_funcop_1(A,B,C,D)) = k4_relat_1(k9_funcop_1(A,B,C,D)))))))))) # label(t73_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2062 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (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]. 21.77/22.97 2063 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (m2_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_1(E) -> (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]. 21.77/22.97 2064 (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_xboole_0 = k1_relat_1(A) -> B = A))))) # label(t4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2065 $T # label(t5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2066 (all A all B all C all D all E (-v1_xboole_0(B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(D,A) & v1_funct_1(E) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_1(k8_funcop_1(A,B,C,D,E)) & 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))) # label(dt_k8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2067 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (k7_relat_1(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]. 21.77/22.97 2068 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(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 (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]. 21.77/22.97 2069 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m2_relset_1(E,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) -> ((all G (m1_subset_1(G,A) -> k2_binop_1(B,B,B,C,k8_funct_2(A,B,D,G),k8_funct_2(A,B,E,G)) = k8_funct_2(A,B,F,G))) -> F = k6_funcop_1(B,A,C,D,E)))))))))))))) # label(t49_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2070 (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) -> (v3_binop_1(C,B) -> k6_funcop_1(B,A,C,D,D) = D))))))))) # label(t81_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2071 (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) -> (all F (v1_funct_2(F,A,B) & m2_relset_1(F,A,B) & v1_funct_1(F) -> (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]. 21.77/22.97 2072 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k2_binop_1(A,A,A,C,E,k8_funct_2(B,A,D,F)) = k8_funct_2(B,A,k8_funcop_1(A,B,C,E,D),F))))))))))))) # label(t66_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2073 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> (v1_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]. 21.77/22.97 2074 $T # label(t12_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2075 (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]. 21.77/22.97 2076 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D 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]. 21.77/22.97 2077 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k5_funcop_1(C,D,k7_relat_1(A,B)) = k5_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A))))))) # label(t46_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2078 (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]. 21.77/22.97 2079 $T # label(dt_k5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2080 (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]. 21.77/22.97 2081 (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 k4_funcop_1(k5_relat_1(C,A),B,D) = k5_relat_1(k4_funcop_1(C,B,D),A)))))))) # label(t38_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2082 (all A all B all C all D (-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_xboole_0(A) -> k10_funcop_1(A,B,C,D) = k1_funcop_1(D))) # label(redefinition_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2083 (all A all B all C (r2_hidden(B,A) -> C = k1_funct_1(k2_funcop_1(A,C),B))) # label(t13_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2084 $T # label(t33_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2085 $T # label(t68_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2086 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (r2_hidden(C,k1_relat_1(k4_funcop_1(B,A,D))) -> k1_binop_1(B,k1_funct_1(A,C),D) = k1_funct_1(k4_funcop_1(B,A,D),C))))))) # label(t35_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2087 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> 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]. 21.77/22.97 2088 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,B,A) & m2_relset_1(D,B,A) & v1_funct_1(D) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> k8_funct_2(B,A,k7_funcop_1(A,B,C,D,E),F) = k2_binop_1(A,A,A,C,k8_funct_2(B,A,D,F),E))))))))))))) # label(t60_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2089 (all A all B all C (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_funct_1(C) & v1_relat_1(C) & v1_relat_1(B) -> v1_relat_1(k3_funcop_1(A,B,C)) & v1_funct_1(k3_funcop_1(A,B,C)))) # label(fc4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2090 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,B) -> 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]. 21.77/22.97 2091 (all A all B (v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(A) & v1_relat_1(A) -> v1_relat_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)))) # label(fc8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2092 (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) -> (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]. 21.77/22.97 2093 (all A (v1_relat_1(A) -> (all B all C (A = k2_zfmisc_1(B,C) -> B = k1_xboole_0 | k1_xboole_0 = C | B = k1_relat_1(A) & C = k2_relat_1(A))))) # label(t1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2094 (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]. 21.77/22.97 2095 (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_funct_1(D) & v1_relat_1(D) -> k3_funcop_1(k5_relat_1(D,A),B,C) = k5_relat_1(k3_funcop_1(D,B,C),A))))))))) # label(t32_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2096 (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_funct_1(D) & v1_relat_1(D) -> (k1_relat_1(k3_funcop_1(C,A,B)) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(D,E) = k1_binop_1(C,k1_funct_1(A,E),k1_funct_1(B,E)))) -> D = k3_funcop_1(C,A,B)))))))))) # label(t27_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2097 (all A all B all C all D all E (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) & v1_funct_2(E,B,A) & m1_relset_1(E,B,A) & v1_funct_1(E) & v1_funct_2(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)) & v1_funct_2(k6_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k6_funcop_1(A,B,C,D,E),B,A))) # label(dt_k6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2098 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(D) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k9_funcop_1(A,B,C,D) = k2_relat_1(D))) # label(redefinition_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2099 (exists A (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(A))) # label(rc1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2100 (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 (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]. 21.77/22.97 2101 (all A all B (v1_xboole_0(B) -> v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)))) # label(fc3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2102 (all A all B all C all D (-v1_xboole_0(A) & -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) -> m2_relset_1(k9_funcop_1(A,B,C,D),B,C))) # label(dt_k9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2103 (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) & m1_relset_1(D,B,A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(B) -> 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]. 21.77/22.97 2104 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> k1_funcop_1(k13_funct_3(B,A)) = k13_funct_3(A,B))))) # label(t6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2105 $T # label(dt_k4_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2106 (all A all B all C k2_funcop_1(k3_xboole_0(A,C),B) = k7_relat_1(k2_funcop_1(A,B),C)) # label(t18_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2107 (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)) -> m2_relset_1(k2_relat_1(D),B,C))))))))) # label(t72_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2108 $T # label(dt_k3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2109 (all A all B all C (v1_funct_1(A) & v1_funct_1(C) & v1_relat_1(C) & v1_relat_1(A) -> v1_funct_1(k5_funcop_1(A,B,C)) & v1_relat_1(k5_funcop_1(A,B,C)))) # label(fc6_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2110 (all A all B (-v1_xboole_0(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)))) # label(fc9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2111 (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(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(E) & m1_relset_1(E,B,A) & v1_funct_2(E,B,A) & m1_subset_1(D,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]. 21.77/22.97 2112 $T # label(t50_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2113 (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) -> k2_binop_1(A,A,A,B,C,C) = k8_funct_2(A,A,k7_funcop_1(A,A,B,k6_partfun1(A),C),C))))))) # label(t64_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2114 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & m1_relset_1(D,A,k2_zfmisc_1(B,C)) & -v1_xboole_0(B) -> m2_relset_1(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & v1_funct_2(k10_funcop_1(A,B,C,D),A,k2_zfmisc_1(C,B)) & v1_funct_1(k10_funcop_1(A,B,C,D)))) # label(dt_k10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2115 (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]. 21.77/22.97 2116 (all A (v1_relat_1(A) & v1_funct_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]. 21.77/22.97 2117 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C k2_funcop_1(k10_relat_1(A,B),C) = k5_relat_1(A,k2_funcop_1(B,C))))) # label(t25_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2118 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_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]. 21.77/22.97 2119 (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]. 21.77/22.97 2120 (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]. 21.77/22.97 2121 (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 (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]. 21.77/22.97 2122 $T # label(dt_k2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2123 (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) -> 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]. 21.77/22.97 2124 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,A,B) & m2_relset_1(E,A,B) & v1_funct_1(E) -> (all F (m1_subset_1(F,B) -> (v2_binop_1(C,B) -> k6_funcop_1(B,A,C,k7_funcop_1(B,A,C,D,F),E) = k6_funcop_1(B,A,C,D,k8_funcop_1(B,A,C,F,E))))))))))))))) # label(t75_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2125 (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,k2_zfmisc_1(B,C)) & v1_funct_2(D,A,k2_zfmisc_1(B,C)) & v1_funct_1(D) -> (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]. 21.77/22.97 2126 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C k3_funcop_1(B,A,k2_funcop_1(k1_relat_1(A),C)) = k4_funcop_1(B,A,C)))))) # label(t34_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2127 (all A k12_funct_3(A) = k1_funcop_1(k12_funct_3(A))) # label(t9_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2128 (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,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,k8_funcop_1(A,B,C,k8_funct_2(B,A,D,E),D),E) = k8_funct_2(B,A,D,E)))))))))))) # label(t82_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2129 (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) -> k5_relat_1(k13_funct_3(B,C),A) = k3_funcop_1(A,B,C))))))) # label(d3_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2130 (all A all B (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_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]. 21.77/22.97 2131 (all A all B all C (r2_hidden(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(t57_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2132 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C all D (v1_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,A,E),C) = k7_relat_1(k4_funcop_1(D,B,E),C))))))))) # label(t36_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2133 (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(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]. 21.77/22.97 2134 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> (all D (v1_funct_2(D,A,A) & m2_relset_1(D,A,A) & v1_funct_1(D) -> k8_funct_2(A,A,k6_funcop_1(A,A,B,D,k6_partfun1(A)),C) = k2_binop_1(A,A,A,B,k8_funct_2(A,A,D,C),C))))))))) # label(t55_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2135 (all A all B all C all D all E (-v1_xboole_0(B) & v1_funct_2(D,B,A) & m1_subset_1(E,A) & 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) & v1_funct_1(C) & -v1_xboole_0(A) -> v1_funct_1(k7_funcop_1(A,B,C,D,E)) & v1_funct_2(k7_funcop_1(A,B,C,D,E),B,A) & m2_relset_1(k7_funcop_1(A,B,C,D,E),B,A))) # label(dt_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2136 (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]. 21.77/22.97 2137 (all A all B k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B))) # label(d2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2138 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (r2_hidden(D,k1_relat_1(k3_funcop_1(C,A,B))) -> k1_funct_1(k3_funcop_1(C,A,B),D) = k1_binop_1(C,k1_funct_1(A,D),k1_funct_1(B,D)))))))))) # label(t28_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2139 (all A (v2_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_xboole_0(k2_funcop_1(k1_xboole_0,A)))) # label(fc2_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2140 (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]. 21.77/22.97 2141 (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]. 21.77/22.97 2142 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_relat_1(C) & v1_funct_1(C) -> k5_relat_1(k13_funct_3(k2_funcop_1(k1_relat_1(C),B),C),A) = k5_funcop_1(A,B,C))))) # label(d5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2143 $T # label(t40_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2144 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k13_funct_3(k7_relat_1(A,C),B) = k7_relat_1(k13_funct_3(A,B),C)))))) # label(t10_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2145 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_1(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,B,A) & v1_funct_2(E,B,A) -> (all F (m1_subset_1(F,A) -> ((all G (m1_subset_1(G,B) -> k8_funct_2(B,A,D,G) = k2_binop_1(A,A,A,C,F,k8_funct_2(B,A,E,G)))) -> D = k8_funcop_1(A,B,C,F,E)))))))))))))) # label(t67_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2146 (all A (v1_funct_1(A) & v1_relat_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]. 21.77/22.97 2147 (all A (-v1_xboole_0(A) -> (all B (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m2_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all C (m1_subset_1(C,A) -> 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]. 21.77/22.97 2148 (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]. 21.77/22.97 2149 $T # label(t8_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2150 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k1_funcop_1(A)) & v1_funct_1(k1_funcop_1(A)))) # label(dt_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2151 (all A all B all C (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k4_funcop_1(A,B,C)) & v1_funct_1(k4_funcop_1(A,B,C)))) # label(fc5_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2152 (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) -> (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]. 21.77/22.97 2153 (all A all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,B) -> v1_funct_2(k2_funcop_1(A,C),A,B) & m2_relset_1(k2_funcop_1(A,C),A,B) & v1_funct_1(k2_funcop_1(A,C)))))) # label(t58_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2154 (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]. 21.77/22.97 2155 (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 all E (v1_relat_1(E) & v1_funct_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,D) -> k7_relat_1(k3_funcop_1(E,C,B),D) = k7_relat_1(k3_funcop_1(E,C,A),D)))))))))) # label(t30_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2156 (all A all B (A = k1_relat_1(k2_funcop_1(A,B)) & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)))) # label(t19_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2157 (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(k13_funct_3(A,B),C) = k13_funct_3(A,k7_relat_1(B,C))))))) # label(t11_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.97 2158 (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]. 21.77/22.98 2159 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> 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]. 21.77/22.98 2160 (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,B) -> (v3_binop_1(C,A) -> k8_funct_2(B,A,D,E) = k8_funct_2(B,A,k7_funcop_1(A,B,C,D,k8_funct_2(B,A,D,E)),E)))))))))))) # label(t83_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2161 (all A (v1_funct_1(A) & v1_relat_1(A) -> A = k1_funcop_1(k1_funcop_1(A)))) # label(involutiveness_k1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2162 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m2_relset_1(C,k2_zfmisc_1(B,B),B) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,B) & m2_relset_1(E,A,B) -> (v1_binop_1(C,B) -> k6_funcop_1(B,A,C,E,D) = k6_funcop_1(B,A,C,D,E)))))))))))) # label(t80_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2163 (all A (v1_funct_1(A) & v1_relat_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]. 21.77/22.98 2164 (all A all B all C all D all E (-v1_xboole_0(A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_subset_1(E,A) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & -v1_xboole_0(B) -> k4_funcop_1(C,D,E) = k7_funcop_1(A,B,C,D,E))) # label(redefinition_k7_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2165 (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,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]. 21.77/22.98 2166 (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]. 21.77/22.98 2167 (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_funcop_1(C,D,k5_relat_1(B,A)) = k5_relat_1(B,k5_funcop_1(C,D,A))))))))) # label(t44_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2168 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C -(k1_xboole_0 != B & r2_hidden(C,k1_relat_1(A)) & k1_xboole_0 = k1_relat_1(k5_relat_1(k2_funcop_1(B,C),A)))))) # label(t24_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2169 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D k4_funcop_1(C,k7_relat_1(A,B),D) = k5_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D))))))) # label(t39_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2170 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_funcop_1(A) = 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(B,C) = k4_tarski(E,D))) & -(k1_funct_1(A,C) != k1_funct_1(B,C) & (all D all E k1_funct_1(A,C) != k4_tarski(D,E))))) & k1_relat_1(A) = k1_relat_1(B)))))) # label(d1_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2171 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k7_relat_1(A,D) = k7_relat_1(B,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]. 21.77/22.98 2172 (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) -> m2_relset_1(k3_funcop_1(C,D,E),A,B) & v1_funct_2(k3_funcop_1(C,D,E),A,B) & v1_funct_1(k3_funcop_1(C,D,E)))))))))))) # label(t47_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2173 (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)) & m2_relset_1(k4_funcop_1(C,D,E),A,B) & v1_funct_2(k4_funcop_1(C,D,E),A,B))))))))))) # label(t59_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2174 $T # label(t62_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2175 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_2(C,k2_zfmisc_1(B,B),B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,B,B) & m2_relset_1(E,B,B) & v1_funct_1(E) -> k6_funcop_1(B,A,C,D,k7_funct_2(A,B,B,D,E)) = k7_funct_2(A,B,B,D,k6_funcop_1(B,B,C,k6_partfun1(B),E)))))))))))) # label(t51_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2176 (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 k5_relat_1(k5_funcop_1(C,D,B),A) = k5_funcop_1(k5_relat_1(C,A),D,B)))))))) # label(t45_funcop_1) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2177 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(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]. 21.77/22.98 2178 (all A (v1_relat_1(A) & v1_funct_1(A) -> k1_funct_4(A,k1_xboole_0) = A)) # label(t22_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2179 (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(C)) <-> (exists E exists F exists G exists H (r2_hidden(k4_tarski(E,F),k1_relat_1(A)) & r2_hidden(k4_tarski(G,H),k1_relat_1(B)) & k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) = D)))) & (all D all E all F all G (r2_hidden(k4_tarski(F,G),k1_relat_1(B)) & r2_hidden(k4_tarski(D,E),k1_relat_1(A)) -> k4_tarski(k1_funct_1(A,k4_tarski(D,E)),k1_funct_1(B,k4_tarski(F,G))) = k1_funct_1(C,k4_tarski(k4_tarski(D,F),k4_tarski(E,G))))) <-> C = k3_funct_4(A,B)))))))) # label(d3_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2180 (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]. 21.77/22.98 2181 (all A all B (r1_tarski(k6_partfun1(A),k6_partfun1(B)) <-> r1_tarski(A,B))) # label(t4_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2182 (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) -> 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]. 21.77/22.98 2183 (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]. 21.77/22.98 2184 $T # label(dt_k4_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2185 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> r1_tarski(A,k1_funct_4(A,B))))))) # label(t29_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2186 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_relat_1(C) = k2_relat_1(k2_funct_4(C))))) # label(t48_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2187 (all A all B (v1_relat_1(A) & v1_funct_1(A) & v1_funct_1(B) & v1_relat_1(B) -> k1_funct_4(A,A) = A)) # label(idempotence_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2188 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(C,D) -> r1_tarski(k7_relat_1(k8_relat_1(A,C),B),k7_relat_1(k8_relat_1(A,D),B))))))) # label(t10_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2189 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> r1_tarski(k2_funcop_1(k1_tarski(A),k1_funct_1(B,A)),B)))) # label(t8_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2190 (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_1(H) & m2_relset_1(H,k2_zfmisc_1(D,E),F) & v1_funct_2(H,k2_zfmisc_1(D,E),F) -> -(k1_xboole_0 != C & -(m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,E)),k2_zfmisc_1(C,F)) & v1_funct_1(k3_funct_4(G,H))) & k1_xboole_0 != F))))) # label(t63_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2191 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k3_funct_4(A,B)) & v1_funct_1(k3_funct_4(A,B)))) # label(dt_k3_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2192 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k2_zfmisc_1(A,B) = k1_relat_1(C) -> k1_relat_1(k2_funct_4(C)) = k2_zfmisc_1(B,A)))) # label(t47_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2193 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)))))) # label(t30_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2194 (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]. 21.77/22.98 2195 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k2_funct_4(A)),k2_relat_1(A)))) # label(t42_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2196 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (all F (v1_funct_1(F) & v1_relat_1(F) -> (r1_tarski(k1_relat_1(E),k2_zfmisc_1(A,B)) & r1_tarski(k1_relat_1(F),k2_zfmisc_1(C,D)) -> r1_tarski(k1_relat_1(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)))))))) # label(t60_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2197 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) -> (C != k1_xboole_0 -> m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D))))) # label(t50_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2198 $T # label(t3_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2199 (all A all B all C k2_funcop_1(k2_tarski(A,B),C) = k4_funct_4(A,B,C,C)) # label(t68_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2200 (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]. 21.77/22.98 2201 (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]. 21.77/22.98 2202 (all A all B all C all D (C != A -> k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)))) # label(t71_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2203 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(A,B) = k1_funct_4(B,A)))))) # label(t35_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2204 (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]. 21.77/22.98 2205 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(k2_funct_4(C))) -> k1_funct_1(k2_funct_4(C),k4_tarski(A,B)) = k1_funct_1(C,k4_tarski(B,A))))) # label(t44_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2206 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_funct_4(k2_funct_4(A)),A))) # label(t52_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2207 (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]. 21.77/22.98 2208 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> k1_funct_4(B,A) = B & k1_funct_4(A,B) = B))))) # label(t79_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2209 (all A all B all C all D all E (-v1_xboole_0(A) & m1_subset_1(E,A) & m1_subset_1(D,A) -> v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & v1_funct_1(k5_funct_4(A,B,C,D,E)))) # label(dt_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2210 (all A -((all B all C -r1_tarski(A,k2_zfmisc_1(B,C))) & (all B -((all C all D B != k4_tarski(C,D)) & r2_hidden(B,A))))) # label(t1_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2211 (all A (v1_relat_1(A) & v1_funct_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]. 21.77/22.98 2212 (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]. 21.77/22.98 2213 (all A all B all C all D (k2_tarski(A,B) = k1_relat_1(k4_funct_4(A,B,C,D)) & 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]. 21.77/22.98 2214 (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) -> (k2_zfmisc_1(C,D) = k1_relat_1(F) & 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]. 21.77/22.98 2215 (all A all B all C all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> D = k2_funct_4(k2_funct_4(D)))) # label(t54_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2216 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k2_funct_4(k2_funct_4(C)) = C))) # label(t53_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2217 (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) -> D = k2_funct_4(k2_funct_4(D)))))) # label(t56_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2218 (all A all B all C all D (B != A -> C = k1_funct_1(k4_funct_4(A,B,C,D),A) & D = k1_funct_1(k4_funct_4(A,B,C,D),B))) # label(t66_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2219 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(A,k1_funct_4(B,A)))))) # label(t26_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2220 (all A all B all C all D all E all F (k4_funct_4(A,B,C,D) = k4_funct_4(A,B,E,F) -> A = B | D = F & C = E)) # label(t72_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2221 (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]. 21.77/22.98 2222 (all A all B all C all D k1_funct_4(k2_funcop_1(k1_tarski(A),C),k2_funcop_1(k1_tarski(B),D)) = k4_funct_4(A,B,C,D)) # label(d4_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2223 (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(C) = k1_relat_1(B) -> k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,C)))))))) # label(t78_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2224 (all A all B (v1_funct_1(B) & m2_relset_1(B,A,A) & v1_funct_2(B,A,A) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> C = k1_funct_4(B,C))))) # label(t39_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2225 (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)) -> A = k7_relat_1(k1_funct_4(A,B),k1_relat_1(A))))))) # label(t34_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2226 (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_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]. 21.77/22.98 2227 (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(A,C)))))))) # label(t28_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2228 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> r1_tarski(k1_relat_1(B),k1_relat_1(k1_funct_4(A,B))) & r1_tarski(k1_relat_1(A),k1_relat_1(k1_funct_4(A,B))))))) # label(t11_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2229 (all A all B all C all D all E (v1_funct_1(E) & v1_relat_1(E) -> (k2_tarski(A,B) = k1_relat_1(E) & k1_funct_1(E,B) = D & k1_funct_1(E,A) = C -> E = k4_funct_4(A,B,C,D)))) # label(t69_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2230 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (-r2_hidden(A,k1_relat_1(B)) -> k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A)))))) # label(t12_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2231 (all A all B all C all D all E (-v1_xboole_0(E) -> (all F (-v1_xboole_0(F) -> (all G (m2_relset_1(G,k2_zfmisc_1(A,B),E) & v1_funct_2(G,k2_zfmisc_1(A,B),E) & v1_funct_1(G) -> (all H (v1_funct_2(H,k2_zfmisc_1(C,D),F) & m2_relset_1(H,k2_zfmisc_1(C,D),F) & v1_funct_1(H) -> v1_funct_1(k3_funct_4(G,H)) & v1_funct_2(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)) & m2_relset_1(k3_funct_4(G,H),k2_zfmisc_1(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)),k2_zfmisc_1(E,F)))))))))) # label(t64_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2232 (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)) -> A = k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)))))) # label(t74_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2233 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (r1_tarski(k1_relat_1(A),C) & r1_xboole_0(k1_relat_1(B),C) -> k7_relat_1(k1_funct_4(A,B),C) = A)))))) # label(t82_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2234 (all A all B all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D) -> ((B = k1_xboole_0 -> k1_xboole_0 = A) -> D = k1_funct_4(C,D)))))) # label(t38_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2235 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(B)) & r1_partfun1(B,C) -> k1_funct_1(B,A) = k1_funct_1(k1_funct_4(B,C),A)))))) # label(t16_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2236 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> B = k7_relat_1(k1_funct_4(A,B),k1_relat_1(B)))))) # label(t24_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2237 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_1(A) -> v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)))) # label(dt_k1_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2238 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (r1_xboole_0(k1_relat_1(A),C) -> k7_relat_1(k1_funct_4(A,B),C) = k7_relat_1(B,C))))))) # label(t77_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2239 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C k1_funct_4(k7_relat_1(A,B),k7_relat_1(A,C)) = k7_relat_1(A,k2_xboole_0(B,C))))) # label(t83_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2240 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B k1_funct_4(A,k7_relat_1(A,B)) = A))) # label(t80_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2241 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> ((all C all D (r2_hidden(k4_tarski(C,D),k1_relat_1(A)) -> k1_funct_1(B,k4_tarski(D,C)) = k1_funct_1(A,k4_tarski(C,D)))) & (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E (k4_tarski(E,D) = C & r2_hidden(k4_tarski(D,E),k1_relat_1(A)))))) <-> k2_funct_4(A) = B))))) # label(d2_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2242 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))))))) # label(t18_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2243 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k1_funct_4(B,A))))))) # label(t19_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2244 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C k1_funct_4(k7_relat_1(A,C),k7_relat_1(B,C)) = k7_relat_1(k1_funct_4(A,B),C)))))) # label(t75_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2245 (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) -> (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(C,D) = k1_funct_1(A,D)) & (r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_funct_1(C,D)))) <-> C = k1_funct_4(A,B)))))))) # label(d1_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2246 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_partfun1(A,k1_funct_4(B,C)) -> r1_partfun1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),k1_relat_1(C))),B)))))))) # label(t27_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2247 (all A all B all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> v1_funct_2(k2_funct_4(D),k2_zfmisc_1(B,A),C) & m2_relset_1(k2_funct_4(D),k2_zfmisc_1(B,A),C) & v1_funct_1(k2_funct_4(D)))))) # label(t51_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2248 (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]. 21.77/22.98 2249 (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]. 21.77/22.98 2250 (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]. 21.77/22.98 2251 (all A all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> k1_funct_4(C,D) = D)))))) # label(t40_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2252 (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) -> D = k1_funct_4(C,D)))))) # label(t37_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2253 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_partfun1(A,B) <-> k1_funct_4(A,B) = k2_xboole_0(A,B)))))) # label(t31_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2254 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(A,k1_relat_1(C)) | r2_hidden(A,k1_relat_1(B)) <-> r2_hidden(A,k1_relat_1(k1_funct_4(B,C)))))))) # label(t13_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2255 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (all C all D (r1_tarski(k1_relat_1(A),C) & r1_tarski(k1_relat_1(B),D) & r1_xboole_0(C,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]. 21.77/22.98 2256 (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)) -> k2_xboole_0(A,B) = k1_funct_4(A,B)))))) # label(t32_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2257 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E))) # label(redefinition_k5_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2258 (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)) -> r1_tarski(A,k1_funct_4(A,B))))))) # label(t33_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2259 (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]. 21.77/22.98 2260 (all A all B all C all D (r1_tarski(k2_funcop_1(A,B),k2_funcop_1(C,D)) -> B = D | k1_xboole_0 = A)) # label(t7_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2261 (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]. 21.77/22.98 2262 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(B,A),k1_relat_1(k2_funct_4(C))) <-> r2_hidden(k4_tarski(A,B),k1_relat_1(C))))) # label(t43_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2263 (all A all B all C all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (C != k1_xboole_0 -> k2_funct_4(k2_funct_4(D)) = D))) # label(t55_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.77/22.98 2264 (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 (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(D),k1_relat_1(B)) & r1_partfun1(A,B) & r1_tarski(k2_relat_1(C),k1_relat_1(A)) -> k1_funct_4(k5_relat_1(C,A),k5_relat_1(D,B)) = k5_relat_1(k1_funct_4(C,D),k1_funct_4(A,B))))))))))) # label(t73_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2265 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> k5_relat_1(B,A) = k5_relat_1(B,k7_relat_1(A,k2_relat_1(B))))))) # label(t2_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2266 (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_funct_4(A,k1_funct_4(B,C)) = k1_funct_4(k1_funct_4(A,B),C))))))) # label(t15_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2267 (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]. 21.89/23.06 2268 (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(B,A) = k1_funct_1(k1_funct_4(C,B),A)))))) # label(t14_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2269 (all A all B all C all D (B != A -> k2_tarski(C,D) = k2_relat_1(k4_funct_4(A,B,C,D)))) # label(t67_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2270 (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]. 21.89/23.06 2271 (all A (v1_funct_1(A) & v1_relat_1(A) -> k1_funct_4(k1_xboole_0,A) = A)) # label(t21_funct_4) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2272 (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]. 21.89/23.06 2273 $T # label(t33_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2274 (all A (v1_funct_1(A) & v5_ordinal1(A) & v1_relat_1(A) -> v3_ordinal1(k8_ordinal2(A)))) # label(dt_k8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2275 (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]. 21.89/23.06 2276 (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]. 21.89/23.06 2277 (all A all B (B = k2_ordinal2(A) <-> (all C (v3_ordinal1(C) & r2_hidden(C,A) <-> r2_hidden(C,B))))) # label(d2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2278 $T # label(t8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2279 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(k4_ordinal2,A) & A = k16_ordinal2(A,k4_ordinal2))) # label(t63_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2280 (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]. 21.89/23.06 2281 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> k15_ordinal2(k1_ordinal1(A),B) = k14_ordinal2(k15_ordinal2(A,B),B))))) # label(t53_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2282 (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]. 21.89/23.06 2283 $T # label(dt_k3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2284 (all A all B (v5_ordinal1(B) & v1_ordinal2(B) & v1_funct_1(B) & v1_relat_1(B) & v3_ordinal1(A) -> v3_ordinal1(k13_ordinal2(A,B)))) # label(dt_k13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2285 (r2_hidden(k1_xboole_0,f3_s6_ordinal2) -> f4_s6_ordinal2 = k1_funct_1(f1_s6_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s6_ordinal2) -> k1_funct_1(f1_s6_ordinal2,k1_ordinal1(A)) = f5_s6_ordinal2(A,k1_funct_1(f1_s6_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s6_ordinal2) -> A = k1_xboole_0 | f6_s6_ordinal2(A,k2_ordinal1(f1_s6_ordinal2,A)) = k1_funct_1(f1_s6_ordinal2,A)))) & f3_s6_ordinal2 = k1_relat_1(f1_s6_ordinal2) & (all A (v3_ordinal1(A) -> (all B (f2_s6_ordinal2(A) = B <-> (exists C (v5_ordinal1(C) & f4_s6_ordinal2 = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s6_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s6_ordinal2(D,k2_ordinal1(C,D))))) & k1_relat_1(C) = k1_ordinal1(A) & k1_ordinal2(C) = B & v1_funct_1(C) & v1_relat_1(C))))))) -> (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]. 21.89/23.06 2286 $T # label(t21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2287 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k14_ordinal2(A,B) <-> (exists D (v1_funct_1(D) & v5_ordinal1(D) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k1_ordinal1(k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(B)) & v4_ordinal1(E) -> k8_ordinal2(k2_ordinal1(D,E)) = k1_funct_1(D,E) | E = k1_xboole_0))) & k1_funct_1(D,k1_xboole_0) = A & k1_relat_1(D) = k1_ordinal1(B) & C = k1_ordinal2(D) & v1_ordinal2(D) & v1_relat_1(D)))))))))) # label(d18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2288 (all A v3_ordinal1(k6_ordinal2(A))) # label(dt_k6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2289 $T # label(t36_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2290 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(C,D) = k6_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D))))))) & k1_relat_1(A) = k1_relat_1(C) & B = k8_ordinal2(C) & v1_relat_1(C))) <-> B = k11_ordinal2(A)))))) # label(d12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2291 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_ordinal1(A) = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f3_s15_ordinal2(D,k2_ordinal1(C,D)) | D = k1_xboole_0))) & (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_funct_1(C,k1_xboole_0) = f1_s15_ordinal2 & k1_ordinal2(C) = B & v1_ordinal2(C) & v1_funct_1(C))) <-> B = f4_s15_ordinal2(A)))))) -> (all A (v3_ordinal1(A) -> f4_s15_ordinal2(k1_ordinal1(A)) = f2_s15_ordinal2(A,f4_s15_ordinal2(A)))) # label(s15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2292 $T # label(t42_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2293 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) -> ((exists B (r1_ordinal2(B,A) & v3_ordinal1(B))) -> (all B (v3_ordinal1(B) -> (r1_ordinal2(B,A) <-> B = k12_ordinal2(A))))))) # label(d14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.06 2294 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & f1_s9_ordinal2 = k1_funct_1(C,k1_xboole_0) & (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_xboole_0 = D | f3_s9_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & k1_ordinal1(A) = k1_relat_1(C) & v1_funct_1(C))) <-> B = f4_s9_ordinal2(A))))) -> (all A (v3_ordinal1(A) -> f2_s9_ordinal2(A,f4_s9_ordinal2(A)) = f4_s9_ordinal2(k1_ordinal1(A)))) # label(s9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2295 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all C (v5_ordinal1(C) & v1_ordinal2(C) & v1_funct_1(C) & v1_relat_1(C) -> ((all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k16_ordinal2(B,D) = k1_funct_1(C,D)))) & k1_relat_1(C) = A -> k16_ordinal2(B,A) = k12_ordinal2(C))))))))) # label(t62_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2296 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> ((exists D (v1_ordinal2(D) & k1_relat_1(D) = k1_ordinal1(A) & (all E (v3_ordinal1(E) -> (r2_hidden(E,k1_ordinal1(A)) & v4_ordinal1(E) -> k3_tarski(k8_ordinal2(k2_ordinal1(D,E))) = k1_funct_1(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_xboole_0 = k1_funct_1(D,k1_xboole_0) & k1_ordinal2(D) = C & v5_ordinal1(D) & v1_funct_1(D) & v1_relat_1(D))) <-> C = k15_ordinal2(A,B)))))))) # label(d19_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2297 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k6_ordinal2(k2_relat_1(A)) = k9_ordinal2(A) & k8_ordinal2(A) = k7_ordinal2(k2_relat_1(A)))) # label(t35_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2298 (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]. 21.89/23.08 2299 (all A (v3_ordinal1(A) -> r1_ordinal1(k3_tarski(A),A))) # label(t5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2300 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (B = k9_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_relat_1(A)) -> k7_ordinal2(k2_relat_1(k7_relat_1(A,k4_xboole_0(k1_relat_1(A),D)))) = k1_funct_1(C,D)))) & k1_relat_1(C) = k1_relat_1(A) & v1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) <-> B = k10_ordinal2(A)))))) # label(d11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2301 (all A (v3_ordinal1(A) -> r1_tarski(k1_ordinal1(A),k1_zfmisc_1(A)))) # label(t3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2302 $T # label(dt_k1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2303 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k1_xboole_0) = A)) # label(t44_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2304 $T # label(t20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2305 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> v3_ordinal1(k11_ordinal2(A)))) # label(dt_k11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2306 (all A (v3_ordinal1(A) -> A = k7_ordinal2(A))) # label(t26_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2307 (all A all B (v3_ordinal1(B) -> (B = k7_ordinal2(A) <-> r1_tarski(k2_ordinal2(A),B) & (all C (v3_ordinal1(C) -> (r1_tarski(k2_ordinal2(A),C) -> r1_ordinal1(B,C))))))) # label(d7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2308 (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]. 21.89/23.08 2309 (all A (v3_ordinal1(A) -> k2_ordinal2(A) = A)) # label(t10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2310 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> (A != k1_xboole_0 -> (r1_ordinal2(A,B) <-> (all C (v3_ordinal1(C) -> (all D (v3_ordinal1(D) -> -(r2_hidden(A,D) & (all E (v3_ordinal1(E) -> -((all F (v3_ordinal1(F) -> (r2_hidden(F,k1_relat_1(B)) & r1_ordinal1(E,F) -> 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(C,A)))))))) & (k1_xboole_0 = A -> ((exists C (r2_hidden(C,k1_relat_1(B)) & (all D (v3_ordinal1(D) -> (r1_ordinal1(C,D) & r2_hidden(D,k1_relat_1(B)) -> k1_funct_1(B,D) = k1_xboole_0))) & v3_ordinal1(C))) <-> r1_ordinal2(A,B))))))) # label(d13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 21.89/23.08 2311 (all A all B -((exists C (B = k1_ordinal2(C) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) & v4_ordinal1(D) -> D = k1_xboole_0 | f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) & B != A & (exists C (v1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f2_s7_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(f1_s7_ordinal2)) -> k1_xboole_0 = D | f4_s7_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s7_ordinal2(D,k1_funct_1(C,D))))) & k1_relat_1(C) = k1_ordinal1(f1_s7_ordinal2) & A = k1_ordinal2(C) & v5_ordinal1(C) & v1_funct_1(C))))) # label(s7_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2312 (exists A exists B (v1_relat_1(B) & v1_funct_1(B) & f2_s7_ordinal2 = k1_funct_1(B,k1_xboole_0) & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s7_ordinal2)) -> k1_xboole_0 = C | k1_funct_1(B,C) = f4_s7_ordinal2(C,k2_ordinal1(B,C))))) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s7_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s7_ordinal2(C,k1_funct_1(B,C))))) & k1_ordinal1(f1_s7_ordinal2) = k1_relat_1(B) & A = k1_ordinal2(B) & v5_ordinal1(B))) # label(s7_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2313 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_funct_1(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)) -> f5_s16_ordinal2(D,k1_funct_1(C,D)) = k1_funct_1(C,k1_ordinal1(D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> k1_xboole_0 = D | f6_s16_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & f4_s16_ordinal2 = k1_funct_1(C,k1_xboole_0) & v1_ordinal2(C) & v5_ordinal1(C) & v1_relat_1(C))) <-> B = f3_s16_ordinal2(A)))))) & f2_s16_ordinal2 = k1_relat_1(f1_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) & k1_xboole_0 != f2_s16_ordinal2 -> f6_s16_ordinal2(f2_s16_ordinal2,f1_s16_ordinal2) = f3_s16_ordinal2(f2_s16_ordinal2) # label(s16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2314 (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]. 22.03/23.22 2315 (exists A (v1_funct_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s3_ordinal2) -> f2_s3_ordinal2(B) = k1_funct_1(A,B)))) & k1_relat_1(A) = f1_s3_ordinal2 & v1_ordinal2(A) & v5_ordinal1(A) & v1_relat_1(A))) # label(s3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2316 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (B = f2_s12_ordinal2(A) <-> (exists C (v1_relat_1(C) & v5_ordinal1(C) & k1_ordinal2(C) = B & k1_ordinal1(A) = k1_relat_1(C) & k1_funct_1(C,k1_xboole_0) = f4_s12_ordinal2 & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_funct_1(C,D) = f6_s12_ordinal2(D,k2_ordinal1(C,D)) | k1_xboole_0 = D))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f5_s12_ordinal2(D,k1_funct_1(C,D))))) & v1_ordinal2(C) & v1_funct_1(C)))))))) & f3_s12_ordinal2 = k1_relat_1(f1_s12_ordinal2) & (r2_hidden(k1_xboole_0,f3_s12_ordinal2) -> f4_s12_ordinal2 = k1_funct_1(f1_s12_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(A,f3_s12_ordinal2) -> k1_xboole_0 = A | k1_funct_1(f1_s12_ordinal2,A) = f6_s12_ordinal2(A,k2_ordinal1(f1_s12_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f3_s12_ordinal2) -> k1_funct_1(f1_s12_ordinal2,k1_ordinal1(A)) = f5_s12_ordinal2(A,k1_funct_1(f1_s12_ordinal2,A))))) -> (all A (v3_ordinal1(A) -> (r2_hidden(A,k1_relat_1(f1_s12_ordinal2)) -> k1_funct_1(f1_s12_ordinal2,A) = f2_s12_ordinal2(A)))) # label(s12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2317 (all A (v3_ordinal1(A) -> k15_ordinal2(A,k1_xboole_0) = k1_xboole_0)) # label(t55_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2318 (all A (v3_ordinal1(A) -> A = k14_ordinal2(k1_xboole_0,A))) # label(t47_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2319 (all A (v3_ordinal1(A) -> k7_ordinal2(k1_tarski(A)) = k1_ordinal1(A))) # label(t31_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2320 $T # label(t6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2321 $T # label(t43_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2322 $T # label(dt_k5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2323 (all A (v3_ordinal1(A) -> (all B (B = f3_s10_ordinal2(A) <-> (exists C (v1_relat_1(C) & v1_funct_1(C) & B = k1_ordinal2(C) & k1_relat_1(C) = k1_ordinal1(A) & k1_funct_1(C,k1_xboole_0) = f4_s10_ordinal2 & (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) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> k1_xboole_0 = D | k1_funct_1(C,D) = f6_s10_ordinal2(D,k2_ordinal1(C,D))))) & v5_ordinal1(C))))))) & f2_s10_ordinal2 != k1_xboole_0 & f2_s10_ordinal2 = k1_relat_1(f1_s10_ordinal2) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f2_s10_ordinal2) -> f3_s10_ordinal2(A) = k1_funct_1(f1_s10_ordinal2,A)))) & v4_ordinal1(f2_s10_ordinal2) -> f6_s10_ordinal2(f2_s10_ordinal2,f1_s10_ordinal2) = f3_s10_ordinal2(f2_s10_ordinal2) # label(s10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2324 $T # label(t37_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2325 (exists A (v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s11_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s11_ordinal2) -> f3_s11_ordinal2(B,k1_funct_1(A,B)) = k1_funct_1(A,k1_ordinal1(B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s11_ordinal2) & v4_ordinal1(B) -> B = k1_xboole_0 | f4_s11_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (r2_hidden(k1_xboole_0,f1_s11_ordinal2) -> f2_s11_ordinal2 = k1_funct_1(A,k1_xboole_0)) & v1_ordinal2(A) & v1_relat_1(A))) # label(s11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2326 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (v4_ordinal1(A) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_ordinal2(C) -> (A = k1_relat_1(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,A) -> k1_funct_1(C,D) = k14_ordinal2(B,D)))) -> k8_ordinal2(C) = k14_ordinal2(B,A)))) | k1_xboole_0 = A))))) # label(t46_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2327 (all A all B (v1_funct_1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v5_ordinal1(A) & v1_relat_1(A) -> v1_ordinal1(k1_funct_1(A,B)) & v2_ordinal1(k1_funct_1(A,B)) & v3_ordinal1(k1_funct_1(A,B)))) # label(fc3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.03/23.22 2328 (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]. 22.03/23.22 2329 (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]. 22.03/23.22 2330 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (C = k16_ordinal2(A,B) <-> (exists D (v1_relat_1(D) & v5_ordinal1(D) & v1_ordinal2(D) & k1_relat_1(D) = k1_ordinal1(B) & k4_ordinal2 = k1_funct_1(D,k1_xboole_0) & (all E (v3_ordinal1(E) -> (r2_hidden(k1_ordinal1(E),k1_ordinal1(B)) -> k15_ordinal2(A,k1_funct_1(D,E)) = k1_funct_1(D,k1_ordinal1(E))))) & (all E (v3_ordinal1(E) -> (v4_ordinal1(E) & r2_hidden(E,k1_ordinal1(B)) -> k1_funct_1(D,E) = k12_ordinal2(k2_ordinal1(D,E)) | k1_xboole_0 = E))) & C = k1_ordinal2(D) & v1_funct_1(D)))))))))) # label(d20_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2331 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A))) # label(rc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2332 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) & v5_ordinal1(A) -> ((all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (r2_hidden(B,C) & r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,B),k1_funct_1(A,C))))))) <-> v2_ordinal2(A)))) # label(d16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2333 (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]. 22.08/23.24 2334 (all A all B (v3_ordinal1(A) & v3_ordinal1(B) -> v3_ordinal1(k15_ordinal2(A,B)))) # label(dt_k15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2335 (all A (v3_ordinal1(A) -> k4_ordinal2 = k16_ordinal2(A,k1_xboole_0))) # label(t60_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2336 (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]. 22.08/23.24 2337 (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]. 22.08/23.24 2338 (all A all B (v3_ordinal1(B) & v3_ordinal1(A) -> v3_ordinal1(k14_ordinal2(A,B)))) # label(dt_k14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2339 (all A r1_tarski(k2_ordinal2(A),A)) # label(t9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2340 (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]. 22.08/23.24 2341 $T # label(t39_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2342 $T # label(t41_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2343 (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)))) & (all A (v3_ordinal1(A) -> (p1_s1_ordinal2(A) -> p1_s1_ordinal2(k1_ordinal1(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]. 22.08/23.24 2344 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) & r2_hidden(k1_xboole_0,A) -> r1_ordinal1(k5_ordinal2,A)))) # label(t19_ordinal2_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2345 (all A all B ((all C ((exists D (v4_ordinal1(D) & C = D & v3_ordinal1(D))) & r2_hidden(C,A) <-> r2_hidden(C,B))) <-> B = k3_ordinal2(A))) # label(d3_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2346 (all A (v3_ordinal1(A) -> k15_ordinal2(k4_ordinal2,A) = A & A = k15_ordinal2(A,k4_ordinal2))) # label(t56_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2347 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_ordinal2(A),k2_ordinal2(B)))) # label(t11_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2348 (all A r1_tarski(k3_ordinal2(A),A)) # label(t13_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2349 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) -> (k1_ordinal1(A) = k1_relat_1(B) -> k1_ordinal2(B) = k1_funct_1(B,A)))))) # label(t7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2350 (all A (v3_ordinal1(A) -> k14_ordinal2(A,k4_ordinal2) = k1_ordinal1(A))) # label(t48_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.24 2351 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> -((exists C (v1_ordinal2(C) & k1_ordinal2(C) = B & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s13_ordinal2(D,k1_funct_1(C,D))))) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(f1_s13_ordinal2)) & v4_ordinal1(D) -> k1_xboole_0 = D | k1_funct_1(C,D) = f4_s13_ordinal2(D,k2_ordinal1(C,D))))) & k1_funct_1(C,k1_xboole_0) = f2_s13_ordinal2 & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_relat_1(C))) & A != B & (exists C (v5_ordinal1(C) & v1_ordinal2(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) -> f4_s13_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_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_funct_1(C) & v1_relat_1(C)))))))) # label(s13_ordinal2_AndLHS) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2352 (exists A ((exists B (v1_relat_1(B) & v1_ordinal2(B) & A = k1_ordinal2(B) & k1_funct_1(B,k1_xboole_0) = f2_s13_ordinal2 & (all C (v3_ordinal1(C) -> (v4_ordinal1(C) & r2_hidden(C,k1_ordinal1(f1_s13_ordinal2)) -> C = k1_xboole_0 | f4_s13_ordinal2(C,k2_ordinal1(B,C)) = k1_funct_1(B,C)))) & (all C (v3_ordinal1(C) -> (r2_hidden(k1_ordinal1(C),k1_ordinal1(f1_s13_ordinal2)) -> k1_funct_1(B,k1_ordinal1(C)) = f3_s13_ordinal2(C,k1_funct_1(B,C))))) & k1_ordinal1(f1_s13_ordinal2) = k1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B))) & v3_ordinal1(A))) # label(s13_ordinal2_AndRHS) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2353 (all A (v3_ordinal1(A) -> (exists B (v3_ordinal1(B) & v4_ordinal1(B) & r2_hidden(A,B))))) # label(t16_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2354 (all A (v5_ordinal1(A) & v1_funct_1(A) & v1_relat_1(A) -> k7_ordinal2(k2_relat_1(A)) = k8_ordinal2(A))) # label(d9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2355 (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]. 22.08/23.25 2356 (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]. 22.08/23.25 2357 (all A (v3_ordinal1(A) -> (all B (v1_relat_1(B) & v1_ordinal2(B) & v5_ordinal1(B) & v1_funct_1(B) -> k13_ordinal2(A,B) = k12_ordinal2(k2_ordinal1(B,A)))))) # label(d15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2358 $T # label(t38_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2359 (all A k1_setfam_1(k2_ordinal2(A)) = k6_ordinal2(A)) # label(d6_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2360 (all A (r2_hidden(A,k5_ordinal2) <-> v4_ordinal2(A))) # label(d21_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2361 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) -> (v3_ordinal2(A) <-> (all B (v3_ordinal1(B) -> (all C (v3_ordinal1(C) -> (v4_ordinal1(B) & C = k1_funct_1(A,B) & r2_hidden(B,k1_relat_1(A)) -> r1_ordinal2(C,k2_ordinal1(A,B)) | k1_xboole_0 = B)))))))) # label(d17_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2362 (exists A (v1_relat_1(A) & v1_funct_1(A) & f1_s5_ordinal2 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(k1_ordinal1(B),f1_s5_ordinal2) -> k1_funct_1(A,k1_ordinal1(B)) = f3_s5_ordinal2(B,k1_funct_1(A,B))))) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s5_ordinal2) & v4_ordinal1(B) -> B = k1_xboole_0 | f4_s5_ordinal2(B,k2_ordinal1(A,B)) = k1_funct_1(A,B)))) & (r2_hidden(k1_xboole_0,f1_s5_ordinal2) -> k1_funct_1(A,k1_xboole_0) = f2_s5_ordinal2) & v5_ordinal1(A))) # label(s5_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2363 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> ((exists C (v1_relat_1(C) & v1_ordinal2(C) & (all D (v3_ordinal1(D) -> (r2_hidden(D,k1_ordinal1(A)) & v4_ordinal1(D) -> D = k1_xboole_0 | k1_funct_1(C,D) = f4_s14_ordinal2(D,k2_ordinal1(C,D))))) & (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))))) & f2_s14_ordinal2 = k1_funct_1(C,k1_xboole_0) & k1_relat_1(C) = k1_ordinal1(A) & k1_ordinal2(C) = B & v5_ordinal1(C) & v1_funct_1(C))) <-> f1_s14_ordinal2(A) = B))))) -> f2_s14_ordinal2 = f1_s14_ordinal2(k1_xboole_0) # label(s14_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2364 (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]. 22.08/23.25 2365 (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]. 22.08/23.25 2366 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> v3_ordinal1(k10_ordinal2(A)))) # label(dt_k10_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2367 (all A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) -> v3_ordinal1(k9_ordinal2(A)))) # label(dt_k9_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2368 (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]. 22.08/23.25 2369 (all A all B (v3_ordinal1(B) -> v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_ordinal2(k2_funcop_1(A,B)))) # label(fc4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2370 (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]. 22.08/23.25 2371 (all A (v3_ordinal1(A) -> (exists B (v3_ordinal1(B) & (exists C (v3_ordinal1(C) & v4_ordinal1(B) & A = k14_ordinal2(B,C) & v4_ordinal2(C))))))) # label(t65_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2372 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & k1_ordinal1(A) = k1_relat_1(C) & f2_s8_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 | f4_s8_ordinal2(D,k2_ordinal1(C,D)) = k1_funct_1(C,D)))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = f3_s8_ordinal2(D,k1_funct_1(C,D))))) & B = k1_ordinal2(C))) <-> B = f1_s8_ordinal2(A))))) -> f2_s8_ordinal2 = f1_s8_ordinal2(k1_xboole_0) # label(s8_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2373 (all A v3_ordinal1(k7_ordinal2(A))) # label(dt_k7_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2374 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v1_funct_1(A) -> v3_ordinal1(k12_ordinal2(A)))) # label(dt_k12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2375 (all A r1_ordinal1(k6_ordinal2(A),k7_ordinal2(A))) # label(t32_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2376 (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]. 22.08/23.25 2377 (all A (v3_ordinal1(A) -> k3_tarski(k1_ordinal1(A)) = A)) # label(t2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2378 (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]. 22.08/23.25 2379 $T # label(dt_k2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2380 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> k1_funct_1(A,k3_tarski(k1_relat_1(A))) = k1_ordinal2(A))) # label(d1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2381 $T # label(t18_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2382 (all A (v3_ordinal1(A) -> k15_ordinal2(k1_xboole_0,A) = k1_xboole_0)) # label(t52_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.25 2383 $T # label(t40_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2384 $T # label(t64_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2385 (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) -> k15_ordinal2(D,B) = k1_funct_1(C,D)))) -> k15_ordinal2(A,B) = k3_tarski(k8_ordinal2(C))))) | k1_xboole_0 = A))))) # label(t54_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2386 (all A (v3_ordinal1(A) -> (all B (m1_ordinal1(B,A) -> v1_ordinal2(B))))) # label(cc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2387 (exists A (v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & k1_relat_1(A) = f1_s2_ordinal2 & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s2_ordinal2) -> f2_s2_ordinal2(B) = k1_funct_1(A,B)))))) # label(s2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2388 (exists A (v1_ordinal1(A) & v4_ordinal1(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(rc1_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2389 (all A r1_tarski(k3_ordinal2(A),k2_ordinal2(A))) # label(t15_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2390 (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]. 22.08/23.29 2391 $T # label(t12_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2392 (all A all B (v1_relat_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v3_ordinal1(B) & v1_funct_1(A) -> v1_funct_1(k7_relat_1(A,B)) & v1_ordinal2(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc2_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2393 k1_relat_1(f5_s4_ordinal2) = f1_s4_ordinal2 & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f5_s4_ordinal2,k1_xboole_0)) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> f3_s4_ordinal2(A,k1_funct_1(f5_s4_ordinal2,A)) = k1_funct_1(f5_s4_ordinal2,k1_ordinal1(A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> k1_funct_1(f5_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f5_s4_ordinal2,A)) | A = k1_xboole_0))) & (all A (v3_ordinal1(A) -> (r2_hidden(k1_ordinal1(A),f1_s4_ordinal2) -> k1_funct_1(f6_s4_ordinal2,k1_ordinal1(A)) = f3_s4_ordinal2(A,k1_funct_1(f6_s4_ordinal2,A))))) & (all A (v3_ordinal1(A) -> (r2_hidden(A,f1_s4_ordinal2) & v4_ordinal1(A) -> k1_funct_1(f6_s4_ordinal2,A) = f4_s4_ordinal2(A,k2_ordinal1(f6_s4_ordinal2,A)) | A = k1_xboole_0))) & (r2_hidden(k1_xboole_0,f1_s4_ordinal2) -> f2_s4_ordinal2 = k1_funct_1(f6_s4_ordinal2,k1_xboole_0)) & f1_s4_ordinal2 = k1_relat_1(f6_s4_ordinal2) -> f5_s4_ordinal2 = f6_s4_ordinal2 # label(s4_ordinal2) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2394 (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]. 22.08/23.29 2395 $T # label(t10_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2396 (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]. 22.08/23.29 2397 (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]. 22.08/23.29 2398 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (v1_finset_1(A) -> v1_finset_1(k9_relat_1(B,A))))) # label(t17_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2399 (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]. 22.08/23.29 2400 $T # label(t3_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2401 (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]. 22.08/23.29 2402 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_xboole_0(A,B)))) # label(t14_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2403 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k5_xboole_0(A,B)))) # label(fc17_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2404 (all A all B all C (v1_finset_1(C) & v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k3_zfmisc_1(A,B,C)))) # label(t20_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2405 (all A all B (v1_finset_1(k2_tarski(A,B)) & -v1_xboole_0(k2_tarski(A,B)))) # label(fc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2406 (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 -((all D (r1_tarski(C,D) & r2_hidden(D,B) -> D = C)) & r2_hidden(C,B)))))))) # label(t18_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2407 (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]. 22.08/23.29 2408 (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]. 22.08/23.29 2409 (all A -(v6_ordinal1(A) & (all B -(r2_hidden(B,A) & (all C (r2_hidden(C,A) -> r1_tarski(B,C))))) & k1_xboole_0 != A & v1_finset_1(A))) # label(t30_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2410 (all A (v1_finset_1(A) <-> v1_finset_1(k1_zfmisc_1(A)))) # label(t24_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2411 (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]. 22.08/23.29 2412 (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]. 22.08/23.29 2413 (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]. 22.08/23.29 2414 (all A all B (r2_hidden(A,f1_s2_finset_1) & p1_s2_finset_1(B) & r1_tarski(B,f1_s2_finset_1) -> p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))))) & p1_s2_finset_1(k1_xboole_0) & 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]. 22.08/23.29 2415 (all A (v1_xboole_0(A) -> v1_finset_1(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2416 (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]. 22.08/23.29 2417 $T # label(t8_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2418 (all A ((all B (r2_hidden(B,A) -> v1_finset_1(B))) & v1_finset_1(A) <-> v1_finset_1(k3_tarski(A)))) # label(t25_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2419 (all A all B (v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k2_zfmisc_1(A,B)))) # label(fc14_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2420 (all A (v1_finset_1(A) <-> (exists B (v1_relat_1(B) & v1_funct_1(B) & k2_relat_1(B) = A & r2_hidden(k1_relat_1(B),k5_ordinal2))))) # label(d1_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2421 (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]. 22.08/23.29 2422 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k2_xboole_0(A,B)))) # label(fc9_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2423 $T # label(t9_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2424 $T # label(t4_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2425 (all A -(A != k1_xboole_0 & (all B -((all C (r2_hidden(C,A) -> r1_tarski(C,B))) & r2_hidden(B,A))) & v6_ordinal1(A) & v1_finset_1(A))) # label(t31_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2426 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & v1_finset_1(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2427 (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]. 22.08/23.29 2428 (all A (v1_finset_1(k1_tarski(A)) & -v1_xboole_0(k1_tarski(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2429 (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]. 22.08/23.29 2430 (all A (-v1_xboole_0(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) & v1_finset_1(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2431 $T # label(t12_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2432 (all A all B all C all D (v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(D) & v1_finset_1(C) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(fc16_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2433 (all A all B (v1_relat_1(A) & v1_finset_1(B) & v1_funct_1(A) -> v1_finset_1(k9_relat_1(A,B)))) # label(fc13_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2434 (all A all B all C all D (v1_finset_1(D) & v1_finset_1(C) & v1_finset_1(B) & v1_finset_1(A) -> v1_finset_1(k4_zfmisc_1(A,B,C,D)))) # label(t21_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2435 (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]. 22.08/23.29 2436 (exists A (v1_finset_1(A) & -v1_xboole_0(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2437 (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]. 22.08/23.29 2438 $T # label(t2_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2439 (exists A (v1_funct_1(A) & f1_s1_finset_1 = k1_relat_1(A) & (all B (v3_ordinal1(B) -> (r2_hidden(B,f1_s1_finset_1) -> (-p1_s1_finset_1(B) -> k1_funct_1(A,B) = f3_s1_finset_1(B)) & (p1_s1_finset_1(B) -> f2_s1_finset_1(B) = k1_funct_1(A,B))))) & v1_relat_1(A))) # label(s1_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2440 $T # label(t5_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2441 (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]. 22.08/23.29 2442 (all A all B (r1_tarski(A,B) & v1_finset_1(B) -> v1_finset_1(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2443 (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]. 22.08/23.29 2444 (all A all B all C v1_finset_1(k1_enumset1(A,B,C))) # label(fc3_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2445 (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]. 22.08/23.29 2446 $T # label(t1_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2447 (all A exists B (v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) & v3_ordinal1(B) & v2_ordinal1(B) & v1_relat_1(B) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2448 $T # label(t6_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2449 $T # label(t7_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2450 $T # label(t11_finset_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2451 (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]. 22.08/23.29 2452 (all A ((exists B (p1_s19_fraenkel(B,f4_s19_fraenkel) & A = f3_s19_fraenkel(B,f4_s19_fraenkel) & m1_subset_1(B,f1_s19_fraenkel))) <-> r2_hidden(A,a_0_35_fraenkel))) # label(fraenkel_a_0_35_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2453 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> (all E (m1_subset_1(E,k1_funct_2(C,D)) -> (exists F (k7_relat_1(F,C) = E & m2_fraenkel(F,B,A,k1_fraenkel(B,A)))))) | k1_funct_2(C,D) = k1_xboole_0)))) # label(t14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2454 (all A all B (-v1_xboole_0(B) -> k1_fraenkel(A,B) = k1_funct_2(A,B))) # label(redefinition_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2455 $T # label(t9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2456 (all A (r2_hidden(A,a_0_31_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s16_fraenkel) & m1_subset_1(C,f2_s16_fraenkel) & p2_s16_fraenkel(B,C) & A = f3_s16_fraenkel(B,C))))) # label(fraenkel_a_0_31_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2457 (all A (m1_subset_1(A,f1_s2_fraenkel) -> (all B (m1_subset_1(B,f2_s2_fraenkel) -> (p1_s2_fraenkel(A,B) -> p2_s2_fraenkel(A,B)))))) -> r1_tarski(a_0_2_fraenkel,a_0_3_fraenkel) # label(s2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2458 $T # label(t1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2459 (all A (m1_subset_1(A,f1_s7_fraenkel) -> (all B (m1_subset_1(B,f2_s7_fraenkel) -> f3_s7_fraenkel(A,B) = f4_s7_fraenkel(A,B))))) -> a_0_12_fraenkel = a_0_13_fraenkel # label(s7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2460 (all A (r2_hidden(A,a_0_27_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & m1_subset_1(C,f2_s15_fraenkel) & r2_hidden(B,a_0_28_fraenkel) & p1_s15_fraenkel(B,C) & f3_s15_fraenkel(B,C) = A)))) # label(fraenkel_a_0_27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2461 (all A (-v1_xboole_0(A) -> (all B all C all D (r1_tarski(D,A) & r1_tarski(C,B) -> k1_xboole_0 = k1_funct_2(C,D) | (all E (m1_subset_1(E,k1_funct_2(C,D)) -> v1_funct_1(E) & m2_relset_1(E,B,A))))))) # label(t6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2462 (all A ((exists B (r2_hidden(B,f3_s9_fraenkel) & p2_s9_fraenkel(B) & k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f5_s9_fraenkel,B) = A & m1_subset_1(B,f1_s9_fraenkel))) <-> r2_hidden(A,a_0_17_fraenkel))) # label(fraenkel_a_0_17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2463 (all A (r2_hidden(A,a_0_5_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & p2_s3_fraenkel(B) & f2_s3_fraenkel(B) = A)))) # label(fraenkel_a_0_5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2464 (all A all B all C (m1_fraenkel(C,A,B) -> v1_fraenkel(C) & -v1_xboole_0(C))) # label(dt_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2465 (all A (v1_fraenkel(A) -> (all B (m1_subset_1(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(cc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2466 (all A all B v1_fraenkel(k1_funct_2(A,B))) # label(fc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2467 (all A (m1_subset_1(A,f1_s23_fraenkel) -> p1_s23_fraenkel(A,A))) & (all A (m1_subset_1(A,f1_s23_fraenkel) -> (all B (m1_subset_1(B,f1_s23_fraenkel) -> (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(B,C) & p1_s23_fraenkel(A,B) -> p1_s23_fraenkel(A,C)))))))) -> (all A (m1_subset_1(A,f1_s23_fraenkel) -> -((all B (m1_subset_1(B,f1_s23_fraenkel) -> -(r2_hidden(B,f2_s23_fraenkel) & p1_s23_fraenkel(B,A) & (all C (m1_subset_1(C,f1_s23_fraenkel) -> (p1_s23_fraenkel(C,B) & r2_hidden(C,f2_s23_fraenkel) -> p1_s23_fraenkel(B,C))))))) & r2_hidden(A,f2_s23_fraenkel)))) # label(s23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2468 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_fraenkel(k1_funct_2(A,B)) & v1_finset_1(k1_funct_2(A,B)))) # label(fc2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2469 (all A ((exists B exists C (m1_subset_1(B,f1_s19_fraenkel) & f3_s19_fraenkel(B,C) = A & p2_s19_fraenkel(B,C) & m1_subset_1(C,f2_s19_fraenkel))) <-> r2_hidden(A,a_0_34_fraenkel))) # label(fraenkel_a_0_34_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2470 (all A ((exists B exists C (m1_subset_1(B,f1_s4_fraenkel) & m1_subset_1(C,f2_s4_fraenkel) & A = f3_s4_fraenkel(B,C) & p1_s4_fraenkel(B,C))) <-> r2_hidden(A,a_0_6_fraenkel))) # label(fraenkel_a_0_6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2471 (all A ((exists B exists C (m1_subset_1(B,f1_s2_fraenkel) & m1_subset_1(C,f2_s2_fraenkel) & p2_s2_fraenkel(B,C) & f3_s2_fraenkel(B,C) = A)) <-> r2_hidden(A,a_0_3_fraenkel))) # label(fraenkel_a_0_3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2472 (all A (v1_fraenkel(A) -> (all B (r1_tarski(B,A) -> v1_fraenkel(B))))) # label(t17_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2473 (all A (r2_hidden(A,a_0_20_fraenkel) <-> (exists B exists C (p1_s12_fraenkel(B,C) & A = f3_s12_fraenkel(B,C) & m1_subset_1(C,f2_s12_fraenkel) & m1_subset_1(B,f1_s12_fraenkel))))) # label(fraenkel_a_0_20_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2474 (all A (m1_subset_1(A,f1_s19_fraenkel) -> (all B (m1_subset_1(B,f2_s19_fraenkel) -> (p1_s19_fraenkel(A,B) & f4_s19_fraenkel = B <-> p2_s19_fraenkel(A,B)))))) -> a_0_35_fraenkel = a_0_34_fraenkel # label(s19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2475 (all A all B all C (m2_relset_1(C,A,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> m1_fraenkel(k2_setwiseo(k1_zfmisc_1(k2_zfmisc_1(A,B)),C),A,B))) # label(t10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2476 (all A (m1_subset_1(A,f1_s4_fraenkel) -> (all B (m1_subset_1(B,f2_s4_fraenkel) -> (p1_s4_fraenkel(A,B) <-> p2_s4_fraenkel(A,B)))))) -> a_0_6_fraenkel = a_0_7_fraenkel # label(s4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2477 (all A (r2_hidden(A,a_0_0_fraenkel) <-> (exists B (p1_s1_fraenkel(B) & A = f2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))))) # label(fraenkel_a_0_0_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2478 (all A (r2_hidden(A,a_0_39_fraenkel) <-> (exists B exists C (A = f5_s22_fraenkel(B,C) & r2_hidden(C,f4_s22_fraenkel) & r2_hidden(B,f3_s22_fraenkel) & m1_subset_1(C,f2_s22_fraenkel) & m1_subset_1(B,f1_s22_fraenkel))))) # label(fraenkel_a_0_39_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2479 (all A (r2_hidden(A,a_0_18_fraenkel) <-> (exists B (m1_subset_1(B,f1_s10_fraenkel) & p1_s10_fraenkel(B) & B = A)))) # label(fraenkel_a_0_18_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2480 (all A ((exists B exists C (m1_subset_1(B,f1_s16_fraenkel) & m1_subset_1(C,f2_s16_fraenkel) & f3_s16_fraenkel(B,C) = A & p1_s16_fraenkel(B,C))) <-> r2_hidden(A,a_0_30_fraenkel))) # label(fraenkel_a_0_30_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2481 (all A (r2_hidden(A,a_0_11_fraenkel) <-> (exists B (m1_subset_1(B,f1_s6_fraenkel) & p1_s6_fraenkel(B) & f3_s6_fraenkel(B) = A)))) # label(fraenkel_a_0_11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2482 (all A ((exists B exists C (m1_subset_1(C,f2_s13_fraenkel) & p1_s13_fraenkel(B,C) & A = f4_s13_fraenkel(B,C) & m1_subset_1(B,f1_s13_fraenkel))) <-> r2_hidden(A,a_0_22_fraenkel))) # label(fraenkel_a_0_22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2483 (all A all B all C (-v1_xboole_0(C) & v1_fraenkel(C) -> (m1_fraenkel(C,A,B) <-> (all D (m1_subset_1(D,C) -> m2_relset_1(D,A,B) & v1_funct_2(D,A,B) & v1_funct_1(D)))))) # label(d2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2484 (all A ((exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & f4_s7_fraenkel(B,C) = A & p1_s7_fraenkel(B,C) & m1_subset_1(B,f1_s7_fraenkel))) <-> r2_hidden(A,a_0_13_fraenkel))) # label(fraenkel_a_0_13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2485 (all A all B (-v1_xboole_0(B) -> m1_fraenkel(k1_fraenkel(A,B),A,B))) # label(dt_k1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2486 (all A (-v1_xboole_0(A) -> (all B m1_fraenkel(k1_funct_2(B,A),B,A)))) # label(t11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2487 (all A all B (v1_finset_1(A) & v1_finset_1(B) -> v1_finset_1(k1_funct_2(A,B)))) # label(t16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2488 (all A (r2_hidden(A,a_0_10_fraenkel) <-> (exists B (m1_subset_1(B,f1_s6_fraenkel) & p1_s6_fraenkel(B) & A = f2_s6_fraenkel(B))))) # label(fraenkel_a_0_10_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2489 (all A (m1_subset_1(A,f1_s12_fraenkel) -> (all B (m1_subset_1(B,f2_s12_fraenkel) -> (p1_s12_fraenkel(A,B) -> p2_s12_fraenkel(f3_s12_fraenkel(A,B))))))) -> (all A (r2_hidden(A,a_0_20_fraenkel) -> p2_s12_fraenkel(A))) # label(s12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2490 (all A ((exists B exists C (m1_subset_1(C,f2_s4_fraenkel) & f3_s4_fraenkel(B,C) = A & p2_s4_fraenkel(B,C) & m1_subset_1(B,f1_s4_fraenkel))) <-> r2_hidden(A,a_0_7_fraenkel))) # label(fraenkel_a_0_7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2491 (all A ((exists B exists C (m1_subset_1(B,f1_s11_fraenkel) & f3_s11_fraenkel(B,C) = A & p1_s11_fraenkel(B,C) & m1_subset_1(C,f2_s11_fraenkel))) <-> r2_hidden(A,a_0_19_fraenkel))) # label(fraenkel_a_0_19_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2492 (all A all B all C (-v1_xboole_0(B) & m1_fraenkel(C,A,B) -> (exists D m2_fraenkel(D,A,B,C)))) # label(existence_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2493 (all A ((exists B exists C (p2_s8_fraenkel(B,C) & f3_s8_fraenkel(C,B) = A & m1_subset_1(C,f2_s8_fraenkel) & m1_subset_1(B,f1_s8_fraenkel))) <-> r2_hidden(A,a_0_15_fraenkel))) # label(fraenkel_a_0_15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2494 (all A ((exists B (p2_s14_fraenkel(B) & B = A & m1_subset_1(B,f1_s14_fraenkel))) <-> r2_hidden(A,a_0_25_fraenkel))) # label(fraenkel_a_0_25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2495 (all A (r2_hidden(A,a_0_19_fraenkel) -> p2_s11_fraenkel(A))) -> (all A (m1_subset_1(A,f1_s11_fraenkel) -> (all B (m1_subset_1(B,f2_s11_fraenkel) -> (p1_s11_fraenkel(A,B) -> p2_s11_fraenkel(f3_s11_fraenkel(A,B))))))) # label(s11_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2496 (all A (r2_hidden(A,a_0_36_fraenkel) <-> (exists B exists C (f3_s20_fraenkel(B,C) = A & C = f4_s20_fraenkel & p1_s20_fraenkel(B,C) & m1_subset_1(C,f2_s20_fraenkel) & m1_subset_1(B,f1_s20_fraenkel))))) # label(fraenkel_a_0_36_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2497 (all A (r2_hidden(A,a_0_38_fraenkel) <-> (exists B (f3_s21_fraenkel(B) = A & r2_hidden(B,f2_s21_fraenkel) & m1_subset_1(B,f1_s21_fraenkel))))) # label(fraenkel_a_0_38_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2498 (all A ((exists B (p1_s5_fraenkel(B) & A = f3_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))) <-> r2_hidden(A,a_0_9_fraenkel))) # label(fraenkel_a_0_9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2499 (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> (p2_s8_fraenkel(A,B) <-> p1_s8_fraenkel(A,B)))))) & (all A (m1_subset_1(A,f1_s8_fraenkel) -> (all B (m1_subset_1(B,f2_s8_fraenkel) -> f3_s8_fraenkel(B,A) = f3_s8_fraenkel(A,B))))) -> a_0_14_fraenkel = a_0_15_fraenkel # label(s8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2500 (all A ((exists B (m1_subset_1(B,f1_s17_fraenkel) & A = f3_s17_fraenkel(B) & p1_s17_fraenkel(B) & r2_hidden(f3_s17_fraenkel(B),f2_s17_fraenkel))) <-> r2_hidden(A,a_0_32_fraenkel))) # label(fraenkel_a_0_32_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2501 (all A (r2_hidden(A,a_0_24_fraenkel) <-> (exists B (r2_hidden(B,a_0_25_fraenkel) & p1_s14_fraenkel(B) & f2_s14_fraenkel(B) = A & m1_subset_1(B,f1_s14_fraenkel))))) # label(fraenkel_a_0_24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2502 (all A (m1_subset_1(A,f1_s6_fraenkel) -> (p1_s6_fraenkel(A) -> f3_s6_fraenkel(A) = f2_s6_fraenkel(A)))) -> a_0_10_fraenkel = a_0_11_fraenkel # label(s6_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2503 v1_finset_1(f3_s22_fraenkel) & v1_finset_1(f4_s22_fraenkel) -> v1_finset_1(a_0_39_fraenkel) # label(s22_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2504 (all A (m1_subset_1(A,f1_s26_fraenkel) -> -((all B (m1_subset_1(B,f2_s26_fraenkel) -> -p1_s26_fraenkel(A,B))) & r2_hidden(A,f3_s26_fraenkel)))) -> (exists A (v1_funct_2(A,f1_s26_fraenkel,f2_s26_fraenkel) & m2_relset_1(A,f1_s26_fraenkel,f2_s26_fraenkel) & (all B (m1_subset_1(B,f1_s26_fraenkel) -> (r2_hidden(B,f3_s26_fraenkel) -> p1_s26_fraenkel(B,k8_funct_2(f1_s26_fraenkel,f2_s26_fraenkel,A,B))))) & v1_funct_1(A))) # label(s26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2505 $T # label(t12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2506 (all A (m1_subset_1(A,f1_s27_fraenkel) -> -((all B (m1_subset_1(B,f2_s27_fraenkel) -> -p1_s27_fraenkel(A,B))) & r2_hidden(A,f3_s27_fraenkel)))) -> (exists A (m2_fraenkel(A,f1_s27_fraenkel,f2_s27_fraenkel,k1_fraenkel(f1_s27_fraenkel,f2_s27_fraenkel)) & (all B (m1_subset_1(B,f1_s27_fraenkel) -> (r2_hidden(B,f3_s27_fraenkel) -> p1_s27_fraenkel(B,k8_funct_2(f1_s27_fraenkel,f2_s27_fraenkel,A,B))))))) # label(s27_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2507 (all A (r2_hidden(A,a_0_33_fraenkel) <-> (exists B (p1_s18_fraenkel(B) & -r2_hidden(f3_s18_fraenkel(B),f2_s18_fraenkel) & A = f3_s18_fraenkel(B) & m1_subset_1(B,f1_s18_fraenkel))))) # label(fraenkel_a_0_33_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2508 (exists A (m1_subset_1(A,k5_finsub_1(f1_s24_fraenkel)) & (all B (m1_subset_1(B,f1_s24_fraenkel) -> ((exists C (r2_hidden(C,f3_s24_fraenkel) & B = f4_s24_fraenkel(C) & p1_s24_fraenkel(B,C) & m1_subset_1(C,f2_s24_fraenkel))) <-> r2_hidden(B,A)))))) # label(s24_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2509 (all A (r2_hidden(A,a_0_14_fraenkel) <-> (exists B exists C (p1_s8_fraenkel(B,C) & A = f3_s8_fraenkel(B,C) & m1_subset_1(C,f2_s8_fraenkel) & m1_subset_1(B,f1_s8_fraenkel))))) # label(fraenkel_a_0_14_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2510 (all A (m1_subset_1(A,f1_s3_fraenkel) -> (p2_s3_fraenkel(A) <-> p1_s3_fraenkel(A)))) -> a_0_4_fraenkel = a_0_5_fraenkel # label(s3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2511 (all A (m1_subset_1(A,f1_s5_fraenkel) -> f2_s5_fraenkel(A) = f3_s5_fraenkel(A))) -> a_0_8_fraenkel = a_0_9_fraenkel # label(s5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2512 (all A (r2_hidden(A,a_0_4_fraenkel) <-> (exists B (m1_subset_1(B,f1_s3_fraenkel) & p1_s3_fraenkel(B) & A = f2_s3_fraenkel(B))))) # label(fraenkel_a_0_4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2513 (all A ((exists B (A = B & p2_s15_fraenkel(B) & m1_subset_1(B,f1_s15_fraenkel))) <-> r2_hidden(A,a_0_28_fraenkel))) # label(fraenkel_a_0_28_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2514 (all A ((exists B exists C (m1_subset_1(B,f1_s13_fraenkel) & m1_subset_1(C,f2_s13_fraenkel) & A = f4_s13_fraenkel(B,C) & p2_s13_fraenkel(f4_s13_fraenkel(B,C)) & p1_s13_fraenkel(B,C))) <-> r2_hidden(A,a_0_23_fraenkel))) # label(fraenkel_a_0_23_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2515 $T # label(t7_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2516 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m1_subset_1(D,C) <-> m2_fraenkel(D,A,B,C))))) # label(redefinition_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2517 (all A (r2_hidden(A,a_0_12_fraenkel) <-> (exists B exists C (m1_subset_1(C,f2_s7_fraenkel) & f3_s7_fraenkel(B,C) = A & p1_s7_fraenkel(B,C) & m1_subset_1(B,f1_s7_fraenkel))))) # label(fraenkel_a_0_12_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2518 (all A (v1_fraenkel(A) <-> (all B (r2_hidden(B,A) -> v1_funct_1(B) & v1_relat_1(B))))) # label(d1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2519 (all A ((exists B (m1_subset_1(B,f1_s20_fraenkel) & A = f3_s20_fraenkel(B,f4_s20_fraenkel) & p1_s20_fraenkel(B,f4_s20_fraenkel))) <-> r2_hidden(A,a_0_37_fraenkel))) # label(fraenkel_a_0_37_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.29 2520 (all A (m1_subset_1(A,f1_s16_fraenkel) -> (all B (m1_subset_1(B,f2_s16_fraenkel) -> -(p1_s16_fraenkel(A,B) & (all C (m1_subset_1(C,f1_s16_fraenkel) -> -(p2_s16_fraenkel(C,B) & f3_s16_fraenkel(C,B) = f3_s16_fraenkel(A,B))))))))) -> r1_tarski(a_0_30_fraenkel,a_0_31_fraenkel) # label(s16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2521 (all A (r2_hidden(A,a_0_29_fraenkel) <-> (exists B exists C (m1_subset_1(B,f1_s15_fraenkel) & m1_subset_1(C,f2_s15_fraenkel) & A = f3_s15_fraenkel(B,C) & p1_s15_fraenkel(B,C) & p2_s15_fraenkel(B))))) # label(fraenkel_a_0_29_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2522 (all A (m1_subset_1(A,f1_s1_fraenkel) -> (p1_s1_fraenkel(A) -> p2_s1_fraenkel(A)))) -> r1_tarski(a_0_0_fraenkel,a_0_1_fraenkel) # label(s1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2523 (all A (r2_hidden(A,a_0_8_fraenkel) <-> (exists B (p1_s5_fraenkel(B) & A = f2_s5_fraenkel(B) & m1_subset_1(B,f1_s5_fraenkel))))) # label(fraenkel_a_0_8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2524 (exists A (v1_fraenkel(A) & -v1_xboole_0(A))) # label(rc1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2525 (all A ((exists B (r1_tarski(k2_funct_2(f1_s25_fraenkel,f2_s25_fraenkel,B,f3_s25_fraenkel),f4_s25_fraenkel) & f5_s25_fraenkel(B) = A & m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)))) <-> r2_hidden(A,a_0_40_fraenkel))) # label(fraenkel_a_0_40_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2526 $T # label(t4_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2527 (all A (r2_hidden(A,a_0_1_fraenkel) <-> (exists B (A = f2_s1_fraenkel(B) & p2_s1_fraenkel(B) & m1_subset_1(B,f1_s1_fraenkel))))) # label(fraenkel_a_0_1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2528 k7_relat_1(f4_s9_fraenkel,f3_s9_fraenkel) = k7_relat_1(f5_s9_fraenkel,f3_s9_fraenkel) & (all A (m1_subset_1(A,f1_s9_fraenkel) -> (r2_hidden(A,f3_s9_fraenkel) -> (p1_s9_fraenkel(A) <-> p2_s9_fraenkel(A))))) -> a_0_17_fraenkel = a_0_16_fraenkel # label(s9_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2529 $T # label(t2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2530 (all A (r2_hidden(A,a_0_2_fraenkel) <-> (exists B exists C (A = f3_s2_fraenkel(B,C) & p1_s2_fraenkel(B,C) & m1_subset_1(C,f2_s2_fraenkel) & m1_subset_1(B,f1_s2_fraenkel))))) # label(fraenkel_a_0_2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2531 (all A (r2_hidden(A,a_0_26_fraenkel) <-> (exists B (m1_subset_1(B,f1_s14_fraenkel) & f2_s14_fraenkel(B) = A & p1_s14_fraenkel(B) & p2_s14_fraenkel(B))))) # label(fraenkel_a_0_26_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2532 v1_finset_1(f2_s21_fraenkel) -> v1_finset_1(a_0_38_fraenkel) # label(s21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2533 v1_finset_1(f3_s25_fraenkel) & v1_finset_1(f4_s25_fraenkel) & (all A (m2_fraenkel(A,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (all B (m2_fraenkel(B,f1_s25_fraenkel,f2_s25_fraenkel,k1_fraenkel(f1_s25_fraenkel,f2_s25_fraenkel)) -> (k7_relat_1(B,f3_s25_fraenkel) = k7_relat_1(A,f3_s25_fraenkel) -> f5_s25_fraenkel(B) = f5_s25_fraenkel(A)))))) -> v1_finset_1(a_0_40_fraenkel) # label(s25_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2534 (all A (-v1_xboole_0(A) -> (all B all C all D (m2_fraenkel(D,B,A,k1_fraenkel(B,A)) -> k7_relat_1(D,k3_xboole_0(B,C)) = k7_relat_1(D,C))))) # label(t15_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2535 (all A all B r1_tarski(k1_funct_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B)))) # label(t5_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2536 $T # label(t13_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2537 (all A (r2_hidden(A,a_0_21_fraenkel) <-> (exists B (p2_s13_fraenkel(B) & r2_hidden(B,a_0_22_fraenkel) & A = B & m1_subset_1(B,f3_s13_fraenkel))))) # label(fraenkel_a_0_21_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2538 (all A all B all C (m1_fraenkel(C,A,B) & -v1_xboole_0(B) -> (all D (m2_fraenkel(D,A,B,C) -> v1_funct_1(D) & m2_relset_1(D,A,B) & v1_funct_2(D,A,B))))) # label(dt_m2_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2539 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (k7_relat_1(C,E) = k7_relat_1(D,E) -> (all F (m1_subset_1(F,A) -> (r2_hidden(F,E) -> k8_funct_2(A,B,D,F) = k8_funct_2(A,B,C,F)))))))))))))) # label(t3_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2540 (all A all B exists C m1_fraenkel(C,A,B)) # label(existence_m1_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2541 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k1_tarski(A)))) # label(t8_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2542 (all A ((exists B (A = k8_funct_2(f1_s9_fraenkel,f2_s9_fraenkel,f4_s9_fraenkel,B) & r2_hidden(B,f3_s9_fraenkel) & p1_s9_fraenkel(B) & m1_subset_1(B,f1_s9_fraenkel))) <-> r2_hidden(A,a_0_16_fraenkel))) # label(fraenkel_a_0_16_fraenkel) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2543 $T # label(dt_k3_numbers) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2544 $T # label(dt_k4_numbers) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2545 $T # label(dt_k2_numbers) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2546 $T # label(dt_k1_numbers) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2547 (all A ((exists B (m1_subset_1(B,k1_funct_2(k2_tarski(np__0,k13_arytm_3),k1_numbers)) & B = A & k1_funct_1(B,k13_arytm_3) = np__0)) <-> r2_hidden(A,a_0_0_numbers))) # label(fraenkel_a_0_0_numbers) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2548 (all A (-v3_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc26_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2549 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc15_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2550 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v2_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) & -v1_xboole_0(k6_xcmplx_0(B,A)))) # label(fc18_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2551 (all A (v1_xreal_0(A) & -v2_xreal_0(A) -> v1_xreal_0(k5_xcmplx_0(A)) & -v2_xreal_0(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)))) # label(fc25_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2552 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2553 (all A (v1_xreal_0(A) -> (all B (v1_xreal_0(B) -> (r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) -> ((exists C (m1_subset_1(C,k2_arytm_2) & (exists D (B = k4_tarski(np__0,D) & r1_arytm_2(D,C) & A = k4_tarski(np__0,C) & m1_subset_1(D,k2_arytm_2))))) <-> r1_xreal_0(A,B))) & -(-(r1_xreal_0(A,B) <-> r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(B,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2)) & r2_hidden(A,k2_zfmisc_1(k1_tarski(np__0),k2_arytm_2))) & -(r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2))) & (r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_arytm_2) -> (r1_xreal_0(A,B) <-> (exists C (m1_subset_1(C,k2_arytm_2) & (exists D (C = A & D = B & r1_arytm_2(C,D) & m1_subset_1(D,k2_arytm_2))))))))))) # label(d2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2554 (all A all B (-v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k7_xcmplx_0(A,B)) & -v2_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc27_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2555 (all A all B (v1_xreal_0(B) & -v3_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)) & v1_xcmplx_0(k7_xcmplx_0(A,B)))) # label(fc29_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2556 (exists A (v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A))) # label(rc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2557 (all A (-v3_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v1_xboole_0(A))) # label(cc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2558 (all A all B (v3_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & -v1_xboole_0(k2_xcmplx_0(A,B)))) # label(fc11_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2559 (all A (v1_xreal_0(A) -> v1_xcmplx_0(A))) # label(cc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2560 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc23_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2561 (all A (v1_xreal_0(A) -> (-r1_xreal_0(np__0,A) <-> v3_xreal_0(A)))) # label(d4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2562 (all A (v2_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(A) & v1_xcmplx_0(A) & -v3_xreal_0(A) & v1_xreal_0(A))) # label(cc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2563 (all A (v1_xreal_0(A) & -v3_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & -v2_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc14_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2564 (all A (-v1_xboole_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) -> v2_xreal_0(A) & v1_xreal_0(A) & v1_xcmplx_0(A))) # label(cc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2565 (all A (v1_xreal_0(A) -> (v2_xreal_0(A) <-> -r1_xreal_0(A,np__0)))) # label(d3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2566 (all A all B (-v3_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) & v1_xreal_0(A) -> -v3_xreal_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc24_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2567 (all A all B (-v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & -v2_xreal_0(k7_xcmplx_0(B,A)))) # label(fc28_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2568 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> r1_xreal_0(A,A))) # label(reflexivity_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2569 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)))) # label(fc4_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2570 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) -> -v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & -v1_xboole_0(k2_xcmplx_0(B,A)))) # label(fc12_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2571 (all A (v4_ordinal2(A) -> v1_xreal_0(A))) # label(cc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2572 (all A all B (v1_xreal_0(A) & -v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & -v2_xreal_0(k3_xcmplx_0(B,A)))) # label(fc22_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2573 (all A (-v2_xreal_0(A) & v1_xreal_0(A) -> -v3_xreal_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc13_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2574 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v3_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & -v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & -v1_xboole_0(k6_xcmplx_0(A,B)))) # label(fc19_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2575 (exists A (v1_xreal_0(A) & -v2_xreal_0(A) & v3_xreal_0(A) & v1_xcmplx_0(A) & -v1_xboole_0(A))) # label(rc3_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2576 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)))) # label(fc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2577 (all A all B (-v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2578 (all A (v1_xreal_0(A) -> v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2579 (all A all B (v1_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) & -v3_xreal_0(A) -> v1_xcmplx_0(k6_xcmplx_0(B,A)) & -v2_xreal_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)))) # label(fc16_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2580 (all A all B (v1_xreal_0(B) & -v2_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc8_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2581 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> r1_xreal_0(B,A) | r1_xreal_0(A,B))) # label(connectedness_r1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2582 (all A (v3_xreal_0(A) & v1_xreal_0(A) -> -v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & -v2_xreal_0(A))) # label(cc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2583 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)))) # label(fc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2584 (all A (-v1_xboole_0(A) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A))) # label(cc6_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2585 (all A all B (v1_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v2_xreal_0(A) -> -v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & -v3_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)))) # label(fc9_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2586 (all A all B (v1_xreal_0(B) & v1_xreal_0(A) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc5_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2587 (all A all B (v3_xreal_0(A) & -v3_xreal_0(B) & v1_xreal_0(B) & v1_xreal_0(A) -> -v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & -v3_xreal_0(k6_xcmplx_0(B,A)))) # label(fc20_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2588 (exists A (v1_xcmplx_0(A) & v2_xreal_0(A) & -v3_xreal_0(A) & v1_xreal_0(A) & -v1_xboole_0(A))) # label(rc2_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2589 (all A all B (v1_xreal_0(A) & -v2_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) -> v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & -v3_xreal_0(k7_xcmplx_0(A,B)))) # label(fc30_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2590 (exists A (v1_xcmplx_0(A) & v1_xreal_0(A))) # label(rc1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2591 (all A (v1_xreal_0(A) & v1_xboole_0(A) -> v1_xreal_0(A) & -v2_xreal_0(A) & -v3_xreal_0(A) & v1_xcmplx_0(A))) # label(cc7_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2592 (all A all B (v1_xreal_0(A) & v2_xreal_0(A) & -v2_xreal_0(B) & v1_xreal_0(B) -> -v1_xboole_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & -v3_xreal_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc17_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2593 (all A all B (-v3_xreal_0(B) & v1_xreal_0(B) & -v2_xreal_0(A) & v1_xreal_0(A) -> v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & -v2_xreal_0(k3_xcmplx_0(A,B)))) # label(fc21_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2594 (all A all B (v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & -v3_xreal_0(B) -> -v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & -v3_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc10_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2595 (all A (v1_xreal_0(A) <-> r2_hidden(A,k1_numbers))) # label(d1_xreal_0) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2596 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k1_real_1(np__1) = B & k1_real_1(np__1) = A | B = np__1 & np__1 = A <-> k3_xcmplx_0(A,B) = np__1))))) # label(t22_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2597 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_int_1(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_xcmplx_0(k3_xcmplx_0(B,A)))) # label(fc7_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2598 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k5_int_1(A,B)))) # label(dt_k5_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2599 $T # label(t73_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2600 $T # label(t15_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2601 $T # label(t9_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2602 (exists A (m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_int_1(A) & v1_xreal_0(A))) # label(rc1_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2603 (all A (v1_xreal_0(A) -> (all B (v4_ordinal2(B) -> (A = k4_xcmplx_0(B) | A = B -> v1_int_1(A)))))) # label(t7_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2604 $T # label(t11_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2605 (all A (v1_xreal_0(A) -> -(-v1_int_1(A) & r1_xreal_0(A,k1_int_1(A))) & -(v1_int_1(A) & -r1_xreal_0(A,k1_int_1(A))))) # label(t48_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2606 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_int_1(k6_int_1(A,B)))) # label(dt_k6_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2607 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k6_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t43_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2608 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(k2_xcmplx_0(A,np__1),B)))))) # label(t20_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2609 $T # label(dt_k3_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2610 $T # label(t14_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2611 (all A (A = k4_numbers <-> (all B (r2_hidden(B,A) <-> -(all C (m2_subset_1(C,k1_numbers,k5_numbers) -> B != C & B != k1_real_1(C))))))) # label(d1_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2612 $T # label(t2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2613 (all A (v1_xreal_0(A) -> m1_subset_1(k4_int_1(A),k1_numbers))) # label(dt_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2614 $T # label(t5_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2615 $T # label(t56_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2616 $T # label(t10_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2617 $T # label(t3_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2618 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & k3_xcmplx_0(A,B) = C -> r1_int_1(D,E,A)))))))))))) # label(t41_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2619 p1_s3_int_1(f1_s3_int_1) & (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) & p1_s3_int_1(A) -> p1_s3_int_1(k6_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> (r1_xreal_0(A,f1_s3_int_1) -> p1_s3_int_1(A)))) # label(s3_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2620 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (k2_int_1(A) = B <-> -r1_xreal_0(k2_xcmplx_0(A,np__1),B) & r1_xreal_0(A,B)))))) # label(d5_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2621 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> np__0 = k4_int_1(A)))) # label(t71_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2622 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r1_xreal_0(A,B) -> r2_hidden(k6_xcmplx_0(B,A),k5_numbers)))))) # label(t18_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2623 (exists A ((all B (v1_int_1(B) -> (r2_hidden(B,A) <-> p1_s1_int_1(B)))) & m1_subset_1(A,k1_zfmisc_1(k4_numbers)))) # label(s1_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2624 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(k2_xcmplx_0(A,B),C,D) <-> r1_int_1(A,k6_xcmplx_0(C,B),D)))))))))) # label(t40_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2625 $T # label(t4_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2626 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k2_int_1(A),np__1),A) & -r1_xreal_0(k2_int_1(A),k6_xcmplx_0(A,np__1)))) # label(t57_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2627 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> r1_xreal_0(np__0,k5_int_1(A,B)))))) # label(t82_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2628 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (k3_xcmplx_0(A,B) = k1_real_1(np__1) <-> np__1 = A & B = k1_real_1(np__1) | k1_real_1(np__1) = A & B = np__1))))) # label(t23_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2629 (all A (v1_xreal_0(A) -> A = k2_xcmplx_0(k1_int_1(A),k4_int_1(A)))) # label(t68_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2630 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & -r1_xreal_0(k4_int_1(A),np__0)) & -(r1_xreal_0(k4_int_1(A),np__0) & -v1_int_1(A)))) # label(t72_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2631 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(A,B,C) -> r1_int_1(B,A,C)))))))) # label(t35_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2632 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> k1_int_1(k7_xcmplx_0(A,B)) = k5_int_1(A,B))))) # label(d7_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2633 p1_s2_int_1(f1_s2_int_1) & (all A (v1_int_1(A) -> (p1_s2_int_1(A) & r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(k2_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> (r1_xreal_0(f1_s2_int_1,A) -> p1_s2_int_1(A)))) # label(s2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2634 $T # label(t49_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2635 (all A (v1_xreal_0(A) -> v1_int_1(k1_int_1(A)))) # label(dt_k1_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2636 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (r2_int_1(A,B) <-> (exists C (v1_int_1(C) & B = k3_xcmplx_0(A,C)))))))) # label(d9_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2637 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,A) -> r1_xreal_0(A,k6_xcmplx_0(B,np__1))))))) # label(t79_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2638 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(B,A) & r1_xreal_0(C,A) -> r1_xreal_0(C,k6_xcmplx_0(A,np__1)) | C = B | r1_xreal_0(B,k6_xcmplx_0(A,np__1))))))))) # label(t44_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2639 (exists A v1_int_1(A)) # label(rc2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2640 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (r1_int_1(B,D,C) & r1_int_1(A,B,C) -> r1_int_1(A,D,C)))))))))) # label(t36_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2641 (all A all B (v1_int_1(B) & m1_subset_1(A,k5_numbers) -> v1_int_1(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)))) # label(fc6_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2642 $T # label(t46_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2643 (all A (v1_xreal_0(A) -> k1_int_1(A) = k1_int_1(k1_int_1(A)))) # label(t63_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2644 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_int_1(A) & v2_ordinal1(A))) # label(cc2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2645 $T # label(t53_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2646 (all A all B (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) -> v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)))) # label(fc9_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2647 $T # label(t13_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2648 $T # label(t6_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2649 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(D,E,C) & r1_int_1(A,B,C) -> r1_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E),C)))))))))))) # label(t39_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2650 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (B = np__0 -> k6_int_1(A,B) = np__0) & (np__0 != B -> k6_int_1(A,B) = k6_xcmplx_0(A,k3_xcmplx_0(k5_int_1(A,B),B))))))) # label(d8_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2651 (all A (v1_int_1(A) -> (all B (v1_xreal_0(B) -> (r1_xreal_0(A,B) -> r1_xreal_0(A,k1_int_1(B))))))) # label(t81_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2652 (all A all B (v1_int_1(A) & v1_int_1(B) -> r2_int_1(A,A))) # label(reflexivity_r2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2653 (all A (v1_xreal_0(A) -> (v1_int_1(A) -> v1_int_1(k6_xcmplx_0(A,np__1)) & v1_int_1(k2_xcmplx_0(A,np__1))))) # label(t17_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2654 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (k2_xcmplx_0(B,A) = C -> r1_xreal_0(B,C)))))))) # label(t19_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2655 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k2_xcmplx_0(k2_int_1(A),B) = k2_int_1(k2_xcmplx_0(A,B)))))) # label(t58_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2656 (all A all B (m1_subset_1(A,k5_numbers) & v1_int_1(B) -> v1_int_1(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)))) # label(fc8_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2657 (all A (v1_xreal_0(A) -> k2_int_1(k1_int_1(A)) = k1_int_1(A))) # label(t65_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2658 $T # label(t26_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2659 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)))) # label(fc1_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2660 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_int_1(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)))) # label(fc2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2661 (all A (v1_xreal_0(A) -> (v1_int_1(A) <-> k2_int_1(A) = k1_int_1(A)))) # label(t59_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2662 (all A (v1_xreal_0(A) -> (k1_int_1(A) = A <-> v1_int_1(A)))) # label(t47_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2663 (all A (v1_int_1(A) -> r1_int_1(A,np__0,A) & r1_int_1(np__0,A,A))) # label(t33_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2664 $T # label(t24_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2665 (all A (v1_int_1(A) -> (r1_xreal_0(np__0,A) -> r2_hidden(A,k5_numbers)))) # label(t16_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2666 (all A (v1_xreal_0(A) -> (k2_xcmplx_0(k1_int_1(A),np__1) != k2_int_1(A) <-> k1_int_1(A) = k2_int_1(A)))) # label(t66_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2667 $T # label(t31_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2668 (all A all B (v1_int_1(A) & v1_int_1(B) -> v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)))) # label(fc4_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2669 (all A (v1_xreal_0(A) -> k3_int_1(A) = k4_int_1(A))) # label(redefinition_k4_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2670 $T # label(t25_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2671 (all A (v1_xreal_0(A) -> -(v1_int_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> k1_real_1(B) != A & A != B))))) # label(t8_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2672 (all A (v1_xreal_0(A) -> np__0 = k1_int_1(k4_int_1(A)))) # label(t70_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2673 (all A (v1_xreal_0(A) -> r1_xreal_0(k1_int_1(A),k2_int_1(A)))) # label(t61_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2674 (all A (v1_xreal_0(A) -> k2_int_1(k2_int_1(A)) = k2_int_1(A))) # label(t64_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2675 (all A (v1_int_1(A) -> (np__0 != A -> k5_int_1(A,A) = np__1))) # label(t76_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2676 $T # label(t29_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2677 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),C)))))))))))) # label(t37_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2678 (all A (m1_subset_1(A,k4_numbers) -> v1_int_1(A))) # label(cc1_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2679 (all A (v1_xreal_0(A) -> r1_xreal_0(np__0,k4_int_1(A)) & -r1_xreal_0(np__1,k4_int_1(A)))) # label(t69_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2680 (all A (v1_int_1(A) -> v1_xcmplx_0(A) & v1_xreal_0(A))) # label(cc4_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2681 p1_s4_int_1(f1_s4_int_1) & (all A (v1_int_1(A) -> (p1_s4_int_1(A) -> p1_s4_int_1(k6_xcmplx_0(A,np__1)) & p1_s4_int_1(k2_xcmplx_0(A,np__1))))) -> (all A (v1_int_1(A) -> p1_s4_int_1(A))) # label(s4_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2682 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,B,np__1))))) # label(t34_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2683 $T # label(t28_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2684 $T # label(t27_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2685 (all A (v1_xreal_0(A) -> -(-r1_xreal_0(k2_int_1(A),A) & v1_int_1(A)) & -(-v1_int_1(A) & r1_xreal_0(k2_int_1(A),A)))) # label(t55_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2686 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> ((exists D (k3_xcmplx_0(C,D) = k6_xcmplx_0(A,B) & v1_int_1(D))) <-> r1_int_1(A,B,C)))))))) # label(d3_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2687 (all A (v1_xreal_0(A) -> -r1_xreal_0(A,k6_xcmplx_0(k1_int_1(A),np__1)) & -r1_xreal_0(k2_xcmplx_0(A,np__1),k1_int_1(A)))) # label(t50_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2688 (all A (v1_int_1(A) -> np__0 = k5_int_1(A,np__0))) # label(t75_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2689 (all A (v1_xreal_0(A) -> v1_int_1(k2_int_1(A)))) # label(dt_k2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2690 (exists A (p1_s6_int_1(A) & v1_int_1(A))) & (all A (v1_int_1(A) -> (p1_s6_int_1(A) -> r1_xreal_0(A,f1_s6_int_1)))) -> (exists A ((all B (v1_int_1(B) -> (p1_s6_int_1(B) -> r1_xreal_0(B,A)))) & p1_s6_int_1(A) & v1_int_1(A))) # label(s6_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2691 $T # label(t67_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2692 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (all D (v1_int_1(D) -> (all E (v1_int_1(E) -> (r1_int_1(A,B,C) & r1_int_1(D,E,C) -> r1_int_1(k6_xcmplx_0(A,D),k6_xcmplx_0(B,E),C)))))))))))) # label(t38_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2693 (all A (v1_xreal_0(A) -> k3_int_1(A) = k6_xcmplx_0(A,k1_int_1(A)))) # label(d6_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2694 (all A (v1_xreal_0(A) -> v1_xcmplx_0(k3_int_1(A)) & v1_xreal_0(k3_int_1(A)))) # label(fc10_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2695 (all A (v1_xreal_0(A) -> (r1_xreal_0(np__0,A) -> r1_xreal_0(np__0,k2_int_1(A)) & m2_subset_1(k1_int_1(A),k1_numbers,k5_numbers) & m2_subset_1(k2_int_1(A),k1_numbers,k5_numbers) & r1_xreal_0(np__0,k1_int_1(A))))) # label(t80_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2696 (all A (m1_subset_1(A,k5_numbers) -> -v2_xreal_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc5_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2697 $T # label(t30_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2698 $T # label(t1_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2699 (all A (v1_int_1(A) -> v1_int_1(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)))) # label(fc3_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2700 (all A (v4_ordinal2(A) -> v1_int_1(A))) # label(cc3_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2701 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_xreal_0(A,C) & r1_xreal_0(A,B) -> r1_xreal_0(k2_xcmplx_0(A,np__1),B) | r1_xreal_0(k2_xcmplx_0(A,np__1),C) | C = B))))))) # label(t45_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2702 (all A (v1_xreal_0(A) -> -r1_xreal_0(k2_xcmplx_0(k1_int_1(A),np__1),A))) # label(t52_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2703 $T # label(t12_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2704 (all A (v1_xreal_0(A) -> (A != np__0 -> np__1 = k1_int_1(k7_xcmplx_0(A,A))))) # label(t74_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2705 (all A (v1_xreal_0(A) -> k2_int_1(A) = k1_int_1(k2_int_1(A)))) # label(t62_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2706 (all A (v1_int_1(A) -> np__0 = k6_int_1(A,A))) # label(t77_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2707 (all A (r2_hidden(A,k4_numbers) <-> v1_int_1(A))) # label(d2_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2708 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> k1_int_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k1_int_1(A),B))))) # label(t51_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2709 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> -(-r1_xreal_0(B,A) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(C = k6_xcmplx_0(B,A) & r1_xreal_0(np__1,C))))))))) # label(t78_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2710 (all A (v1_xreal_0(A) -> -(r1_xreal_0(k2_int_1(A),k1_int_1(A)) & -v1_int_1(A)) & -(v1_int_1(A) & -r1_xreal_0(k2_int_1(A),k1_int_1(A))))) # label(t60_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2711 (all A (v1_int_1(A) -> (-r1_xreal_0(np__0,A) -> r1_xreal_0(A,k1_real_1(np__1))))) # label(t21_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2712 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> r1_int_1(A,A,B))))) # label(t32_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2713 (all A (v1_xreal_0(A) -> (all B (v1_int_1(B) -> (-r1_xreal_0(B,k6_xcmplx_0(A,np__1)) & r1_xreal_0(B,A) <-> B = k1_int_1(A)))))) # label(d4_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2714 (all A (v1_xreal_0(A) -> (A = k2_int_1(A) <-> v1_int_1(A)))) # label(t54_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2715 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v1_int_1(C) -> (r1_int_1(k2_xcmplx_0(A,C),B,C) <-> r1_int_1(A,B,C)))))))) # label(t42_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2716 (exists A (v1_int_1(A) & p1_s5_int_1(A))) & (all A (v1_int_1(A) -> (p1_s5_int_1(A) -> r1_xreal_0(f1_s5_int_1,A)))) -> (exists A (v1_int_1(A) & (all B (v1_int_1(B) -> (p1_s5_int_1(B) -> r1_xreal_0(A,B)))) & p1_s5_int_1(A))) # label(s5_int_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2717 (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]. 22.08/23.30 2718 (all A all B all C (v1_xreal_0(A) & v1_xreal_0(C) & v1_xreal_0(B) -> v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc18_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2719 (all A (v1_int_1(A) -> v1_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)))) # label(fc10_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2720 (all A (v1_membered(A) -> r1_tarski(A,k2_numbers))) # label(t1_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2721 (all A all B (v1_int_1(B) & v1_int_1(A) -> v1_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)))) # label(fc15_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2722 (exists A (v1_membered(A) & (all B (v1_xcmplx_0(B) -> (r2_hidden(B,A) <-> p1_s1_membered(B)))))) # label(s1_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2723 (all A all B (v1_membered(A) & v1_membered(B) -> v1_membered(k2_xboole_0(A,B)))) # label(fc22_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2724 (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]. 22.08/23.30 2725 (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]. 22.08/23.30 2726 (all A all B all C (v1_xcmplx_0(A) & v1_xcmplx_0(C) & v1_xcmplx_0(B) -> v1_membered(k1_enumset1(A,B,C)))) # label(fc17_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2727 (all A all B all C (v4_ordinal2(A) & v4_ordinal2(C) & v4_ordinal2(B) -> v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)))) # label(fc21_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2728 (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]. 22.08/23.30 2729 (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]. 22.08/23.30 2730 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)))) # label(fc32_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2731 (all A (v3_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_rat_1(B))))) # label(t8_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2732 (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]. 22.08/23.30 2733 (all A (v3_membered(A) -> v2_membered(A))) # label(cc3_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2734 (all A all B (v1_membered(A) -> v1_membered(k4_xboole_0(A,B)))) # label(fc37_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2735 (all A (v1_xreal_0(A) -> v2_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc8_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2736 (all A (v2_membered(A) -> r1_tarski(A,k1_numbers))) # label(t2_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2737 (all A (v3_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xcmplx_0(B) & v1_rat_1(B) & v1_xreal_0(B))))) # label(cc12_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2738 (all A all B all C (v1_int_1(A) & v1_int_1(B) & v1_int_1(C) -> v4_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc20_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2739 (all A (v1_xcmplx_0(A) -> v1_membered(k1_tarski(A)))) # label(fc7_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2740 (all A (m1_subset_1(A,k1_zfmisc_1(k1_numbers)) -> v2_membered(A) & v1_membered(A))) # label(cc6_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.30 2741 (all A all B (v4_ordinal2(B) & v4_ordinal2(A) -> v1_membered(k2_tarski(A,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)))) # label(fc16_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2742 (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]. 22.08/23.31 2743 (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]. 22.08/23.31 2744 (all A ((all B (r2_hidden(B,A) -> v1_int_1(B))) <-> v4_membered(A))) # label(d4_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2745 (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]. 22.08/23.31 2746 (all A all B (v5_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)))) # label(fc35_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2747 (all A all B (v2_membered(A) & v2_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc23_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2748 (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]. 22.08/23.31 2749 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(B,A)))) # label(fc28_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2750 (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]. 22.08/23.31 2751 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A)))) <-> r1_xboole_0(A,B)))))) # label(d16_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2752 (all A (v2_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_xcmplx_0(B))))) # label(cc11_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2753 (all A all B (v3_membered(B) & v3_membered(A) -> 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]. 22.08/23.31 2754 (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]. 22.08/23.31 2755 (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]. 22.08/23.31 2756 (all A (v5_membered(A) -> r1_tarski(A,k5_numbers))) # label(t5_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2757 (all A all B (v5_membered(A) & v5_membered(B) -> v2_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)) & v5_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc46_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2758 (exists A ((all B (v1_xreal_0(B) -> (r2_hidden(B,A) <-> p1_s2_membered(B)))) & v2_membered(A))) # label(s2_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2759 (all A all B (v4_membered(B) -> (r1_tarski(A,B) -> v4_membered(A)))) # label(t19_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2760 (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]. 22.08/23.31 2761 (all A (v2_membered(A) -> v1_membered(A))) # label(cc4_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2762 (all A (v4_membered(A) -> (all B (v4_membered(B) -> (r1_tarski(A,B) <-> (all C (v1_int_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B))))))))) # label(d9_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2763 (exists A (v3_membered(A) & v5_membered(A) & v4_membered(A) & v2_membered(A) & v1_membered(A) & -v1_xboole_0(A))) # label(rc1_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2764 (all A (v1_membered(A) <-> (all B (r2_hidden(B,A) -> v1_xcmplx_0(B))))) # label(d1_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2765 (all A all B (v2_membered(B) & v2_membered(A) -> v2_membered(k5_xboole_0(A,B)) & v1_membered(k5_xboole_0(A,B)))) # label(fc43_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2766 (all A all B (v5_membered(B) & v5_membered(A) -> v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)))) # label(fc26_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2767 (all A all B (v5_membered(A) -> v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_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]. 22.08/23.31 2768 (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]. 22.08/23.31 2769 (all A (v1_membered(A) -> (all B (v1_membered(B) -> ((all C (v1_xcmplx_0(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d11_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2770 (all A all B (v3_membered(B) -> (r1_tarski(A,B) -> v3_membered(A)))) # label(t18_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2771 (all A all B (v4_membered(A) -> v1_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)))) # label(fc34_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2772 (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]. 22.08/23.31 2773 (all A (v5_membered(A) -> (all B (m1_subset_1(B,A) -> v1_int_1(B) & v1_rat_1(B) & v1_xreal_0(B) & v4_ordinal2(B) & v1_xcmplx_0(B))))) # label(cc14_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2774 (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_xboole_0(A,B)))))) # label(d19_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2775 (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]. 22.08/23.31 2776 (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]. 22.08/23.31 2777 (all A all B (v1_membered(A) -> v1_membered(k3_xboole_0(A,B)))) # label(fc27_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2778 (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]. 22.08/23.31 2779 (all A ((all B (r2_hidden(B,A) -> v4_ordinal2(B))) <-> v5_membered(A))) # label(d5_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2780 (all A (v4_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v4_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc19_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2781 (all A (v3_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v1_membered(B) & v2_membered(B) & v3_membered(B))))) # label(cc18_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2782 (all A (-v1_xboole_0(A) & v2_membered(A) -> (exists B (v1_xreal_0(B) & r2_hidden(B,A))))) # label(t7_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2783 (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]. 22.08/23.31 2784 (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]. 22.08/23.31 2785 (all A (v4_ordinal2(A) -> v2_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v1_membered(k1_tarski(A)))) # label(fc11_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2786 (all A all B (v2_membered(B) -> (r1_tarski(A,B) -> v2_membered(A)))) # label(t17_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2787 (all A (v5_membered(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) -> v2_membered(B) & v4_membered(B) & v5_membered(B) & v3_membered(B) & v1_membered(B))))) # label(cc20_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2788 (all A all B (v3_membered(A) -> v1_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)))) # label(fc39_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2789 (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]. 22.08/23.31 2790 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d13_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2791 (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]. 22.08/23.31 2792 (all A all B (v1_xreal_0(A) & v1_xreal_0(B) -> v2_membered(k2_tarski(A,B)) & v1_membered(k2_tarski(A,B)))) # label(fc13_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2793 (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]. 22.08/23.31 2794 (all A ((all B (r2_hidden(B,A) -> v1_rat_1(B))) <-> v3_membered(A))) # label(d3_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2795 (all A (m1_subset_1(A,k1_zfmisc_1(k2_numbers)) -> v1_membered(A))) # label(cc5_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2796 (all A (v4_membered(A) -> v3_membered(A))) # label(cc2_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2797 (all A all B (v1_membered(B) -> (r1_tarski(A,B) -> v1_membered(A)))) # label(t16_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2798 (all A all B all C (v1_rat_1(B) & v1_rat_1(C) & v1_rat_1(A) -> v3_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v1_membered(k1_enumset1(A,B,C)))) # label(fc19_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2799 (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]. 22.08/23.31 2800 (all A (v5_membered(A) -> v4_membered(A))) # label(cc1_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2801 (all A all B (r2_hidden(B,A) & v3_membered(B) -> v3_membered(k1_setfam_1(A)))) # label(t28_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2802 (all A (v2_membered(A) -> (all B (v2_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v1_xreal_0(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d17_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2803 (exists A (v5_membered(A) & (all B (v4_ordinal2(B) -> (r2_hidden(B,A) <-> p1_s5_membered(B)))))) # label(s5_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2804 (all A (v1_xboole_0(A) -> v1_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v2_membered(A))) # label(cc15_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2805 (all A ((all B (r2_hidden(B,A) -> v1_xreal_0(B))) <-> v2_membered(A))) # label(d2_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2806 (all A (v3_membered(A) -> (all B (v3_membered(B) -> ((all C (v1_rat_1(C) -> (r2_hidden(C,A) -> r2_hidden(C,B)))) <-> r1_tarski(A,B)))))) # label(d8_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2807 (all A all B (v3_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc31_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2808 (all A all B (v4_membered(A) -> v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v1_membered(k3_xboole_0(A,B)))) # label(fc33_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2809 (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]. 22.08/23.31 2810 (all A all B (v2_membered(A) -> v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)))) # label(fc29_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2811 (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]. 22.08/23.31 2812 (all A (v4_membered(A) & -v1_xboole_0(A) -> (exists B (r2_hidden(B,A) & v1_int_1(B))))) # label(t9_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2813 (all A all B (v4_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc40_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2814 (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]. 22.08/23.31 2815 (all A all B (v2_membered(A) -> v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc38_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2816 (all A all B (v5_membered(A) -> v5_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v1_membered(k4_xboole_0(A,B)))) # label(fc41_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2817 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (B = A <-> (all C (v4_ordinal2(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A))))))))) # label(d15_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2818 (all A (v4_membered(A) -> (all B (v4_membered(B) -> ((all C (v1_int_1(C) -> (r2_hidden(C,B) <-> r2_hidden(C,A)))) <-> B = A))))) # label(d14_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2819 (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]. 22.08/23.31 2820 (all A (v4_membered(A) -> (all B (m1_subset_1(B,A) -> v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) & v1_xcmplx_0(B))))) # label(cc13_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2821 (all A (m1_subset_1(A,k1_zfmisc_1(k3_numbers)) -> v3_membered(A) & v2_membered(A) & v1_membered(A))) # label(cc7_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2822 (all A all B (v4_membered(A) & v4_membered(B) -> v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v1_membered(k2_xboole_0(A,B)))) # label(fc25_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2823 (all A (m1_subset_1(A,k1_zfmisc_1(k4_numbers)) -> v1_membered(A) & v4_membered(A) & v3_membered(A) & v2_membered(A))) # label(cc8_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2824 (all A all B (v5_membered(B) & r2_hidden(B,A) -> v5_membered(k1_setfam_1(A)))) # label(t30_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2825 (all A (v3_membered(A) -> r1_tarski(A,k3_numbers))) # label(t3_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2826 (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]. 22.08/23.31 2827 (all A (v4_membered(A) -> r1_tarski(A,k4_numbers))) # label(t4_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2828 (all A (-v1_xboole_0(A) & v1_membered(A) -> (exists B (r2_hidden(B,A) & v1_xcmplx_0(B))))) # label(t6_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2829 (all A (v5_membered(A) -> (all B (v5_membered(B) -> (r1_xboole_0(A,B) <-> (all C (v4_ordinal2(C) -> -(r2_hidden(C,B) & r2_hidden(C,A))))))))) # label(d20_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2830 (all A all B (v4_membered(B) & v4_membered(A) -> v1_membered(k5_xboole_0(A,B)) & v2_membered(k5_xboole_0(A,B)) & v4_membered(k5_xboole_0(A,B)) & v3_membered(k5_xboole_0(A,B)))) # label(fc45_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2831 (all A all B (v5_membered(B) -> (r1_tarski(A,B) -> v5_membered(A)))) # label(t20_membered) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2832 (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]. 22.08/23.31 2833 (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) -> B = A))))) # label(t71_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2834 (all A (v1_card_1(A) -> ((all B (v1_card_1(B) -> k2_card_1(B) != A)) <-> v2_card_1(A)))) # label(d7_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2835 (all A (v3_ordinal1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t36_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2836 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (r2_wellord2(A,B) <-> B = A))))) # label(t8_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2837 $T # label(t9_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2838 (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]. 22.08/23.31 2839 (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]. 22.08/23.31 2840 (all A (v3_ordinal1(A) -> r1_ordinal1(k1_card_1(A),A))) # label(t24_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2841 $T # label(d9_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2842 $T # label(d2_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2843 (all A (r2_hidden(A,k5_ordinal2) -> v1_card_1(A))) # label(t65_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2844 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r1_xreal_0(A,B) <-> r1_tarski(k1_card_1(A),k1_card_1(B))))))) # label(t72_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2845 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (-r1_tarski(B,A) <-> r2_hidden(A,B)))))) # label(t14_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2846 $T # label(t63_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2847 $T # label(t11_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2848 $T # label(t1_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2849 (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]. 22.08/23.31 2850 $T # label(t53_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2851 $T # label(t19_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2852 (all A (v1_finset_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k1_card_1(B) = k1_card_1(A) <-> k4_card_1(A) = B))))) # label(d11_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2853 (all A -r2_wellord2(A,k1_zfmisc_1(A))) # label(t29_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2854 $T # label(t16_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2855 (all A (m1_subset_1(A,k5_numbers) -> v1_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_card_1(A) & -v3_xreal_0(A) & v1_finset_1(A) & v4_ordinal2(A) & v3_ordinal1(A) & v2_ordinal1(A))) # label(cc3_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2856 $T # label(t57_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2857 $T # label(t18_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2858 (all A (v3_ordinal1(A) -> k3_card_1(k1_ordinal1(A)) = k2_card_1(k3_card_1(A)))) # label(t39_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2859 $T # label(t31_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2860 $T # label(d3_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2861 (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]. 22.08/23.31 2862 (all A all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_relat_1(C) = B & r1_tarski(A,k2_relat_1(C)))) <-> r1_tarski(k1_card_1(A),k1_card_1(B)))) # label(t28_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2863 $T # label(t37_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2864 (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]. 22.08/23.31 2865 (all A all B all C all D (r1_xboole_0(A,B) & r1_xboole_0(C,D) & r2_wellord2(A,C) & r2_wellord2(B,D) -> r2_wellord2(k2_xboole_0(A,B),k2_xboole_0(C,D)))) # label(t58_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2866 (all A -(v1_finset_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -r2_wellord2(A,B))))) # label(t74_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2867 $T # label(t7_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2868 (all A all B (r1_tarski(k1_card_1(A),k1_card_1(B)) <-> (exists C (v1_funct_1(C) & v2_funct_1(C) & r1_tarski(k2_relat_1(C),B) & A = k1_relat_1(C) & v1_relat_1(C))))) # label(t26_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2869 $T # label(t5_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2870 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> (A != B & r1_tarski(A,B) <-> r2_hidden(A,B)))))) # label(t13_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2871 $T # label(t3_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2872 (exists A v1_card_1(A)) # label(rc1_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2873 (all A all B (r2_wellord2(A,B) & v1_finset_1(A) -> v1_finset_1(B))) # label(t68_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2874 $T # label(d4_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2875 (all A (v1_card_1(A) <-> (exists B (v3_ordinal1(B) & B = A & (all C (v3_ordinal1(C) -> (r2_wellord2(C,B) -> r1_ordinal1(B,C)))))))) # label(d1_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2876 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k3_card_1(A),k3_card_1(B))))))) # label(t41_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2877 (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) -> p1_s1_card_1(A) | k1_xboole_0 = 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]. 22.08/23.31 2878 (all A (v1_finset_1(A) -> v1_finset_1(k2_card_1(A)))) # label(t82_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2879 (all A exists B (v3_ordinal1(B) & r2_wellord2(A,B))) # label(t4_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2880 (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]. 22.08/23.31 2881 (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]. 22.08/23.31 2882 (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]. 22.08/23.31 2883 (all A v1_card_1(k2_card_1(A))) # label(dt_k2_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2884 $T # label(t17_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2885 $T # label(t77_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2886 (all A r2_hidden(k1_card_1(k1_xboole_0),k2_card_1(A))) # label(t33_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2887 (all A k4_ordinal2 = k1_card_1(k1_tarski(A))) # label(t50_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2888 (all A v1_card_1(k1_card_1(A))) # label(dt_k1_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2889 (all A np__1 = k4_card_1(k1_tarski(A))) # label(t79_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2890 (all A (v1_card_1(A) -> r2_hidden(A,k2_card_1(A)))) # label(t32_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2891 (exists A (v1_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) & v2_ordinal1(A))) # label(rc2_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2892 (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]. 22.08/23.31 2893 (all A (v3_ordinal1(A) -> (v4_ordinal1(A) -> A = k1_xboole_0 | (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> ((all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k3_card_1(C) = k1_funct_1(B,C)))) & k1_relat_1(B) = A -> k3_card_1(A) = k1_card_1(k8_ordinal2(B)))))))) # label(t40_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2894 (all A all B (k1_card_1(B) = k1_card_1(A) <-> r2_wellord2(A,B))) # label(t21_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2895 $T # label(t55_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2896 $T # label(t67_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2897 (all A all B ((exists C A = k1_tarski(C)) <-> r2_wellord2(A,k1_tarski(B)))) # label(t48_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2898 (all A (v1_finset_1(A) -> v2_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_ordinal1(k1_card_1(A)))) # label(fc2_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2899 (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) <-> B = k2_card_1(A)))) # label(d6_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2900 $T # label(t20_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2901 $T # label(t62_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2902 $T # label(t2_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2903 $T # label(t10_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2904 (all A all B (r1_tarski(k1_zfmisc_1(A),B) -> r2_hidden(k1_card_1(A),k1_card_1(B)) & -r2_wellord2(A,B))) # label(t45_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2905 $T # label(t12_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2906 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (-r1_xreal_0(B,A) <-> r2_hidden(k1_card_1(A),k1_card_1(B))))))) # label(t73_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2907 (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]. 22.08/23.31 2908 $T # label(dt_k3_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2909 (all A all B all C all D (r2_hidden(C,A) & r2_hidden(D,B) & r2_wellord2(A,B) -> r2_wellord2(k4_xboole_0(A,k1_tarski(C)),k4_xboole_0(B,k1_tarski(D))))) # label(t61_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2910 $T # label(t75_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2911 (all A all B all C (r2_wellord2(A,C) & r1_tarski(B,C) & r1_tarski(A,B) -> r2_wellord2(A,B) & r2_wellord2(B,C))) # label(t44_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2912 $T # label(t15_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2913 (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]. 22.08/23.31 2914 (all A (v1_finset_1(A) -> (all B (v1_finset_1(B) -> (r2_wellord2(A,B) -> k4_card_1(B) = k4_card_1(A)))))) # label(t81_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2915 (all A all B (v1_card_1(B) -> (B = k1_card_1(A) <-> r2_wellord2(A,B)))) # label(d5_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2916 (all A all B (k1_card_1(A) = k1_card_1(B) -> k2_card_1(A) = k2_card_1(B))) # label(t34_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2917 (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]. 22.08/23.31 2918 (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]. 22.08/23.31 2919 $T # label(t6_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2920 $T # label(t54_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2921 (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]. 22.08/23.31 2922 (all A all B all C (r2_hidden(A,B) & r2_hidden(C,B) -> r2_wellord2(k4_xboole_0(B,k1_tarski(A)),k4_xboole_0(B,k1_tarski(C))))) # label(t59_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2923 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,k1_relat_1(B)) & v2_funct_1(B) -> r2_wellord2(A,k9_relat_1(B,A))))) # label(t60_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2924 (all A (r2_wellord2(A,k1_xboole_0) <-> A = k1_xboole_0)) # label(t46_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2925 (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]. 22.08/23.31 2926 $T # label(t70_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2927 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_wellord2(A,B) -> B = A))))) # label(t64_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2928 (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]. 22.08/23.31 2929 (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]. 22.08/23.31 2930 (all A (v3_ordinal1(A) -> v1_ordinal1(k3_card_1(A)) & v3_ordinal1(k3_card_1(A)) & v1_card_1(k3_card_1(A)) & v2_ordinal1(k3_card_1(A)))) # label(fc1_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2931 (all A (m1_subset_1(A,k5_numbers) -> v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & -v3_xreal_0(A) & v1_card_1(A) & v3_ordinal1(A) & v2_ordinal1(A) & v1_ordinal1(A))) # label(cc2_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2932 (all A (v1_finset_1(A) -> k4_card_1(A) = k1_card_1(A))) # label(redefinition_k4_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2933 (all A (v1_card_1(A) & v1_finset_1(A) -> (exists B (A = k1_card_1(B) & m2_subset_1(B,k1_numbers,k5_numbers))))) # label(t86_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2934 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_relat_1(C) & v1_funct_1(C) & k1_ordinal2(C) = B & k1_relat_1(C) = k1_ordinal1(A) & k1_card_1(k5_numbers) = k1_funct_1(C,k1_xboole_0) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k2_card_1(k3_tarski(k1_tarski(k1_funct_1(C,D))))))) & (all D (v3_ordinal1(D) -> (v4_ordinal1(D) & r2_hidden(D,k1_ordinal1(A)) -> D = k1_xboole_0 | k1_funct_1(C,D) = k1_card_1(k8_ordinal2(k2_ordinal1(C,D)))))) & v5_ordinal1(C))) <-> B = k3_card_1(A))))) # label(d8_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2935 $T # label(d10_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2936 (all A all B (r2_wellord2(A,B) -> k2_card_1(A) = k2_card_1(B))) # label(t35_card_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.31 2937 (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_finseq_1(k7_relat_1(B,k2_finseq_1(A))) & v1_funct_1(k7_relat_1(B,k2_finseq_1(A))))))) # label(t19_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2938 (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]. 22.08/23.32 2939 (all A m2_finseq_1(k14_finseq_1(A),k5_numbers)) # label(dt_k14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2940 (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]. 22.08/23.32 2941 (all A exists B m1_finseq_1(B,A)) # label(existence_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2942 (all A -v1_xboole_0(k13_finseq_1(A))) # label(fc9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2943 (all A k1_xboole_0 = k6_finseq_1(A)) # label(d6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2944 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k7_finseq_1(A,B) = k1_xboole_0 -> B = k1_xboole_0 & k1_xboole_0 = A))))) # label(t48_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2945 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (A = k1_xboole_0 <-> k1_xboole_0 = k4_finseq_1(A)))) # label(t26_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2946 $T # label(t28_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2947 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (k2_finseq_1(B) = k2_finseq_1(A) -> A = B))))) # label(t8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2948 (all A m2_finseq_1(k1_xboole_0,A)) # label(t29_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2949 (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]. 22.08/23.32 2950 (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]. 22.08/23.32 2951 (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) -> (v2_funct_1(B) & v2_funct_1(A) & k2_relat_1(A) = k2_relat_1(B) -> k3_finseq_1(B) = k3_finseq_1(A)))))) # label(t65_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2952 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> v1_finseq_1(k15_finseq_1(A)) & v1_finset_1(k15_finseq_1(A)) & v1_funct_1(k15_finseq_1(A)) & v1_relat_1(k15_finseq_1(A)))) # label(fc10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2953 (all A (v4_ordinal2(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) -> (r1_xreal_0(A,k3_finseq_1(B)) & k7_relat_1(B,k2_finseq_1(A)) = C -> A = k3_finseq_1(C) & k4_finseq_1(C) = k2_finseq_1(A)))))))) # label(t21_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2954 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (k7_finseq_1(A,B) = C <-> k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(B)) -> k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D)))) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(A)) -> k1_funct_1(C,D) = k1_funct_1(A,D))))))))))) # label(d7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2955 (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_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]. 22.08/23.32 2956 (all 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) -> -(r2_hidden(A,k4_finseq_1(B)) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> -(r2_hidden(k1_nat_1(k3_finseq_1(C),D),k4_finseq_1(k7_finseq_1(C,B))) & A = D)))))))) # label(t40_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2957 (all A (v1_funct_1(A) & v1_relat_1(A) -> -((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & r1_tarski(k1_relat_1(A),k2_finseq_1(B)))) & (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> -r1_tarski(A,B)))))) # label(t15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2958 (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]. 22.08/23.32 2959 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k3_finseq_1(A) = B <-> k2_finseq_1(B) = k1_relat_1(A)))))) # label(d3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2960 (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_finseq_1(C) & v1_funct_1(C) -> (k7_finseq_1(A,B) = k7_finseq_1(C,B) | k7_finseq_1(B,C) = k7_finseq_1(B,A) -> A = C))))))) # label(t46_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2961 (all A all B (m1_finseq_1(B,A) <-> m2_finseq_1(B,A))) # label(redefinition_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2962 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> r1_tarski(k2_relat_1(A),k2_relat_1(k7_finseq_1(B,A))))))) # label(t43_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2963 (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]. 22.08/23.32 2964 (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(k2_relat_1(A),k2_relat_1(k7_finseq_1(A,B))))))) # label(t42_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2965 (all A (v4_ordinal2(A) -> v1_finset_1(k1_finseq_1(A)))) # label(fc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2966 (all A (v4_ordinal2(A) -> A = k4_card_1(k2_finseq_1(A)))) # label(t78_finseq_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2967 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_card_1(k1_card_1(A)) = A & A = k4_card_1(A))) # label(t78_finseq_1_AndRHS) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2968 (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_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(C,k3_finseq_1(A)) & r1_xreal_0(np__1,C) -> k1_funct_1(A,C) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t85_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2969 $T # label(dt_k5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2970 $T # label(dt_k10_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2971 (all A exists B (m1_finseq_1(B,A) & v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_funct_1(B) & v1_relat_1(B))) # label(rc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2972 (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) -> -(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]. 22.08/23.32 2973 (all A all B all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> (C = k10_finseq_1(A,B) <-> k3_finseq_1(C) = np__2 & B = k1_funct_1(C,np__2) & A = k1_funct_1(C,np__1)))) # label(t61_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2974 (all A all B (v1_funct_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_relat_1(k10_finseq_1(A,B)))) # label(fc7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2975 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((exists B (r1_tarski(k1_relat_1(A),k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> v2_finseq_1(A)))) # label(d12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2976 (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) -> k7_relat_1(k7_finseq_1(A,B),k4_finseq_1(A)) = A)))) # label(t33_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2977 (all A (-v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)))) # label(fc16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2978 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (p1_s3_finseq_1(A) -> p1_s3_finseq_1(k7_finseq_1(A,k9_finseq_1(B))))))) & p1_s3_finseq_1(k1_xboole_0) -> (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> p1_s3_finseq_1(A))) # label(s3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2979 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (k2_relat_1(B) = k1_tarski(A) & k2_finseq_1(np__1) = k4_finseq_1(B) <-> B = k9_finseq_1(A)))) # label(t55_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2980 (all A all B (v1_finseq_1(A) & -v1_xboole_0(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & v1_funct_1(A) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)))) # label(fc14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2981 (all A (v4_ordinal2(A) -> (all B (-v1_xboole_0(B) -> (exists C (k3_finseq_1(C) = A & m2_finseq_1(C,B))))))) # label(t24_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2982 (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]. 22.08/23.32 2983 (all A exists B (m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_finseq_1(B) & v1_finset_1(B) & v1_funct_1(B))) # label(rc2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2984 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> v1_relat_1(k7_relat_1(B,A)) & v1_relat_1(k8_relat_1(A,B)) & v1_funct_1(k8_relat_1(A,B)) & v2_finseq_1(k8_relat_1(A,B)) & v2_finseq_1(k7_relat_1(B,A)) & v1_funct_1(k7_relat_1(B,A)))) # label(t69_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2985 (all A (v1_funct_1(A) & v2_finseq_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]. 22.08/23.32 2986 (all A k9_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(t52_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2987 $T # label(dt_k13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2988 (all A all B (m1_finseq_1(B,A) -> v2_funct_1(k16_finseq_1(A,B,np__0)) & v1_finseq_1(k16_finseq_1(A,B,np__0)) & v1_finset_1(k16_finseq_1(A,B,np__0)) & v1_funct_1(k16_finseq_1(A,B,np__0)) & v1_relat_1(k16_finseq_1(A,B,np__0)) & v1_xboole_0(k16_finseq_1(A,B,np__0)))) # label(fc15_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2989 (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]. 22.08/23.32 2990 (all A ((exists B (v1_relat_1(B) & v1_finseq_1(B) & A = k2_relat_1(B) & v1_funct_1(B))) <-> v1_finset_1(A))) # label(t73_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2991 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f2_s5_finseq_1)) & (all B (m1_subset_1(B,f1_s5_finseq_1) -> -p1_s5_finseq_1(A,B)))))) -> (exists A (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]. 22.08/23.32 2992 (all A all B all C all D (v1_finseq_1(D) & v1_funct_1(D) & v1_relat_1(D) -> (D = k11_finseq_1(A,B,C) <-> C = k1_funct_1(D,np__3) & k1_funct_1(D,np__2) = B & A = k1_funct_1(D,np__1) & k3_finseq_1(D) = np__3))) # label(t62_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2993 (all A ((exists B (v4_ordinal2(B) & r1_tarski(A,k2_finseq_1(B)))) -> (all B (m2_finseq_1(B,k5_numbers) -> (B = k14_finseq_1(A) <-> A = k2_relat_1(B) & (all C (v4_ordinal2(C) -> (all D (v4_ordinal2(D) -> (all E (v4_ordinal2(E) -> (all F (v4_ordinal2(F) -> -(r1_xreal_0(np__1,C) & -r1_xreal_0(D,C) & r1_xreal_0(D,k3_finseq_1(B)) & r1_xreal_0(F,E) & k1_funct_1(B,D) = F & k1_funct_1(B,C) = E)))))))))))))) # label(d13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2994 (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 A != k7_finseq_1(B,k9_finseq_1(C))))) & k1_xboole_0 != A))) # label(t63_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2995 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> k1_relat_1(A) = k4_finseq_1(A))) # label(redefinition_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2996 $T # label(t49_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2997 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(B)) -> k1_funct_1(k7_finseq_1(A,B),k1_nat_1(k3_finseq_1(A),C)) = k1_funct_1(B,C)))))))) # label(t86_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2998 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(B)) -> k3_finseq_1(k16_finseq_1(A,B,C)) = C))))) # label(t80_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 2999 (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]. 22.08/23.32 3000 (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]. 22.08/23.32 3001 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(A)) -> k1_funct_1(A,C) = k1_funct_1(B,C)))) & k4_finseq_1(A) = k4_finseq_1(B) -> A = B))))) # label(t17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3002 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (k1_xboole_0 = A <-> np__0 = k3_finseq_1(A)))) # label(t25_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3003 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> v2_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(t68_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3004 (all A (v1_funct_1(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)))) # label(fc3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3005 (all A (m2_finseq_1(k6_finseq_1(A),A) & v1_xboole_0(k6_finseq_1(A)))) # label(dt_k6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3006 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> 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]. 22.08/23.32 3007 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> -(r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) & (all B -p1_s1_finseq_1(A,B))))) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C (p1_s1_finseq_1(A,C) & p1_s1_finseq_1(A,B) & r2_hidden(A,k2_finseq_1(f1_s1_finseq_1)) -> C = B)))) -> (exists A (v1_relat_1(A) & v1_finseq_1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s1_finseq_1)) -> p1_s1_finseq_1(B,k1_funct_1(A,B))))) & k2_finseq_1(f1_s1_finseq_1) = k4_finseq_1(A) & v1_funct_1(A))) # label(s1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3008 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (k3_finseq_1(A) = k3_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(A)) -> k1_funct_1(B,C) = k1_funct_1(A,C)))) -> A = B))))) # label(t18_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3009 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> k7_finseq_1(A,k1_xboole_0) = A & k7_finseq_1(k1_xboole_0,A) = A)) # label(t47_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3010 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_ordinal2(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) -> r1_xreal_0(B,np__0) | r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C))) & r2_hidden(B,k2_finseq_1(A))))))))) # label(t82_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3011 (all A all B (m2_finseq_1(B,A) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(k3_finseq_1(B),C) -> B = k16_finseq_1(A,B,C)))))) # label(t79_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3012 (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]. 22.08/23.32 3013 (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]. 22.08/23.32 3014 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (r1_tarski(k2_relat_1(B),A) <-> m1_finseq_1(B,A)))) # label(d4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3015 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r1_xreal_0(A,B) -> k2_finseq_1(A) = k5_subset_1(k5_numbers,k2_finseq_1(B),k2_finseq_1(A))))))) # label(t9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3016 (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]. 22.08/23.32 3017 (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) -> (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]. 22.08/23.32 3018 (all A k5_finseq_1(A) = k9_finseq_1(A)) # label(redefinition_k9_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3019 $T # label(t1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3020 (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]. 22.08/23.32 3021 (all A all B (m1_subset_1(B,A) & -v1_xboole_0(A) -> k12_finseq_1(A,B) = k5_finseq_1(B))) # label(redefinition_k12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3022 (exists A all B (r2_hidden(B,A) <-> (exists C (r2_hidden(C,k13_finseq_1(f1_s4_finseq_1)) & p1_s4_finseq_1(C) & B = C & v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C))))) # label(s4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3023 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),np__1) = A)) # label(t58_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3024 (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]. 22.08/23.32 3025 (all A (v1_relat_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)))) # label(fc4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3026 (all A all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),np__1)) = A)) # label(t59_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3027 $T # label(dt_k11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3028 (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]. 22.08/23.32 3029 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> v1_finset_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(cc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3030 (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]. 22.08/23.32 3031 (all A (v1_relat_1(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_xboole_0(k5_finseq_1(A)))) # label(fc12_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3032 $T # label(dt_k1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3033 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers))) # label(dt_k3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3034 (all A all B (v1_funct_1(A) & v1_finseq_1(A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & v1_relat_1(A) -> -v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)))) # label(fc13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3035 (all A all B all C (k7_finseq_1(k10_finseq_1(A,B),k9_finseq_1(C)) = k11_finseq_1(A,B,C) & k7_finseq_1(k9_finseq_1(A),k10_finseq_1(B,C)) = k11_finseq_1(A,B,C))) # label(t60_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3036 (all A all B (v1_relat_1(A) & v1_finseq_1(A) & v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) & v1_funct_1(A) -> v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)))) # label(dt_k7_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3037 (exists A (v1_funct_1(A) & v2_finseq_1(A) & v1_relat_1(A))) # label(rc5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3038 (all A (v4_ordinal2(A) -> a_1_0_finseq_1(A) = k1_finseq_1(A))) # label(d1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3039 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k3_finseq_1(k7_finseq_1(A,B))) -> r1_xreal_0(C,k3_finseq_1(A)) | k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t37_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3040 (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]. 22.08/23.32 3041 (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]. 22.08/23.32 3042 (all A (v4_ordinal2(A) -> (all B (v4_ordinal2(B) -> (r2_hidden(A,k2_finseq_1(B)) <-> r1_xreal_0(A,B) & r1_xreal_0(np__1,A)))))) # label(t3_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3043 (all A exists B m2_finseq_1(B,A)) # label(existence_m2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3044 (all A (v4_ordinal2(A) -> np__0 = A | r2_hidden(A,k2_finseq_1(A)))) # label(t5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3045 (exists A (v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A))) # label(rc6_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3046 (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]. 22.08/23.32 3047 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (B = k9_finseq_1(A) <-> k2_finseq_1(np__1) = k1_relat_1(B) & k1_funct_1(B,np__1) = A))) # label(d8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3048 (all A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v4_ordinal2(C) -> (r1_xreal_0(C,k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & r1_xreal_0(k1_nat_1(k3_finseq_1(A),np__1),C) -> k1_funct_1(B,k6_xcmplx_0(C,k3_finseq_1(A))) = k1_funct_1(k7_finseq_1(A,B),C)))))))) # label(t36_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3049 (all A k5_finseq_1(A) = k1_tarski(k4_tarski(np__1,A))) # label(d5_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3050 (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]. 22.08/23.32 3051 $T # label(t31_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3052 (all A (v1_relat_1(A) & v2_finseq_1(A) & v1_funct_1(A) -> k5_relat_1(k14_finseq_1(k1_relat_1(A)),A) = k15_finseq_1(A))) # label(d14_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3053 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (v1_funct_1(D) & v1_finseq_1(D) & v1_relat_1(D) -> -(k7_finseq_1(A,B) = k7_finseq_1(C,D) & r1_xreal_0(k3_finseq_1(A),k3_finseq_1(C)) & (all E (v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) -> C != k7_finseq_1(A,E)))))))))))) # label(t64_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3054 (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]. 22.08/23.32 3055 $T # label(t2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3056 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (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]. 22.08/23.32 3057 (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]. 22.08/23.32 3058 (exists A (k3_finseq_1(A) = f1_s2_finseq_1 & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k2_finseq_1(f1_s2_finseq_1)) -> k1_funct_1(A,B) = f2_s2_finseq_1(B)))) & v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(s2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3059 (all A all B (m1_finseq_1(B,A) -> v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B))) # label(dt_m1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3060 (all A r2_hidden(k1_xboole_0,k13_finseq_1(A))) # label(t66_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3061 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (A = k6_finseq_1(B) <-> k3_finseq_1(A) = np__0)))) # label(t32_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3062 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> (A = k1_funct_1(B,np__1) & k3_finseq_1(B) = np__1 <-> B = k9_finseq_1(A)))) # label(t57_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3063 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (k1_xboole_0 = A <-> k2_relat_1(A) = k1_xboole_0))) # label(t27_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3064 (all A (v1_relat_1(A) -> (all B (v1_relat_1(B) -> ((all C all D ((exists E (v1_relat_1(E) & r1_xreal_0(np__1,k3_finseq_1(E)) & k1_funct_1(E,np__1) = C & (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 & v1_finseq_1(E) & v1_funct_1(E))) & r2_hidden(D,k3_relat_1(A)) & r2_hidden(C,k3_relat_1(A)) <-> r2_hidden(k4_tarski(C,D),B))) <-> k17_finseq_1(A) = B))))) # label(d16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3065 $T # label(t53_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3066 $T # label(t51_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3067 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (k9_finseq_1(A) = B <-> np__1 = k3_finseq_1(B) & k2_relat_1(B) = k1_tarski(A)))) # label(t56_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3068 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)))) # label(dt_k4_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3069 (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]. 22.08/23.32 3070 $T # label(t34_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3071 (all A (v1_funct_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(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]. 22.08/23.32 3072 $T # label(t22_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3073 (all A all B (v4_ordinal2(B) -> ((exists C (A = C & r1_xreal_0(C,B) & r1_xreal_0(np__1,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]. 22.08/23.32 3074 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_1(C) -> k7_finseq_1(A,k7_finseq_1(B,C)) = k7_finseq_1(k7_finseq_1(A,B),C))))))) # label(t45_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3075 (all A (v4_ordinal2(A) -> k1_finseq_1(A) = k2_finseq_1(A))) # label(redefinition_k2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3076 (all A (v1_relat_1(A) -> v1_relat_1(k17_finseq_1(A)))) # label(dt_k17_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3077 (all A all B all C (m1_finseq_1(B,A) & m1_finseq_1(C,A) -> m2_finseq_1(k8_finseq_1(A,B,C),A))) # label(dt_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3078 (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]. 22.08/23.32 3079 (exists A (v1_finseq_1(A) & v1_funct_1(A) & v1_relat_1(A))) # label(rc1_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3080 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> -(r2_hidden(A,B) & (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> -(r2_hidden(C,k4_finseq_1(B)) & A = k4_tarski(C,k1_funct_1(B,C)))))))) # label(t16_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3081 $T # label(t70_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3082 (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]. 22.08/23.32 3083 $T # label(t30_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3084 (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]. 22.08/23.32 3085 (all A (v1_relat_1(A) & v1_finset_1(A) -> v1_finset_1(k2_relat_1(A)))) # label(fc11_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.32 3086 (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]. 22.08/23.32 3087 (all A ((exists B (r1_tarski(A,k2_finseq_1(B)) & m2_subset_1(B,k1_numbers,k5_numbers))) -> (k1_xboole_0 = k14_finseq_1(A) <-> k1_xboole_0 = A))) # label(t72_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3088 (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) -> k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)))))) # label(t44_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3089 (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]. 22.08/23.33 3090 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) -> k2_relat_1(k14_finseq_1(k1_relat_1(A))) = k1_relat_1(A))) # label(t71_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3091 (all A all B all C (m1_finseq_1(C,A) & m1_finseq_1(B,A) -> k8_finseq_1(A,B,C) = k7_finseq_1(B,C))) # label(redefinition_k8_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3092 $T # label(t13_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3093 $T # label(t54_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3094 (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]. 22.08/23.33 3095 (all A (v1_relat_1(A) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & k1_relat_1(A) = k2_finseq_1(B))) <-> v1_finseq_1(A)))) # label(d2_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3096 $T # label(t67_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3097 (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(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))))))) # label(t39_finseq_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3098 $T # label(t26_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3099 (all A (v1_relat_1(A) -> (all B (r4_relat_2(A,B) & r8_relat_2(A,B) & r1_relat_2(A,B) <-> r2_orders_1(A,B))))) # label(d7_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3100 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v1_relat_2(A) <-> v1_orders_1(A)))) # label(d3_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3101 $T # label(t83_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3102 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> r2_orders_1(A,B) & r1_orders_1(A,B))))) # label(t125_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3103 $T # label(t15_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3104 (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]. 22.08/23.33 3105 $T # label(t39_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3106 $T # label(t40_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3107 $T # label(t11_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3108 $T # label(t168_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3109 $T # label(t32_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3110 (all A (v1_relat_1(A) -> (all B all C (r9_orders_1(A,B) & r1_tarski(C,k3_relat_1(A)) & v1_relat_2(A) & r2_hidden(B,C) -> r5_orders_1(A,C))))) # label(t162_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3111 $T # label(t101_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3112 $T # label(t27_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3113 (all A all B (m2_relset_1(B,A,A) -> (r1_relat_2(B,A) -> k3_relat_1(B) = A & k4_relset_1(A,A,B) = A))) # label(t98_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3114 (all A (v1_relat_1(A) -> (all B (r2_orders_1(A,B) -> v4_relat_2(k2_wellord1(A,B)) & v8_relat_2(k2_wellord1(A,B)) & v1_partfun1(k2_wellord1(A,B),B,B) & m2_relset_1(k2_wellord1(A,B),B,B) & v1_relat_2(k2_wellord1(A,B)))))) # label(t141_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3115 (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]. 22.08/23.33 3116 $T # label(t81_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3117 (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]. 22.08/23.33 3118 $T # label(t74_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3119 $T # label(t24_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3120 (all A (v1_relat_1(A) -> (all B all C (r2_wellord1(A,B) & r1_tarski(C,B) -> r2_wellord1(A,C))))) # label(t187_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3121 $T # label(t90_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3122 (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]. 22.08/23.33 3123 $T # label(t57_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3124 $T # label(t50_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3125 $T # label(t102_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3126 (all A (v1_relat_1(A) -> (all B (r2_wellord1(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(t143_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3127 $T # label(t56_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3128 (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]. 22.08/23.33 3129 $T # label(t75_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3130 (all A all B all C (v1_relat_1(C) -> (r1_tarski(B,A) & r4_relat_2(C,A) -> r4_relat_2(C,B)))) # label(t94_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3131 $T # label(t79_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3132 $T # label(t76_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3133 $T # label(t82_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3134 $T # label(t53_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3135 (all A (v1_relat_1(A) -> (all B (r7_orders_1(k4_relat_1(A),B) <-> r6_orders_1(A,B))))) # label(t164_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3136 (all A all B (v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v4_relat_2(B) & v1_relat_2(B) -> v2_orders_1(B))) # label(t110_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3137 $T # label(t145_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3138 (all A (v1_relat_1(A) -> (all B (r4_orders_1(A,B) <-> (all C -(r1_tarski(C,B) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(E,D),A))) & r2_hidden(D,B))) & v3_orders_1(k2_wellord1(A,C)))))))) # label(d9_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3139 $T # label(t72_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3140 $T # label(t154_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3141 (all A (v1_relat_1(A) -> (all B (r9_orders_1(k4_relat_1(A),B) <-> r8_orders_1(A,B))))) # label(t166_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3142 $T # label(t63_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3143 $T # label(t34_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3144 (all A (v1_relat_1(A) -> (all B (r5_orders_1(k4_relat_1(A),B) <-> r4_orders_1(A,B))))) # label(t151_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3145 $T # label(t20_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3146 $T # label(t144_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3147 $T # label(t43_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3148 (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]. 22.08/23.33 3149 (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 -(k9_relat_1(A,C) = B & v1_finset_1(C) & r1_tarski(C,k1_relat_1(A)))))))) # label(t195_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3150 $T # label(t153_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3151 (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]. 22.08/23.33 3152 (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) -> r2_orders_1(B,A))) # label(t140_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3153 $T # label(t103_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3154 $T # label(t22_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3155 (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) & r1_tarski(C,B) & B != C)))) & A != k1_xboole_0)) # label(t176_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3156 (all A (v1_orders_1(k6_partfun1(A)) & v2_orders_1(k6_partfun1(A)))) # label(t120_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3157 (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]. 22.08/23.33 3158 $T # label(t116_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3159 (all A all B (v1_relat_2(B) & v4_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> k3_relat_1(B) = A)) # label(t100_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3160 (all A all B all C all D all E (v1_relat_2(E) & v4_relat_2(E) & v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) -> (r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) & r2_hidden(D,A) & r2_hidden(C,A) & r2_hidden(B,A) -> r2_hidden(k4_tarski(B,D),E)))) # label(t14_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3161 (all A (v1_relat_1(A) -> (all B all C (r3_orders_1(A,B) & r1_tarski(C,B) -> r3_orders_1(A,C))))) # label(t134_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3162 $T # label(t55_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3163 $T # label(t147_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3164 $T # label(t23_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3165 (all A (v1_relat_1(A) -> (v2_orders_1(A) -> v1_orders_1(A)))) # label(t109_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3166 $T # label(t71_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3167 (all A (v1_relat_1(A) -> (all B (r2_hidden(B,k3_relat_1(A)) & (all C (r2_hidden(C,k3_relat_1(A)) -> C = B | r2_hidden(k4_tarski(B,C),A))) <-> r9_orders_1(A,B))))) # label(d14_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3168 (all A (v1_relat_1(A) -> (all B (r6_orders_1(k4_relat_1(A),B) <-> r7_orders_1(A,B))))) # label(t163_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3169 $T # label(t171_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3170 (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)) -> r2_hidden(k4_tarski(C,B),A) | B = C)))))) # label(d13_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3171 $T # label(t61_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3172 (all A (v1_relat_1(A) -> (all B (r4_orders_1(k4_relat_1(A),B) <-> r5_orders_1(A,B))))) # label(t152_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3173 $T # label(t21_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3174 $T # label(t18_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3175 (all A (v1_relat_1(A) -> (all B (r7_orders_1(A,B) <-> (all C -(r2_hidden(C,k3_relat_1(A)) & r2_hidden(k4_tarski(C,B),A) & C != B)) & r2_hidden(B,k3_relat_1(A)))))) # label(d12_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3176 $T # label(t123_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3177 $T # label(t46_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3178 $T # label(t86_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3179 (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]. 22.08/23.33 3180 (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]. 22.08/23.33 3181 (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]. 22.08/23.33 3182 $T # label(t58_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3183 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) <-> r4_relat_2(A,B) & r6_relat_2(A,B) & r8_relat_2(A,B) & r1_relat_2(A,B))))) # label(d8_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3184 (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]. 22.08/23.33 3185 (all A (r2_orders_1(k6_partfun1(A),A) & r1_orders_1(k6_partfun1(A),A))) # label(t146_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3186 (all A (-v1_xboole_0(A) -> (-r2_hidden(k1_xboole_0,A) -> (all B (v1_funct_1(B) & m2_relset_1(B,A,k3_tarski(A)) & v1_funct_2(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]. 22.08/23.33 3187 $T # label(t28_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3188 $T # label(t1_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3189 $T # label(t3_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3190 (all A (v1_relat_1(A) -> (all B (r6_orders_1(A,B) & v6_relat_2(A) -> r8_orders_1(A,B))))) # label(t160_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3191 (all A (-v1_xboole_0(A) -> -v1_xboole_0(k1_orders_1(A)))) # label(fc1_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3192 $T # label(t42_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3193 $T # label(t51_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3194 (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]. 22.08/23.33 3195 $T # label(t2_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3196 $T # label(t17_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3197 (all A (-v1_xboole_0(A) -> (all B (m1_orders_1(B,A) -> v1_funct_1(B) & m2_relset_1(B,A,k3_tarski(A)) & v1_funct_2(B,A,k3_tarski(A)))))) # label(dt_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3198 (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]. 22.08/23.33 3199 (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]. 22.08/23.33 3200 $T # label(t148_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3201 (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]. 22.08/23.33 3202 (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]. 22.08/23.33 3203 $T # label(t59_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3204 $T # label(t73_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3205 (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]. 22.08/23.33 3206 (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]. 22.08/23.33 3207 (all A (-v1_xboole_0(A) -> r2_hidden(A,k1_orders_1(A)))) # label(t7_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3208 (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]. 22.08/23.33 3209 (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]. 22.08/23.33 3210 (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]. 22.08/23.33 3211 (all A (v1_relat_1(A) -> (all B -(r2_orders_1(A,B) & B = k3_relat_1(A) & (all C -r6_orders_1(A,C)) & r4_orders_1(A,B))))) # label(t173_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3212 $T # label(t155_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3213 (all A (v1_relat_1(A) -> (v3_orders_1(A) <-> v1_relat_2(A) & v4_relat_2(A) & v6_relat_2(A) & v8_relat_2(A)))) # label(d5_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3214 $T # label(t118_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3215 $T # label(t29_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3216 $T # label(t37_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3217 (all A (v1_relat_1(A) -> (all B (r5_orders_1(A,B) <-> (all C -(r1_tarski(C,B) & (all D -((all E (r2_hidden(E,C) -> r2_hidden(k4_tarski(D,E),A))) & r2_hidden(D,B))) & v3_orders_1(k2_wellord1(A,C)))))))) # label(d10_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3218 (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]. 22.08/23.33 3219 (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]. 22.08/23.33 3220 (all A -(A != k1_xboole_0 & (all B -((all C -((all D (r2_hidden(D,B) -> r1_tarski(D,C))) & r2_hidden(C,A))) & v6_ordinal1(B) & r1_tarski(B,A))) & (all B -(r2_hidden(B,A) & (all C -(r1_tarski(B,C) & C != B & r2_hidden(C,A))))))) # label(t175_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3221 $T # label(t8_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3222 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> r2_hidden(k1_setfam_1(B),A) | B = k1_xboole_0)) & (all B -((all C -(C != B & r1_tarski(C,B) & r2_hidden(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t178_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3223 (all A (v1_relat_1(A) -> (all B (r6_orders_1(A,B) <-> r2_hidden(B,k3_relat_1(A)) & (all C -(C != B & r2_hidden(k4_tarski(B,C),A) & r2_hidden(C,k3_relat_1(A)))))))) # label(d11_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3224 $T # label(t30_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3225 $T # label(t38_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3226 $T # label(t49_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3227 $T # label(t117_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3228 $T # label(t85_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3229 (all A (v1_relat_1(A) -> (all B (r8_orders_1(k4_relat_1(A),B) <-> r9_orders_1(A,B))))) # label(t165_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3230 $T # label(t78_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3231 (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]. 22.08/23.33 3232 $T # label(t172_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3233 (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]. 22.08/23.33 3234 $T # label(t16_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.08/23.33 3235 (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]. 22.19/23.37 3236 $T # label(t89_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3237 (all A (-v1_xboole_0(A) -> (exists B m1_orders_1(B,A)))) # label(existence_m1_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3238 (all A all B all C (v1_relat_1(C) -> (r1_relat_2(C,A) & r1_tarski(B,A) -> r1_relat_2(C,B)))) # label(t93_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3239 (all A (v1_relat_1(A) -> (all B (r3_orders_1(A,B) -> m2_relset_1(k2_wellord1(A,B),B,B) & v1_partfun1(k2_wellord1(A,B),B,B) & v8_relat_2(k2_wellord1(A,B)) & v4_relat_2(k2_wellord1(A,B)) & v1_relat_2(k2_wellord1(A,B)))))) # label(t142_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3240 $T # label(t41_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3241 (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]. 22.19/23.37 3242 $T # label(dt_k1_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3243 $T # label(t52_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3244 $T # label(t80_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3245 (all A (v1_relat_1(A) -> (all B -(k1_xboole_0 = B & r4_orders_1(A,B))))) # label(t149_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3246 $T # label(t10_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3247 $T # label(t77_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3248 (all A (-(k1_xboole_0 = k3_tarski(A) & (exists B (k1_xboole_0 != B & r2_hidden(B,A)))) & -(k3_tarski(A) != k1_xboole_0 & (all B -(k1_xboole_0 != B & r2_hidden(B,A)))))) # label(t91_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3249 (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]. 22.19/23.37 3250 (all A all B all C (v1_relat_2(C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v4_relat_2(C) -> (r2_hidden(B,A) -> r2_hidden(k4_tarski(B,B),C)))) # label(t12_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3251 (all A (v1_relat_1(A) -> (all B -(k1_xboole_0 = B & r5_orders_1(A,B))))) # label(t150_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3252 (all A (m1_subset_1(A,f1_s2_orders_1) -> p1_s2_orders_1(A,A))) & (all A (m1_subset_1(A,f1_s2_orders_1) -> (all B (m1_subset_1(B,f1_s2_orders_1) -> (p1_s2_orders_1(A,B) & p1_s2_orders_1(B,A) -> B = A))))) & (all A -((all B (m1_subset_1(B,f1_s2_orders_1) -> (all C (m1_subset_1(C,f1_s2_orders_1) -> -(-p1_s2_orders_1(B,C) & -p1_s2_orders_1(C,B) & r2_hidden(C,A) & r2_hidden(B,A)))))) & (all B (m1_subset_1(B,f1_s2_orders_1) -> (exists C (r2_hidden(C,A) & -p1_s2_orders_1(B,C) & 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(B,C) & p1_s2_orders_1(A,B) -> p1_s2_orders_1(A,C)))))))) -> (exists A ((all B (m1_subset_1(B,f1_s2_orders_1) -> -(A != B & p1_s2_orders_1(B,A)))) & m1_subset_1(A,f1_s2_orders_1))) # label(s2_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3253 $T # label(t60_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3254 $T # label(t47_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3255 $T # label(t169_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3256 $T # label(t88_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3257 $T # label(t87_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3258 (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) & k3_relat_1(A) = B)))) # label(t174_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3259 $T # label(t36_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3260 $T # label(t9_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3261 $T # label(t19_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3262 $T # label(t167_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3263 $T # label(t33_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3264 $T # label(t170_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3265 $T # label(t66_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3266 (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]. 22.19/23.37 3267 $T # label(t35_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3268 (all A (v1_relat_1(A) -> (all B (r1_orders_1(A,B) <-> r1_relat_2(A,B) & r8_relat_2(A,B))))) # label(d6_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3269 $T # label(t45_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3270 (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]. 22.19/23.37 3271 $T # label(t25_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3272 (all A (v1_relat_1(A) -> k1_xboole_0 = k2_wellord1(A,k1_xboole_0))) # label(t194_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3273 (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]. 22.19/23.37 3274 (all A (v1_relat_1(A) -> (v2_wellord1(A) -> v3_orders_1(A) & v2_orders_1(A) & v1_orders_1(A)))) # label(t107_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3275 $T # label(t67_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3276 $T # label(t44_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3277 (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]. 22.19/23.37 3278 $T # label(t70_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3279 $T # label(t64_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3280 (all A (v1_relat_1(A) -> (v3_orders_1(A) -> v1_orders_1(A) & v2_orders_1(A)))) # label(t108_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3281 (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) -> (v6_relat_2(B) -> v3_orders_1(B)))) # label(t112_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3282 $T # label(t156_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3283 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) -> A = k3_relat_1(B))) # label(t97_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3284 (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]. 22.19/23.37 3285 $T # label(t31_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3286 (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) -> k4_relset_1(A,A,B) = A & A = k5_relset_1(A,A,B))) # label(t99_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3287 (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]. 22.19/23.37 3288 (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]. 22.19/23.37 3289 $T # label(t122_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3290 (all A (v1_relat_1(A) -> (all B (v4_relat_2(A) & r8_orders_1(A,B) -> r6_orders_1(A,B))))) # label(t158_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3291 $T # label(t84_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3292 $T # label(t65_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3293 $T # label(t54_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.19/23.37 3294 (all A all B all C all D (v1_relat_2(D) & v4_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) -> (r2_hidden(B,A) & r2_hidden(k4_tarski(B,C),D) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(C,A) -> C = B))) # label(t13_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3295 $T # label(t62_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3296 (all A -((all B (v6_ordinal1(B) & r1_tarski(B,A) -> k1_xboole_0 = B | r2_hidden(k3_tarski(B),A))) & (all B -((all C -(C != B & r1_tarski(B,C) & r2_hidden(C,A))) & r2_hidden(B,A))) & k1_xboole_0 != A)) # label(t177_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3297 $T # label(t121_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3298 (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]. 22.24/23.41 3299 $T # label(t68_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3300 (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]. 22.24/23.41 3301 (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]. 22.24/23.41 3302 (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]. 22.24/23.41 3303 (all A (v1_relat_1(A) -> (all B k2_wellord1(k4_relat_1(A),B) = k4_relat_1(k2_wellord1(A,B))))) # label(t193_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3304 (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]. 22.24/23.41 3305 (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]. 22.24/23.41 3306 $T # label(t48_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3307 (all A (m1_subset_1(A,f1_s1_orders_1) -> (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> (p1_s1_orders_1(A,B) & p1_s1_orders_1(B,C) -> p1_s1_orders_1(A,C)))))))) & (all A -((all B (m1_subset_1(B,f1_s1_orders_1) -> (exists C (m1_subset_1(C,f1_s1_orders_1) & r2_hidden(C,A) & -p1_s1_orders_1(C,B))))) & (all B (m1_subset_1(B,f1_s1_orders_1) -> (all C (m1_subset_1(C,f1_s1_orders_1) -> -(r2_hidden(C,A) & -p1_s1_orders_1(B,C) & -p1_s1_orders_1(C,B) & r2_hidden(B,A)))))) & r1_tarski(A,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(B,A) & p1_s1_orders_1(A,B) -> B = A))))) & (all A (m1_subset_1(A,f1_s1_orders_1) -> p1_s1_orders_1(A,A))) -> (exists A ((all B (m1_subset_1(B,f1_s1_orders_1) -> -(p1_s1_orders_1(A,B) & B != A))) & m1_subset_1(A,f1_s1_orders_1))) # label(s1_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3308 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (r2_hidden(A,k1_orders_1(B)) <-> r1_tarski(A,B)))))) # label(t5_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3309 (all A (v1_relat_1(A) -> (all B (r2_wellord1(A,B) -> r1_orders_1(A,B) & r2_orders_1(A,B) & r3_orders_1(A,B))))) # label(t124_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3310 $T # label(t69_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3311 (all A (v1_relat_1(A) -> (v8_relat_2(A) & v4_relat_2(A) & v1_relat_2(A) <-> v2_orders_1(A)))) # label(d4_orders_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3312 (all A exists B m1_eqrel_1(B,A)) # label(existence_m1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3313 (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]. 22.24/23.41 3314 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> m1_eqrel_1(k8_eqrel_1(A,B),A))) # label(dt_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3315 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> m1_eqrel_1(k7_eqrel_1(A,B),A))) # label(t42_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3316 (all A all B (r2_hidden(B,A) -> A = k6_eqrel_1(A,k1_eqrel_1(A),B))) # label(t34_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3317 (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 (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,C) <-> (exists E (r2_hidden(E,A) & k6_eqrel_1(A,B,E) = D))))) <-> C = k7_eqrel_1(A,B)))))) # label(d5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3318 (all A all B (-v1_xboole_0(A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> -v1_xboole_0(k7_eqrel_1(A,B)) & v1_setfam_1(k7_eqrel_1(A,B)))) # label(fc4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3319 (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]. 22.24/23.41 3320 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) -> (all D (m2_relset_1(D,A,A) & v1_partfun1(D,A,A) & v8_relat_2(D) & v3_relat_2(D) -> (D = k5_eqrel_1(A,B,C) <-> r1_tarski(k3_eqrel_1(A,B,C),D) & (all E (v1_partfun1(E,A,A) & m2_relset_1(E,A,A) & v8_relat_2(E) & 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]. 22.24/23.41 3321 (all A all B (v1_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v3_relat_2(B) -> (all C -((all D -r2_hidden(C,k6_eqrel_1(A,B,D))) & r2_hidden(C,A))))) # label(t29_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3322 $T # label(t8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3323 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & 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) -> k4_eqrel_1(A,B,C) = k4_eqrel_1(A,C,B))) # label(commutativity_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3324 $T # label(t41_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3325 (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 (v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> -(k3_eqrel_1(A,B,C) = k1_eqrel_1(A) & k1_eqrel_1(A) != C & k1_eqrel_1(A) != B))))) # label(t38_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3326 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> (all C (r2_hidden(C,A) -> r2_hidden(C,k6_eqrel_1(A,B,C)))))) # label(t28_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3327 (all A (v3_relat_2(k1_eqrel_1(A)) & m2_relset_1(k1_eqrel_1(A),A,A) & v1_partfun1(k1_eqrel_1(A),A,A) & v8_relat_2(k1_eqrel_1(A)))) # label(t7_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3328 (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 all D -(k6_eqrel_1(A,B,C) != k6_eqrel_1(A,B,D) & -r1_xboole_0(k6_eqrel_1(A,B,C),k6_eqrel_1(A,B,D)) & r2_hidden(D,A) & r2_hidden(C,A))))) # label(t32_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3329 (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]. 22.24/23.41 3330 (all A all B all C (m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) & v1_relat_2(B) -> m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)))) # label(dt_k6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3331 $T # label(d2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3332 (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]. 22.24/23.41 3333 (all A all B (m1_eqrel_1(B,A) -> v1_setfam_1(B))) # label(cc2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3334 (all A all B all C all D all E (v8_relat_2(E) & v1_partfun1(E,A,A) & m2_relset_1(E,A,A) -> (r2_hidden(k4_tarski(C,D),E) & r2_hidden(k4_tarski(B,C),E) -> r2_hidden(k4_tarski(B,D),E)))) # label(t13_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3335 (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]. 22.24/23.41 3336 (all A all B (p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(B,A))) & (all A all B all C (p1_s1_eqrel_1(B,C) & p1_s1_eqrel_1(A,B) -> p1_s1_eqrel_1(A,C))) & (all A (r2_hidden(A,f1_s1_eqrel_1) -> p1_s1_eqrel_1(A,A))) -> (exists A (v3_relat_2(A) & v1_partfun1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & (all B all C (r2_hidden(k4_tarski(B,C),A) <-> p1_s1_eqrel_1(B,C) & r2_hidden(C,f1_s1_eqrel_1) & r2_hidden(B,f1_s1_eqrel_1))) & m2_relset_1(A,f1_s1_eqrel_1,f1_s1_eqrel_1) & v8_relat_2(A))) # label(s1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3337 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k3_xboole_0(B,C) = k4_eqrel_1(A,B,C))) # label(redefinition_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3338 (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]. 22.24/23.41 3339 (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]. 22.24/23.41 3340 (all A m2_relset_1(k1_eqrel_1(A),A,A)) # label(dt_k1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3341 $T # label(t10_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3342 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> k5_eqrel_1(A,B,B) = B)) # label(t22_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3343 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> k7_eqrel_1(A,B) = k8_eqrel_1(A,B))) # label(redefinition_k8_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3344 $T # label(t15_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3345 (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) & v3_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) -> k5_eqrel_1(A,B,B) = B)) # label(idempotence_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3346 (all A all B all C (v3_relat_2(C) & m2_relset_1(C,B,B) & v1_partfun1(C,B,B) & v8_relat_2(C) -> -((all D (m1_subset_1(D,B) -> A != k6_eqrel_1(B,C,D))) & r2_hidden(A,k7_eqrel_1(B,C))))) # label(t45_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3347 (all A all B (v3_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) -> (all C (v3_relat_2(C) & 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]. 22.24/23.41 3348 (all A (v3_relat_2(k6_partfun1(A)) & v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A) & v8_relat_2(k6_partfun1(A)))) # label(t6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3349 (all A all B (m2_relset_1(B,A,A) -> (v1_relat_2(B) & v3_relat_2(B) & k3_relat_1(B) = A & v8_relat_2(B) <-> v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m2_relset_1(B,A,A)))) # label(t16_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3350 $T # label(t2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3351 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v1_relat_2(B) -> -(k1_xboole_0 = B & (exists C r2_hidden(C,A))))) # label(t14_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3352 (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]. 22.24/23.41 3353 (all A all B all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_relat_2(C) -> (all D (r2_hidden(D,A) -> (k6_eqrel_1(A,C,B) = k6_eqrel_1(A,C,D) <-> r2_hidden(B,k6_eqrel_1(A,C,D))))))) # label(t31_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3354 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (A = k1_xboole_0 -> k1_xboole_0 = k7_eqrel_1(A,B)))) # label(t40_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3355 (all A all B (v3_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> 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]. 22.24/23.41 3356 (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]. 22.24/23.41 3357 (all A all B all C (v3_relat_2(C) & v8_relat_2(C) & m1_relset_1(C,A,A) & v1_partfun1(C,A,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> 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]. 22.24/23.41 3358 (all A all B all C (m1_relset_1(C,A,A) & m1_relset_1(B,A,A) -> B = k2_eqrel_1(A,B,B))) # label(idempotence_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3359 (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))) -> k1_xboole_0 = B | m2_relset_1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v1_partfun1(k6_setfam_1(k2_zfmisc_1(A,A),B),A,A) & v8_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B)) & v3_relat_2(k6_setfam_1(k2_zfmisc_1(A,A),B))))) # label(t19_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3360 (all A all B (v3_relat_2(B) & v8_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & -v1_xboole_0(A) -> -v1_xboole_0(k7_eqrel_1(A,B)))) # label(fc3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3361 (all A k2_zfmisc_1(A,A) = k1_eqrel_1(A)) # label(d1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3362 (all A all B all C all D (v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v3_relat_2(D) & v1_relat_2(D) -> (r2_hidden(B,k6_eqrel_1(A,D,C)) <-> r2_hidden(k4_tarski(B,C),D)))) # label(t27_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3363 (all A all B all C (v8_relat_2(B) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> k4_eqrel_1(A,B,B) = B)) # label(idempotence_k4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3364 $T # label(t3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3365 (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]. 22.24/23.41 3366 (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]. 22.24/23.41 3367 (all A all B (m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> ((exists C A = k6_eqrel_1(A,B,C)) -> B = k1_eqrel_1(A)))) # label(t35_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3368 (all A all B all C all D all E (v1_relat_2(E) & m2_relset_1(E,A,A) & v1_partfun1(E,A,A) & v8_relat_2(E) & 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]. 22.24/23.41 3369 (all A all B all C all D (v8_relat_2(D) & m2_relset_1(D,B,B) & v1_partfun1(D,B,B) & v3_relat_2(D) -> (all E (v3_relat_2(E) & m2_relset_1(E,B,B) & v1_partfun1(E,B,B) & v8_relat_2(E) -> (r2_hidden(A,B) -> ((exists F (v1_funct_1(F) & v1_finseq_1(F) & k1_funct_1(F,np__1) = A & C = k1_funct_1(F,k3_finseq_1(F)) & (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,G) -> r2_hidden(k4_tarski(k1_funct_1(F,G),k1_funct_1(F,k1_nat_1(G,np__1))),k3_eqrel_1(B,D,E)) | r1_xreal_0(k3_finseq_1(F),G)))) & r1_xreal_0(np__1,k3_finseq_1(F)) & v1_relat_1(F))) <-> r2_hidden(k4_tarski(A,C),k5_eqrel_1(B,D,E)))))))) # label(t36_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3370 (all A all B (v8_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C (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) & v1_partfun1(D,A,A) & m2_relset_1(D,A,A) & v8_relat_2(D) -> (k3_eqrel_1(A,B,C) = D -> (all E -(k6_eqrel_1(A,D,E) != k6_eqrel_1(A,C,E) & k6_eqrel_1(A,D,E) != k6_eqrel_1(A,B,E) & r2_hidden(E,A)))))))))) # label(t37_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3371 $T # label(t26_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3372 $T # label(t9_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3373 $T # label(t39_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3374 $T # label(t21_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3375 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (A != k1_xboole_0 -> ((all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (r2_hidden(C,B) -> k1_xboole_0 != C & (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> -(r2_hidden(D,B) & D != C & -r1_xboole_0(C,D))))))) & k5_setfam_1(A,B) = A <-> m1_eqrel_1(B,A))) & (k1_xboole_0 = A -> (m1_eqrel_1(B,A) <-> k1_xboole_0 = B)))) # label(d6_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3376 (all A all B all C (v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) -> k5_eqrel_1(A,B,C) = k5_eqrel_1(A,C,B))) # label(commutativity_k5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3377 $T # label(t5_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3378 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_xboole_0(B,C) = k2_eqrel_1(A,B,C))) # label(redefinition_k2_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3379 (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]. 22.24/23.41 3380 (all A all B all C (v8_relat_2(B) & 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) & v3_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]. 22.24/23.41 3381 $T # label(t1_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3382 (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]. 22.24/23.41 3383 (all A (r8_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A) & r1_relat_2(k6_partfun1(A),A))) # label(t4_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3384 (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 (v3_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(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]. 22.24/23.41 3385 (all A all B all C (v8_relat_2(C) & v1_partfun1(C,A,A) & m2_relset_1(C,A,A) & v3_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]. 22.24/23.41 3386 (all A all B (v1_partfun1(B,A,A) & m2_relset_1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k4_eqrel_1(A,k6_partfun1(A),B) = k6_partfun1(A))) # label(t17_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3387 (all 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_relset_1(C,A,A) & v1_partfun1(C,A,A) & v8_relat_2(C) & v3_relat_2(C) -> B = k4_eqrel_1(A,B,k5_eqrel_1(A,B,C)))))) # label(t24_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3388 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,A,A) -> k3_eqrel_1(A,B,C) = k2_xboole_0(B,C))) # label(redefinition_k3_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3389 (all A all B all C (m1_relset_1(B,A,A) & m1_relset_1(C,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]. 22.24/23.41 3390 (all A all B (v1_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v3_relat_2(B) -> (all C 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]. 22.24/23.41 3391 (all A all B (m2_relset_1(B,A,A) -> (exists C (v8_relat_2(C) & (all D (v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,A,A) & v1_partfun1(D,A,A) -> (r1_tarski(B,D) -> r1_tarski(C,D)))) & r1_tarski(B,C) & m2_relset_1(C,A,A) & v1_partfun1(C,A,A) & v3_relat_2(C))))) # label(t20_eqrel_1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3392 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_relat_1(k4_funct_5(C)) = k2_zfmisc_1(k1_relat_1(C),A) & k2_zfmisc_1(A,k1_relat_1(C)) = k1_relat_1(k6_funct_5(C))))) # label(t33_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3393 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k3_funct_5(B))) -> v1_relat_1(k1_funct_1(k3_funct_5(B),A)) & v1_funct_1(k1_funct_1(k3_funct_5(B),A))))) # label(t37_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3394 (all A (v1_relat_1(A) & v1_funct_1(A) -> v1_funct_1(k3_funct_5(A)) & v1_relat_1(k3_funct_5(A)))) # label(dt_k3_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3395 (all A all B (r1_tarski(k2_funct_5(k2_zfmisc_1(A,B)),B) & r1_tarski(k1_funct_5(k2_zfmisc_1(A,B)),A))) # label(t12_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3396 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) & r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & k4_funct_5(C) = k4_funct_5(D) -> r2_hidden(k1_xboole_0,k2_relat_1(C)) | r2_hidden(k1_xboole_0,k2_relat_1(D)) | D = C))))) # label(t61_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3397 (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) -> -(A = k1_relat_1(E) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,A) -> k1_funct_1(E,F) = k1_funct_1(D,k4_tarski(F,C)))) & E = k1_funct_1(k5_funct_5(D),C)))) & r2_hidden(C,B) & k1_relat_1(D) = k2_zfmisc_1(A,B) & k1_xboole_0 != k2_zfmisc_1(A,B)))) # label(t39_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3398 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> r1_tarski(k2_relat_1(k4_funct_5(C)),B) & r1_tarski(k2_relat_1(k6_funct_5(C)),B)))) # label(t48_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3399 (all A all B (k1_card_1(A) = k1_card_1(k1_funct_2(k1_tarski(B),A)) & r2_wellord2(A,k1_funct_2(k1_tarski(B),A)))) # label(t65_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3400 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_funct_1(C,A) = D & r2_hidden(B,k1_relat_1(D)) & r2_hidden(A,k1_relat_1(C)) -> r2_hidden(k4_tarski(A,B),k1_relat_1(k4_funct_5(C))) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k4_funct_5(C))) & k1_funct_1(D,B) = k1_funct_1(k4_funct_5(C),k4_tarski(A,B))))))) # label(t45_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3401 $T # label(t22_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3402 (exists A (k1_relat_1(A) = f1_s1_funct_5 & (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(B,f1_s1_funct_5) -> k1_funct_1(A,B) = f2_s1_funct_5(B)))) & v1_funct_1(A) & v1_relat_1(A))) # label(s1_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3403 (all A all B all C (r2_hidden(k4_tarski(A,B),C) -> r2_hidden(B,k2_funct_5(C)) & r2_hidden(A,k1_funct_5(C)))) # label(t4_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3404 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> r1_tarski(k2_relat_1(k5_funct_5(C)),k1_funct_2(A,k2_relat_1(C))) & r1_tarski(k2_relat_1(k3_funct_5(C)),k1_funct_2(B,k2_relat_1(C)))))) # label(t42_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3405 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (D = k1_funct_1(k5_funct_5(C),B) & r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> k1_funct_1(C,k4_tarski(A,B)) = k1_funct_1(D,A) & r2_hidden(A,k1_relat_1(D))))))) # label(t29_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3406 (all A (v1_funct_1(A) & v1_relat_1(A) -> k6_funct_5(A) = k2_funct_4(k4_funct_5(A)))) # label(d6_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3407 (all A (k2_funct_5(A) = k1_xboole_0 | k1_xboole_0 = k1_funct_5(A) -> (all B all C -r2_hidden(k4_tarski(B,C),A)))) # label(t18_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3408 (all A all B ((all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(C,D),A)))) <-> k1_funct_5(A) = B)) # label(d1_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3409 (all A all B all C (A != B -> k1_card_1(k2_zfmisc_1(C,C)) = k1_card_1(k1_funct_2(k2_tarski(A,B),C)) & r2_wellord2(k1_funct_2(k2_tarski(A,B),C),k2_zfmisc_1(C,C)))) # label(t73_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3410 (all A all B all C (r2_wellord2(k1_funct_2(A,k2_zfmisc_1(B,C)),k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))) & k1_card_1(k1_funct_2(A,k2_zfmisc_1(B,C))) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,B),k1_funct_2(A,C))))) # label(t71_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3411 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(D),k4_partfun1(A,B)) & k6_funct_5(C) = k6_funct_5(D) & r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> C = D | r2_hidden(k1_xboole_0,k2_relat_1(D)) | r2_hidden(k1_xboole_0,k2_relat_1(C))))))) # label(t62_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3412 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k1_relat_1(k6_funct_5(C)),k2_zfmisc_1(A,k1_relat_1(C))) & r1_tarski(k1_relat_1(k4_funct_5(C)),k2_zfmisc_1(k1_relat_1(C),A))))) # label(t44_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3413 (all A all B all C all D (v1_funct_1(D) & v1_relat_1(D) -> -(k2_zfmisc_1(A,B) != k1_xboole_0 & (all E (v1_relat_1(E) & v1_funct_1(E) -> -(E = k1_funct_1(k3_funct_5(D),C) & r1_tarski(k2_relat_1(E),k2_relat_1(D)) & (all F (r2_hidden(F,B) -> k1_funct_1(D,k4_tarski(C,F)) = k1_funct_1(E,F))) & k1_relat_1(E) = B))) & r2_hidden(C,A) & k2_zfmisc_1(A,B) = k1_relat_1(D)))) # label(t36_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3414 (all A all B all C all D (k1_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(A,C) & k2_funct_5(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) = k2_tarski(B,D))) # label(t16_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3415 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_relat_1(k6_funct_5(A)) & v1_funct_1(k6_funct_5(A)))) # label(dt_k6_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3416 (all A all B (-(k2_zfmisc_1(A,B) = k1_xboole_0 & k1_xboole_0 = k2_zfmisc_1(B,A) & A = k1_xboole_0) -> B = k1_funct_5(k2_zfmisc_1(B,A)) & B = k2_funct_5(k2_zfmisc_1(A,B)))) # label(t11_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3417 (all A all B k1_funct_2(A,k1_tarski(B)) = k1_tarski(k2_funcop_1(A,B))) # label(t66_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3418 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k5_funct_5(A)) & v1_relat_1(k5_funct_5(A)))) # label(dt_k5_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3419 $T # label(t24_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3420 (all A all B all C (k1_card_1(k1_funct_2(k2_zfmisc_1(A,B),C)) = k1_card_1(k1_funct_2(A,k1_funct_2(B,C))) & r2_wellord2(k1_funct_2(k2_zfmisc_1(A,B),C),k1_funct_2(A,k1_funct_2(B,C))))) # label(t70_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3421 (all A all B all C (r1_xboole_0(A,B) -> k1_card_1(k1_funct_2(k2_xboole_0(A,B),C)) = k1_card_1(k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))) & r2_wellord2(k1_funct_2(k2_xboole_0(A,B),C),k2_zfmisc_1(k1_funct_2(A,C),k1_funct_2(B,C))))) # label(t69_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3422 (all A (v1_relat_1(A) & v1_funct_1(A) -> k2_funct_5(k1_relat_1(A)) = k1_relat_1(k5_funct_5(A)))) # label(t30_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3423 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> k4_funct_5(k3_funct_5(C)) = C & k6_funct_5(k5_funct_5(C)) = C))) # label(t57_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3424 $T # label(t2_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3425 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k6_funct_5(k5_funct_5(C)) = C & k4_funct_5(k3_funct_5(C)) = C))) # label(t56_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3426 (all A all B all C all D (k1_card_1(A) = k1_card_1(B) & k1_card_1(D) = k1_card_1(C) -> k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)))) # label(t68_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3427 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) & k2_zfmisc_1(A,B) = k1_relat_1(D) & k3_funct_5(D) = k3_funct_5(C) -> D = C))))) # label(t51_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3428 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_xboole_0 = A | k5_funct_5(k6_funct_5(C)) = C & k3_funct_5(k4_funct_5(C)) = C))) # label(t55_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3429 $T # label(dt_k1_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3430 (all A ((all B all C -r2_hidden(k4_tarski(B,C),A)) -> k1_xboole_0 = k1_funct_5(A) & k1_xboole_0 = k2_funct_5(A))) # label(t17_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3431 (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(k1_relat_1(C),k2_zfmisc_1(A,B)) & k5_funct_5(C) = k5_funct_5(D) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) -> D = C))))) # label(t60_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3432 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) & r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k6_funct_5(C) = k6_funct_5(D) -> k1_xboole_0 = A | C = D))))) # label(t54_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3433 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B all C -r2_hidden(k4_tarski(B,C),k1_relat_1(A))) -> k3_funct_5(A) = k1_xboole_0 & k5_funct_5(A) = k1_xboole_0))) # label(t34_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3434 (all A (v1_relat_1(A) & v1_funct_1(A) -> r1_tarski(k2_relat_1(k3_funct_5(A)),k4_partfun1(k2_funct_5(k1_relat_1(A)),k2_relat_1(A))) & r1_tarski(k2_relat_1(k5_funct_5(A)),k4_partfun1(k1_funct_5(k1_relat_1(A)),k2_relat_1(A))))) # label(t43_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.41 3435 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_funct_1(k5_funct_5(B),A) = C & r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> r1_tarski(k2_relat_1(C),k2_relat_1(B)) & (all D (r2_hidden(D,k1_relat_1(C)) -> r2_hidden(k4_tarski(D,A),k1_relat_1(B)) & k1_funct_1(C,D) = k1_funct_1(B,k4_tarski(D,A)))) & r1_tarski(k1_relat_1(C),k1_funct_5(k1_relat_1(B))) & k1_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_funct_5(k1_relat_1(B)),k1_tarski(A)))) = k1_relat_1(C)))))) # label(t41_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3436 (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(k3_funct_5(B))) & k1_funct_1(k3_funct_5(B),A) = C -> k1_relat_1(C) = k2_funct_5(k3_xboole_0(k1_relat_1(B),k2_zfmisc_1(k1_tarski(A),k2_funct_5(k1_relat_1(B))))) & r1_tarski(k1_relat_1(C),k2_funct_5(k1_relat_1(B))) & (all D (r2_hidden(D,k1_relat_1(C)) -> k1_funct_1(B,k4_tarski(A,D)) = k1_funct_1(C,D) & r2_hidden(k4_tarski(A,D),k1_relat_1(B)))) & r1_tarski(k2_relat_1(C),k2_relat_1(B))))))) # label(t38_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3437 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (k1_relat_1(B) = k1_funct_5(k1_relat_1(A)) & (all C -((all D (v1_relat_1(D) & v1_funct_1(D) -> -(D = k1_funct_1(B,C) & k2_funct_5(k3_xboole_0(k1_relat_1(A),k2_zfmisc_1(k1_tarski(C),k2_funct_5(k1_relat_1(A))))) = k1_relat_1(D) & (all E (r2_hidden(E,k1_relat_1(D)) -> k1_funct_1(D,E) = k1_funct_1(A,k4_tarski(C,E))))))) & r2_hidden(C,k1_funct_5(k1_relat_1(A))))) <-> k3_funct_5(A) = B))))) # label(d3_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3438 (all A all B (k2_funct_5(k2_xboole_0(A,B)) = k2_xboole_0(k2_funct_5(A),k2_funct_5(B)) & k2_xboole_0(k1_funct_5(A),k1_funct_5(B)) = k1_funct_5(k2_xboole_0(A,B)))) # label(t6_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3439 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (k1_relat_1(C) = k2_zfmisc_1(A,B) -> k1_relat_1(k5_funct_5(C)) = B & A = k1_relat_1(k3_funct_5(C)) | k2_zfmisc_1(A,B) = k1_xboole_0))) # label(t31_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3440 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> v1_funct_1(k1_funct_1(k3_funct_5(C),A)) & v1_relat_1(k1_funct_1(k3_funct_5(C),A)) & r2_hidden(A,k1_relat_1(k3_funct_5(C)))))) # label(t26_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3441 (all A all B (r1_tarski(k5_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k5_xboole_0(A,B))) & r1_tarski(k5_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k5_xboole_0(A,B))))) # label(t9_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3442 (all A (v1_funct_1(A) & v1_relat_1(A) -> ((all B -(v1_funct_1(k1_funct_1(A,B)) & v1_relat_1(k1_funct_1(A,B)) & r2_hidden(B,k1_relat_1(A)))) -> k1_xboole_0 = k6_funct_5(A) & k1_xboole_0 = k4_funct_5(A)))) # label(t35_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3443 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k2_zfmisc_1(A,B) = k1_relat_1(D) & k5_funct_5(D) = k5_funct_5(C) & k2_zfmisc_1(A,B) = k1_relat_1(C) -> C = D))))) # label(t52_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3444 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k2_relat_1(D),k1_funct_2(A,B)) & k4_funct_5(C) = k4_funct_5(D) & r1_tarski(k2_relat_1(C),k1_funct_2(A,B)) -> k1_xboole_0 = A | D = C))))) # label(t53_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3445 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> r1_tarski(k1_funct_5(A),B) & r1_tarski(k2_funct_5(A),C))) # label(t13_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3446 $T # label(dt_k2_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3447 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (r2_hidden(A,k1_relat_1(k5_funct_5(B))) -> v1_funct_1(k1_funct_1(k5_funct_5(B),A)) & v1_relat_1(k1_funct_1(k5_funct_5(B),A))))) # label(t40_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3448 (all A all B (k1_funct_5(k1_tarski(k4_tarski(A,B))) = k1_tarski(A) & k1_tarski(B) = k2_funct_5(k1_tarski(k4_tarski(A,B))))) # label(t15_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3449 (all A (v1_relat_1(A) -> k2_funct_5(A) = k2_relat_1(A) & k1_relat_1(A) = k1_funct_5(A))) # label(t21_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3450 (all A (k1_funct_5(A) = k1_xboole_0 <-> k2_funct_5(A) = k1_xboole_0)) # label(t19_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3451 (all A all B all C (A != B -> r2_wellord2(k1_funct_2(C,k2_tarski(A,B)),k1_zfmisc_1(C)) & k1_card_1(k1_zfmisc_1(C)) = k1_card_1(k1_funct_2(C,k2_tarski(A,B))))) # label(t72_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3452 $T # label(t25_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3453 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> r1_tarski(k2_relat_1(k6_funct_5(C)),B) & r1_tarski(k2_relat_1(k4_funct_5(C)),B)))) # label(t47_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3454 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (k1_funct_1(k3_funct_5(C),A) = D & r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> r2_hidden(B,k1_relat_1(D)) & k1_funct_1(D,B) = k1_funct_1(C,k4_tarski(A,B))))))) # label(t27_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3455 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) -> r1_tarski(k1_relat_1(k5_funct_5(C)),B) & r1_tarski(k1_relat_1(k3_funct_5(C)),A)))) # label(t32_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3456 (all A all B (r1_tarski(A,B) -> r1_tarski(k2_funct_5(A),k2_funct_5(B)) & r1_tarski(k1_funct_5(A),k1_funct_5(B)))) # label(t5_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3457 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r2_hidden(A,k1_relat_1(C)) & D = k1_funct_1(C,A) & r2_hidden(B,k1_relat_1(D)) -> r2_hidden(k4_tarski(B,A),k1_relat_1(k6_funct_5(C))) & k1_funct_1(k6_funct_5(C),k4_tarski(B,A)) = k1_funct_1(D,B) & r2_hidden(k1_funct_1(D,B),k2_relat_1(k6_funct_5(C)))))))) # label(t46_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3458 (all A all B all C (r1_tarski(A,B) -> r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)))) # label(t63_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3459 $T # label(t14_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3460 $T # label(t23_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3461 (all A all B (r1_tarski(k2_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k2_funct_5(A),k2_funct_5(B))) & r1_tarski(k1_funct_5(k3_xboole_0(A,B)),k3_xboole_0(k1_funct_5(A),k1_funct_5(B))))) # label(t7_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3462 (all A all B (r1_tarski(k4_xboole_0(k1_funct_5(A),k1_funct_5(B)),k1_funct_5(k4_xboole_0(A,B))) & r1_tarski(k4_xboole_0(k2_funct_5(A),k2_funct_5(B)),k2_funct_5(k4_xboole_0(A,B))))) # label(t8_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3463 (all A (v1_relat_1(A) & v1_funct_1(A) -> k3_funct_5(k2_funct_4(A)) = k5_funct_5(A))) # label(d5_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3464 (all A all B (k2_funct_5(A) = B <-> (all C (r2_hidden(C,B) <-> (exists D r2_hidden(k4_tarski(D,C),A)))))) # label(d2_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3465 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (r1_tarski(k1_relat_1(C),k2_zfmisc_1(A,B)) & k3_funct_5(D) = k3_funct_5(C) & r1_tarski(k1_relat_1(D),k2_zfmisc_1(A,B)) -> C = D))))) # label(t59_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3466 (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_relat_1(D) & v1_funct_1(D) -> (r2_hidden(C,k1_relat_1(B)) & D = k1_funct_1(A,k1_mcart_1(C)) -> k1_funct_1(B,C) = k1_funct_1(D,k2_mcart_1(C))))) & (all C (r2_hidden(C,k1_relat_1(B)) <-> (exists D exists E ((exists F (k4_tarski(D,F) = C & r2_hidden(F,k1_relat_1(E)) & E = k1_funct_1(A,D) & r2_hidden(D,k1_relat_1(A)))) & v1_funct_1(E) & v1_relat_1(E))))) <-> k4_funct_5(A) = B))))) # label(d4_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3467 $T # label(t3_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3468 (all A k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0)) # label(t64_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3469 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k4_funct_5(A)) & v1_relat_1(k4_funct_5(A)))) # label(dt_k4_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3470 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r2_hidden(k4_tarski(A,B),k1_relat_1(C)) -> v1_funct_1(k1_funct_1(k5_funct_5(C),B)) & v1_relat_1(k1_funct_1(k5_funct_5(C),B)) & r2_hidden(B,k1_relat_1(k5_funct_5(C)))))) # label(t28_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3471 (all A all B all C all D (r2_wellord2(A,B) & r2_wellord2(C,D) -> k1_card_1(k1_funct_2(A,C)) = k1_card_1(k1_funct_2(B,D)) & r2_wellord2(k1_funct_2(A,C),k1_funct_2(B,D)))) # label(t67_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3472 (all A (v1_funct_1(A) & v1_relat_1(A) -> k2_funct_5(k1_relat_1(A)) = k1_funct_5(k1_relat_1(k2_funct_4(A))) & k2_funct_5(k1_relat_1(k2_funct_4(A))) = k1_funct_5(k1_relat_1(A)))) # label(t20_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3473 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r1_tarski(k2_relat_1(C),k4_partfun1(A,B)) -> C = k3_funct_5(k4_funct_5(C)) & k5_funct_5(k6_funct_5(C)) = C | r2_hidden(k1_xboole_0,k2_relat_1(C))))) # label(t58_funct_5) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3474 (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 (m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_2(G,k2_zfmisc_1(A,B),C) & v1_funct_1(G) -> (all H (m2_finseq_1(H,B) -> (k10_finseq_1(E,F) = H -> k5_funcop_1(G,D,H) = k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F))))))))))))))))))) # label(t95_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3475 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,C) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_finseq_1(A),k2_finseq_1(B)) & m2_relset_1(E,k2_finseq_1(A),k2_finseq_1(B)) -> (r1_xreal_0(B,k3_finseq_1(D)) -> np__0 != A & B = np__0 | m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k5_numbers,C,E,D),C)))))))))))) # label(t49_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3476 (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) & 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) -> (I = k11_finseq_1(D,E,F) -> k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) = k4_funcop_1(H,I,G)))))))))))))))))))) # label(t102_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3477 (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]. 22.24/23.42 3478 (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]. 22.24/23.42 3479 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (C = k3_funcop_1(D,A,B) & r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(D)) -> 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]. 22.24/23.42 3480 (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]. 22.24/23.42 3481 (all A all B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) -> k1_nat_1(k3_finseq_1(B),np__1) = k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))))) # label(t19_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3482 (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]. 22.24/23.42 3483 (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]. 22.24/23.42 3484 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]. 22.24/23.42 3485 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B k2_finseq_2(k1_nat_1(A,np__1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B))))) # label(t74_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3486 (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) -> (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]. 22.24/23.42 3487 (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) & m2_relset_1(C,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(C,k2_finseq_1(A),k2_finseq_1(A)) -> (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]. 22.24/23.42 3488 (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,B) -> (k12_finseq_1(B,E) = G -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k5_funcop_1(F,D,G)))))))))))))))) # label(t94_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3489 (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]. 22.24/23.42 3490 (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]. 22.24/23.42 3491 (all A k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k5_numbers,A)),k6_finseq_1(A)) = k4_finseq_2(np__0,A)) # label(t112_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3492 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(B)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(B)) -> (r1_xreal_0(B,k3_finseq_1(C)) -> np__0 != A & B = np__0 | v1_relat_1(k5_relat_1(D,C)) & v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C))))))))))) # label(t42_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3493 (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]. 22.24/23.42 3494 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k5_numbers,B) & m2_relset_1(C,k5_numbers,B) -> m2_finseq_1(k2_partfun1(k5_numbers,B,C,k2_finseq_1(A)),B))))))) # label(t31_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3495 (all A all B all C k2_relat_1(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C)) # label(t148_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3496 (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_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_funcop_1(E,F,G) = D & k3_finseq_1(G) = k3_finseq_1(F) -> k3_finseq_1(G) = k3_finseq_1(D) & k3_finseq_1(D) = k3_finseq_1(F)))))))))))))))) # label(t86_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3497 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (A != np__0 -> (all B (m1_subset_1(B,k2_finseq_1(A)) -> k1_funct_1(k1_finseq_2(A),B) = B))))) # label(t57_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3498 (all A all B (-v1_xboole_0(B) & m1_finseq_2(B,A) -> r1_tarski(B,k3_finseq_2(A)))) # label(t105_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3499 (all A (v1_relat_1(A) & v1_finseq_1(A) & v1_funct_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_relat_1(k5_relat_1(B,A)) & v1_finseq_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)))))) # label(t44_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3500 (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) -> -(k1_nat_1(A,B) = k3_finseq_1(C) & (all D (v1_funct_1(D) & v1_finseq_1(D) & v1_relat_1(D) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> -(k3_finseq_1(D) = A & k7_finseq_1(D,E) = C & B = k3_finseq_1(E))))))))))))) # label(t25_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3501 (all A (v4_ordinal2(A) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_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]. 22.24/23.42 3502 (all A (-v1_xboole_0(k13_finseq_1(A)) & m1_finseq_2(k13_finseq_1(A),A))) # label(t104_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3503 (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) -> (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(B,D) = k1_funct_1(C,D)))) & k3_finseq_1(B) = A -> B = C))))))) # label(t10_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3504 (all A exists B m1_finseq_2(B,A)) # label(existence_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3505 (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]. 22.24/23.42 3506 (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]. 22.24/23.42 3507 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) -> (k2_relat_1(D) = k2_finseq_1(A) & r1_xreal_0(A,k3_finseq_1(B)) & k5_relat_1(D,B) = C -> k3_finseq_1(C) = A))))))))) # label(t45_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3508 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> k2_finseq_1(A) = k4_finseq_1(C))))))) # label(t144_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3509 $T # label(t7_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3510 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> (all E (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]. 22.24/23.42 3511 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> v1_funct_1(B) & m2_relset_1(B,k4_finseq_1(B),A) & v1_funct_2(B,k4_finseq_1(B),A))))) # label(t30_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3512 (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_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,A) -> (all J (m2_finseq_1(J,B) -> (k10_finseq_1(F,G) = J & I = k10_finseq_1(D,E) -> k3_funcop_1(H,I,J) = k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G))))))))))))))))))))))) # label(t89_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3513 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) -> k6_finseq_1(C) = k5_funcop_1(E,D,k6_finseq_1(B)))))))))))) # label(t93_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3514 $T # label(t17_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3515 $T # label(t53_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3516 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) -> (all G (m2_finseq_1(G,A) -> (k12_finseq_1(A,D) = G -> k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) = k4_funcop_1(F,G,E)))))))))))))))) # label(t100_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3517 (all A all B (-v1_xboole_0(B) -> (all C (v1_relat_1(C) & v1_finseq_1(C) & v1_funct_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) -> (C = k1_partfun1(k5_numbers,A,A,B,D,E) -> k3_finseq_1(D) = k3_finseq_1(C)))))))))) # label(t37_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3518 (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]. 22.24/23.42 3519 (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]. 22.24/23.42 3520 (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]. 22.24/23.42 3521 (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) & A = k10_finseq_1(C,D) & m1_subset_1(D,B)))))) # label(fraenkel_a_1_1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3522 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_funct_1(k3_funcop_1(C,A,B)) & v1_finseq_1(k3_funcop_1(C,A,B)) & v1_relat_1(k3_funcop_1(C,A,B))))))))) # label(t78_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3523 (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_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) & v3_funct_2(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]. 22.24/23.42 3524 (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(B,A)) = k6_xcmplx_0(B,A)))))) # label(t4_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3525 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) & v1_relat_1(k2_funcop_1(k2_finseq_1(A),B)))))) # label(t66_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3526 (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]. 22.24/23.42 3527 (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) -> (H = k12_finseq_1(B,E) & G = k12_finseq_1(A,D) -> 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]. 22.24/23.42 3528 (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 (m2_finseq_2(D,B,k4_finseq_2(A,B)) & (exists E (m1_subset_1(E,B) & k8_finseq_1(B,D,k12_finseq_1(B,E)) = C)))))))))) # label(t137_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3529 (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]. 22.24/23.42 3530 (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]. 22.24/23.42 3531 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) -> (r1_xreal_0(A,k3_finseq_1(B)) & C = k5_relat_1(D,B) -> A = k3_finseq_1(C)))))))))) # label(t47_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3532 (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]. 22.24/23.42 3533 (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]. 22.24/23.42 3534 (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]. 22.24/23.42 3535 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,C) & k3_finseq_1(A) = k3_finseq_1(B) & r1_tarski(B,C) -> B = A))))))) # label(t149_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3536 (all A (v4_ordinal2(A) -> (all B A = k3_finseq_1(k2_finseq_2(A,B))))) # label(t69_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3537 (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]. 22.24/23.42 3538 (all A all B (m1_subset_1(B,k4_finseq_2(np__0,A)) -> k6_finseq_1(A) = B)) # label(t113_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3539 (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]. 22.24/23.42 3540 (all A (-v1_xboole_0(A) -> k4_finseq_2(np__3,A) = a_1_2_finseq_2(A))) # label(t122_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3541 $T # label(t106_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3542 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__3,A)) -> (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & (exists E (B = k11_finseq_1(C,D,E) & m1_subset_1(E,A))))))))))) # label(t123_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3543 (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]. 22.24/23.42 3544 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__2,A)) -> (exists C (m1_subset_1(C,A) & (exists D (m1_subset_1(D,A) & k10_finseq_1(C,D) = B)))))))) # label(t120_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3545 (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]. 22.24/23.42 3546 (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]. 22.24/23.42 3547 (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 (v1_funct_2(F,k2_zfmisc_1(B,C),D) & m2_relset_1(F,k2_zfmisc_1(B,C),D) & v1_funct_1(F) -> (all G (m2_finseq_2(G,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]. 22.24/23.42 3548 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(np__0,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> k8_finseq_1(B,C,D) = D & k8_finseq_1(B,D,C) = D)))))))) # label(t115_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3549 (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) -> np__0 = k2_square_1(np__0,k6_xcmplx_0(A,B))))))) # label(t3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3550 (all A all B (v4_ordinal2(A) -> v1_funct_1(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) & v1_relat_1(k2_finseq_2(A,B)))) # label(dt_k2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3551 (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 (m2_relset_1(F,C,D) & v1_funct_2(F,C,D) & v1_funct_1(F) -> (k10_finseq_1(A,B) = E -> k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B)) = k1_partfun1(k5_numbers,C,C,D,E,F)))))))))) # label(t40_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.42 3552 (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]. 22.24/23.43 3553 (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]. 22.24/23.43 3554 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(A,B),C)) -> (exists E (m2_finseq_2(E,C,k4_finseq_2(A,C)) & (exists F (m2_finseq_2(F,C,k4_finseq_2(B,C)) & k8_finseq_1(C,E,F) = D)))))))))))) # label(t126_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3555 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> C = k5_relat_1(k1_finseq_2(A),C))))))) # label(t138_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3556 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> (all C (m2_relset_1(C,k4_finseq_1(B),k4_finseq_1(B)) & v1_funct_2(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]. 22.24/23.43 3557 (all A (v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(A) -> (all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k4_finseq_1(A),k4_finseq_1(A)) & m2_relset_1(C,k4_finseq_1(A),k4_finseq_1(A)) -> (k2_relat_1(C) = k4_finseq_1(A) & k5_relat_1(C,A) = B -> k3_finseq_1(A) = k3_finseq_1(B)))))))) # label(t46_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3558 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_1(E) & m2_relset_1(E,k2_zfmisc_1(B,C),D) & v1_funct_2(E,k2_zfmisc_1(B,C),D) -> (all F (m2_finseq_2(F,B,k4_finseq_2(A,B)) -> (all G (m2_finseq_2(G,C,k4_finseq_2(A,C)) -> m2_finseq_2(k3_funcop_1(E,F,G),D,k4_finseq_2(A,D)))))))))))))))) # label(t140_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3559 (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) -> (A = k3_square_1(B,C) -> 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]. 22.24/23.43 3560 $T # label(dt_m1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3561 (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) -> k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C))))))))))) # label(t99_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3562 (all A all B (v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(C)) -> v1_finseq_1(k5_funcop_1(C,A,B)) & v1_funct_1(k5_funcop_1(C,A,B)) & v1_relat_1(k5_funcop_1(C,A,B))))))) # label(t80_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3563 (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)))) & k3_finseq_1(A) = f1_s1_finseq_2)) # label(s1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3564 (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]. 22.24/23.43 3565 (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) -> ((exists E exists F (A = k8_finseq_1(D,E,F) & m2_finseq_2(F,D,k4_finseq_2(C,D)) & m2_finseq_2(E,D,k4_finseq_2(B,D)))) <-> r2_hidden(A,a_3_0_finseq_2(B,C,D))))) # label(fraenkel_a_3_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3566 (all A k10_finseq_1(A,A) = k2_finseq_2(np__2,A)) # label(t75_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3567 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_1(B,A) -> -(k3_finseq_1(B) != np__0 & (all C (m2_finseq_1(C,A) -> (all D (m1_subset_1(D,A) -> B != k8_finseq_1(A,C,k12_finseq_1(A,D))))))))))) # label(t22_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3568 (all A exists B (m1_finseq_2(B,A) & -v1_xboole_0(B))) # label(rc1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3569 (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]. 22.24/23.43 3570 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C all D (r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(A)) -> k5_relat_1(k11_finseq_1(B,C,D),A) = k11_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C),k1_funct_1(A,D)))))) # label(t146_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3571 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B all C (r2_hidden(C,k1_relat_1(A)) & r2_hidden(B,k1_relat_1(A)) -> k5_relat_1(k10_finseq_1(B,C),A) = k10_finseq_1(k1_funct_1(A,B),k1_funct_1(A,C)))))) # label(t145_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3572 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> k4_square_1(A,np__0) = A & k4_square_1(np__0,A) = A & np__0 = k3_square_1(A,np__0) & np__0 = k3_square_1(np__0,A))) # label(t6_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3573 (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]. 22.24/23.43 3574 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) & -v1_xboole_0(C) -> (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]. 22.24/23.43 3575 (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) -> (r1_tarski(k2_zfmisc_1(k2_relat_1(B),k1_tarski(A)),k1_relat_1(D)) & C = k4_funcop_1(D,B,A) -> k3_finseq_1(C) = k3_finseq_1(B)))))))) # label(t83_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3576 (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]. 22.24/23.43 3577 (all A (v4_ordinal2(A) -> v1_funct_1(k1_finseq_2(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_2(k1_finseq_2(A),k2_finseq_1(A),k2_finseq_1(A)))) # label(t65_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3578 (all A all B (v1_finseq_1(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),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]. 22.24/23.43 3579 (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_relat_1(C) -> (r1_tarski(k2_relat_1(A),k1_relat_1(C)) & B = k5_relat_1(A,C) -> k3_finseq_1(B) = k3_finseq_1(A)))))))) # label(t33_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3580 (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]. 22.24/23.43 3581 (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]. 22.24/23.43 3582 $T # label(t29_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3583 (all A all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_finseq_1(D,B) -> (all E (v1_funct_2(E,B,C) & m2_relset_1(E,B,C) & v1_funct_1(E) -> (D = k9_finseq_1(A) -> k1_partfun1(k5_numbers,B,B,C,D,E) = k9_finseq_1(k1_funct_1(E,A))))))))))) # label(t39_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3584 (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) -> k6_finseq_1(C) = k3_funcop_1(D,k6_finseq_1(A),F) & k6_finseq_1(C) = k3_funcop_1(D,E,k6_finseq_1(B)))))))))))))) # label(t87_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3585 (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) -> (B = k7_relat_1(C,k2_finseq_1(A)) -> k3_square_1(A,k3_finseq_1(C)) = k3_finseq_1(B)))))))) # label(t24_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3586 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(A)) & -v1_xboole_0(B) -> (all C (m1_finseq_2(C,B) & -v1_xboole_0(C) -> m1_finseq_2(C,A) & -v1_xboole_0(C))))))) # label(t107_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3587 (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]. 22.24/23.43 3588 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & v1_finseq_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]. 22.24/23.43 3589 (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_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D B != k7_finseq_1(C,k9_finseq_1(D))))) & k1_nat_1(A,np__1) = k3_finseq_1(B)))))) # label(t21_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3590 (all A k11_finseq_1(A,A,A) = k2_finseq_2(np__3,A)) # label(t76_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3591 (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) -> (r1_xreal_0(k3_finseq_1(C),A) & k7_relat_1(C,k2_finseq_1(A)) = B -> B = C))))))) # label(t23_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3592 (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]. 22.24/23.43 3593 (all A all 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) -> (k7_finseq_1(D,k9_finseq_1(B)) = k7_finseq_1(C,k9_finseq_1(A)) -> A = B & C = D))))) # label(t20_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3594 (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]. 22.24/23.43 3595 (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) & m2_relset_1(G,k2_zfmisc_1(A,B),C) & v1_funct_2(G,k2_zfmisc_1(A,B),C) -> (all H (m2_finseq_1(H,A) -> (H = k10_finseq_1(D,E) -> k4_funcop_1(G,H,F) = k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F))))))))))))))))))) # label(t101_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3596 $T # label(t108_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3597 (all A k13_finseq_1(A) = k3_finseq_2(A)) # label(redefinition_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3598 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (m2_finseq_2(D,B,k4_finseq_2(A,B)) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k2_finseq_1(A)) -> k1_funct_1(C,E) = k1_funct_1(D,E)))) -> C = D))))))))) # label(t139_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3599 (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 (m2_relset_1(E,B,C) & v1_funct_2(E,B,C) & v1_funct_1(E) -> 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]. 22.24/23.43 3600 $T # label(t12_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3601 (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)) & A = k1_funct_1(B,C)))) & r2_hidden(A,k2_relat_1(B))))) # label(t11_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3602 (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]. 22.24/23.43 3603 (all A (v4_ordinal2(A) -> k1_finseq_2(A) = k6_partfun1(k2_finseq_1(A)))) # label(d1_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3604 (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]. 22.24/23.43 3605 (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) -> -(k3_finseq_1(E) = A & D = k8_finseq_1(C,E,F) & k3_finseq_1(F) = B))))) & k3_finseq_1(D) = k1_nat_1(A,B)))))))))) # label(t26_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3606 (all A (v4_ordinal2(A) -> (all B all C (r2_hidden(B,k2_finseq_1(A)) -> k1_funct_1(k2_finseq_2(A,C),B) = C)))) # label(t70_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3607 (all A (v4_ordinal2(A) -> A = k3_finseq_1(k1_finseq_2(A)))) # label(t55_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3608 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,B) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,B) -> (all J (v1_funct_1(J) & v1_funct_2(J,k2_zfmisc_1(A,B),C) & m2_relset_1(J,k2_zfmisc_1(A,B),C) -> (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) -> k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I)) = k3_funcop_1(J,K,L)))))))))))))))))))))))))) # label(t90_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3609 $T # label(t103_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3610 (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]. 22.24/23.43 3611 (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 (m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_2(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> (all G (m2_finseq_1(G,B) -> (k3_funcop_1(E,F,G) = D -> k3_square_1(k3_finseq_1(F),k3_finseq_1(G)) = k3_finseq_1(D)))))))))))))))) # label(t85_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3612 (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) & v1_funct_2(F,k2_zfmisc_1(B,C),D) & m2_relset_1(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]. 22.24/23.43 3613 (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]. 22.24/23.43 3614 (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]. 22.24/23.43 3615 (all A all B (-v1_xboole_0(B) -> ((exists C (k4_finseq_2(C,B) = A & 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]. 22.24/23.43 3616 (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]. 22.24/23.43 3617 (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]. 22.24/23.43 3618 (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(k1_nat_1(B,np__1))) & -r2_hidden(A,k2_finseq_1(B)) & k1_nat_1(B,np__1) != A))))) # label(t8_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3619 (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]. 22.24/23.43 3620 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (B = k2_finseq_1(A) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (all D (m2_finseq_1(D,B) -> (r1_xreal_0(A,k3_finseq_1(C)) -> v1_funct_1(k5_relat_1(D,C)) & v1_finseq_1(k5_relat_1(D,C)) & v1_relat_1(k5_relat_1(D,C)))))))))))) # label(t34_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3621 (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 (m2_relset_1(H,k2_zfmisc_1(A,B),C) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & v1_funct_1(H) -> (all I (m2_finseq_1(I,B) -> (I = k11_finseq_1(E,F,G) -> 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]. 22.24/23.43 3622 (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(k1_nat_1(A,B),C) = a_3_0_finseq_2(A,B,C))))))) # label(t125_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3623 (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]. 22.24/23.43 3624 $T # label(t67_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3625 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_2(C,B,k4_finseq_2(A,B)) -> (all D (v1_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(D,k2_finseq_1(A),k2_finseq_1(A)) & m2_relset_1(D,k2_finseq_1(A),k2_finseq_1(A)) & v1_funct_1(D) -> m2_finseq_2(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k5_numbers,B,D,C),B,k4_finseq_2(A,B)))))))))) # label(t135_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3626 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_finseq_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]. 22.24/23.43 3627 (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(C,B) & k11_finseq_1(C,D,E) = A & m1_subset_1(E,B) & m1_subset_1(D,B)))))) # label(fraenkel_a_1_2_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3628 (all A all B ((all C (r2_hidden(C,B) -> m2_finseq_1(C,A))) <-> m1_finseq_2(B,A))) # label(d3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3629 (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 (m2_relset_1(D,k5_numbers,B) & v1_funct_2(D,k5_numbers,B) & v1_funct_1(D) -> (k2_partfun1(k5_numbers,B,D,k2_finseq_1(A)) = C -> A = k3_finseq_1(C)))))))))) # label(t32_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3630 (all A all B all C (m2_finseq_1(C,A) -> (all D (m2_relset_1(D,A,B) & v1_funct_2(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]. 22.24/23.43 3631 (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]. 22.24/23.43 3632 (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) -> B = A))))))) # label(t130_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3633 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (v1_funct_1(E) & v1_finseq_1(E) & v1_relat_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_2(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> (all G (m2_finseq_1(G,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]. 22.24/23.43 3634 (all A (-v1_xboole_0(A) -> (all B (m2_finseq_2(B,A,k4_finseq_2(np__1,A)) -> (exists C (m1_subset_1(C,A) & k12_finseq_1(A,C) = B)))))) # label(t117_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3635 (all A all B (-v1_xboole_0(B) -> (r2_hidden(A,a_1_0_finseq_2(B)) <-> (exists C (m1_subset_1(C,B) & k12_finseq_1(B,C) = A))))) # label(fraenkel_a_1_0_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3636 (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_1(G) & m2_relset_1(G,D,E) & v1_funct_2(G,D,E) -> (F = k11_finseq_1(A,B,C) -> 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]. 22.24/23.43 3637 (all A k2_finseq_2(np__1,A) = k9_finseq_1(A)) # label(t73_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3638 (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]. 22.24/23.43 3639 (all A k1_xboole_0 = k2_finseq_2(np__0,A)) # label(t72_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3640 (all A all B (v1_finseq_1(B) & v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_finseq_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (all D (v1_relat_1(D) & v1_funct_1(D) -> (C = k5_funcop_1(D,A,B) & r1_tarski(k2_zfmisc_1(k1_tarski(A),k2_relat_1(B)),k1_relat_1(D)) -> k3_finseq_1(B) = k3_finseq_1(C)))))))) # label(t81_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3641 (all A (-v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A))) # label(dt_k3_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3642 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,B) -> (all E (v1_funct_2(E,k2_zfmisc_1(A,B),C) & m2_relset_1(E,k2_zfmisc_1(A,B),C) & v1_funct_1(E) -> (all F (m2_finseq_1(F,A) -> m2_finseq_1(k4_funcop_1(E,F,D),C))))))))))))) # label(t97_finseq_2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3643 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) -> r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t45_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3644 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (C = D & (all E (r2_hidden(E,k1_relat_1(A)) -> r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)))) & k1_relat_1(A) = k1_relat_1(D) & v1_funct_1(D) & v1_relat_1(D))))) <-> k4_card_3(A) = B)))) # label(d5_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3645 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_fraenkel(k4_card_3(A)))) # label(fc3_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3646 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_card_1(k1_funct_1(k2_card_3(A),B)) = k1_funct_1(A,B))))) # label(t40_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3647 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k6_card_3(A) = k1_card_1(k3_card_3(k2_card_3(A))))) # label(d7_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3648 $T # label(dt_k4_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3649 (all A all B all C (v1_relat_1(C) & v1_funct_1(C) -> (r2_hidden(B,k1_relat_1(C)) & r2_hidden(A,k1_relat_1(C)) -> A = B | r1_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B))))) # label(t13_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3650 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> v1_card_1(k7_card_3(A)))) # label(dt_k7_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3651 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k2_card_2(A,B) = k6_card_3(k2_funcop_1(A,B)))))) # label(t52_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3652 (all A -(v6_ordinal1(A) & (all B -(r1_tarski(B,A) & (all C -(C != k1_xboole_0 & (all D -(r2_hidden(D,C) & (all E (r2_hidden(E,C) -> r1_tarski(D,E))))) & r1_tarski(C,B))) & k3_tarski(A) = k3_tarski(B))))) # label(t61_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3653 (all A all B r1_tarski(k1_card_1(k5_card_3(B,A)),k1_card_1(A))) # label(t31_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3654 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k2_card_3(A)) & v1_relat_1(k2_card_3(A)))) # label(dt_k2_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3655 (all A all B all C k5_card_3(C,k2_xboole_0(A,B)) = k2_xboole_0(k5_card_3(C,A),k5_card_3(C,B))) # label(t27_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3656 (all A (v1_card_1(A) -> (all B A = k7_card_3(k2_funcop_1(k1_tarski(B),A))))) # label(t51_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3657 $T # label(t6_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3658 (all A all B (v1_card_1(B) -> v1_ordinal2(k2_funcop_1(A,B)) & v1_card_3(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_relat_1(k2_funcop_1(A,B)))) # label(fc2_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3659 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = k1_relat_1(A) & (all C (r2_hidden(C,k1_relat_1(A)) -> k1_funct_1(B,C) = k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)))) <-> B = k2_card_3(A)))))) # label(d3_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3660 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_card_3(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t46_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3661 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(A)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r2_hidden(k6_card_3(A),k7_card_3(B))))))) # label(t56_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3662 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k3_card_3(k2_card_3(B))) <-> A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) & r2_hidden(k1_mcart_1(A),k1_funct_1(B,k2_mcart_1(A))) & r2_hidden(k2_mcart_1(A),k1_relat_1(B))))) # label(t33_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3663 (all A (v1_funct_1(A) & v1_relat_1(A) -> v1_funct_1(k1_card_3(A)) & v1_card_3(k1_card_3(A)) & v1_relat_1(k1_card_3(A)))) # label(dt_k1_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3664 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(A)))) # label(t55_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3665 (all A all B all C (C = k5_card_3(A,B) <-> (all D (r2_hidden(D,C) <-> (exists E (k1_funct_1(E,A) = D & r2_hidden(E,B) & v1_funct_1(E) & v1_relat_1(E))))))) # label(d6_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3666 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (r2_hidden(k1_xboole_0,k2_relat_1(A)) <-> np__0 = k7_card_3(A)))) # label(t44_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3667 (all A (v1_relat_1(A) & v1_funct_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)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) -> r1_tarski(k4_card_3(A),k4_card_3(B))))))) # label(t38_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3668 $T # label(t2_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3669 $T # label(t5_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3670 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_card_3(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v1_card_1(k1_funct_1(A,B))))))) # label(d1_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3671 (all A (v1_card_1(A) -> (all B k6_card_3(k2_funcop_1(k1_tarski(B),A)) = A))) # label(t50_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3672 (all A all B r1_tarski(k3_card_3(k2_funcop_1(A,B)),B)) # label(t15_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3673 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(k1_card_1(A),k1_card_1(B)) -> r2_hidden(A,B)))))) # label(t59_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3674 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> k1_tarski(k1_funct_1(B,A)) = k5_card_3(A,k1_tarski(B)))) # label(t25_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3675 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k2_card_3(A),k2_card_3(B))))))) # label(t34_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3676 (all A (v1_funct_1(A) & v1_relat_1(A) -> k3_tarski(k2_relat_1(A)) = k3_card_3(A))) # label(d4_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3677 $T # label(t4_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3678 (all A all B k2_funcop_1(k1_tarski(A),k2_zfmisc_1(B,k1_tarski(A))) = k2_card_3(k2_funcop_1(k1_tarski(A),B))) # label(t12_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3679 (all A all B all C r1_tarski(k5_card_3(C,k3_xboole_0(A,B)),k3_xboole_0(k5_card_3(C,A),k5_card_3(C,B)))) # label(t28_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3680 (all A (v1_funct_1(A) & v1_relat_1(A) -> r1_tarski(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))))) # label(t54_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3681 (all A (v1_relat_1(A) & v1_funct_1(A) -> (k4_card_3(A) = k1_xboole_0 <-> r2_hidden(k1_xboole_0,k2_relat_1(A))))) # label(t37_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3682 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (r2_hidden(B,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,B)) = k1_funct_1(A,B))))) # label(t39_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3683 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> k2_tarski(k1_funct_1(B,A),k1_funct_1(C,A)) = k5_card_3(A,k2_tarski(B,C)))))) # label(t26_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3684 (all A all B k1_card_3(k2_funcop_1(A,B)) = k2_funcop_1(A,k1_card_1(B))) # label(t10_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3685 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> k1_card_3(A) = A)) # label(t8_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3686 (all A all B all C (p1_s2_card_3(A,B) & p1_s2_card_3(B,C) -> p1_s2_card_3(A,C))) & (all A all B (p1_s2_card_3(A,B) & p1_s2_card_3(B,A) -> B = A)) & f1_s2_card_3 != k1_xboole_0 -> (exists A ((all B -(p1_s2_card_3(B,A) & B != A & r2_hidden(B,f1_s2_card_3))) & r2_hidden(A,f1_s2_card_3))) # label(s2_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3687 (all A (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_card_1(k6_card_3(A)))) # label(dt_k6_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3688 (all A all B k3_card_3(k2_funcop_1(k1_tarski(A),B)) = B) # label(t17_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3689 $T # label(dt_k3_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3690 (all A all B k2_zfmisc_1(B,A) = k3_card_3(k2_card_3(k2_funcop_1(A,B)))) # label(t36_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3691 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k4_card_3(B)) <-> k1_relat_1(A) = k1_relat_1(B) & (all C (r2_hidden(C,k1_relat_1(B)) -> r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C))))))))) # label(t18_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3692 $T # label(t21_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3693 (exists A (v1_relat_1(A) & v1_card_3(A) & k1_relat_1(A) = f1_s1_card_3 & (all B (r2_hidden(B,f1_s1_card_3) -> f2_s1_card_3(B) = k1_funct_1(A,B))) & v1_funct_1(A))) # label(s1_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3694 (all A (v1_card_1(A) -> np__1 = k7_card_3(k2_funcop_1(k1_xboole_0,A)))) # label(t49_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3695 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> v1_finset_1(k4_classes1(A)))) # label(t57_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3696 $T # label(dt_k5_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3697 (all A all B (k1_xboole_0 != A -> B = k3_card_3(k2_funcop_1(A,B)))) # label(t16_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3698 (all A (v1_finset_1(A) -> r2_hidden(k1_card_1(A),k1_card_1(k5_ordinal2)))) # label(t58_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3699 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> -(r2_hidden(A,k3_card_3(k2_card_3(B))) & (all C all D k4_tarski(C,D) != A)))) # label(t32_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3700 (all A (v1_card_1(A) -> k6_card_3(k2_funcop_1(k1_xboole_0,A)) = np__0)) # label(t48_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3701 $T # label(t41_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3702 (all A (v1_card_1(A) -> (all B ((all C (r2_hidden(C,B) -> r2_hidden(k1_card_1(C),A))) & v6_ordinal1(B) -> r1_tarski(k1_card_1(k3_tarski(B)),A))))) # label(t62_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3703 $T # label(t23_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3704 (all A (v1_card_1(A) -> (all B (v1_card_1(B) -> k3_card_2(B,A) = k7_card_3(k2_funcop_1(A,B)))))) # label(t53_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3705 $T # label(t42_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3706 (all A (v3_ordinal1(A) -> (all B (v1_card_1(B) -> (r2_hidden(k1_card_1(A),B) -> r2_hidden(A,B)))))) # label(t60_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3707 $T # label(t7_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3708 (all A (v1_funct_1(A) & v1_card_3(A) & v1_relat_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> (r1_tarski(A,B) -> r2_hidden(np__0,k2_relat_1(B)) | r1_tarski(k7_card_3(A),k7_card_3(B))))))) # label(t47_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3709 (all A all B all C r1_tarski(k5_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k5_xboole_0(A,C)))) # label(t30_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.43 3710 (all A all B (p1_s3_card_3(A,B) | p1_s3_card_3(B,A))) & (all A all B all C (p1_s3_card_3(B,C) & p1_s3_card_3(A,B) -> p1_s3_card_3(A,C))) & k1_xboole_0 != f1_s3_card_3 -> (exists A (r2_hidden(A,f1_s3_card_3) & (all B (r2_hidden(B,f1_s3_card_3) -> p1_s3_card_3(A,B))))) # label(s3_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3711 (all A all B all C r1_tarski(k4_xboole_0(k5_card_3(B,A),k5_card_3(B,C)),k5_card_3(B,k4_xboole_0(A,C)))) # label(t29_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3712 (all A all B all C (v1_setfam_1(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) -> v1_fraenkel(k4_card_3(C)) & -v1_xboole_0(k4_card_3(C)))) # label(fc4_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3713 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A))) # label(rc1_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3714 (all A (v1_relat_1(A) & v1_funct_1(A) & v2_relat_1(A) -> -v1_xboole_0(k4_card_3(A)) & v1_fraenkel(k4_card_3(A)))) # label(fc5_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3715 (all A (v1_relat_1(A) & v1_card_3(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)))) & k1_relat_1(A) = k1_relat_1(B) -> r1_tarski(k6_card_3(A),k6_card_3(B))))))) # label(t43_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3716 (all A all B (v1_funct_1(B) & v1_relat_1(B) -> (r2_hidden(A,k1_relat_1(B)) -> k1_xboole_0 = k4_card_3(B) | k5_card_3(A,k4_card_3(B)) = k1_funct_1(B,A)))) # label(t22_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3717 (all A all B (v1_card_3(A) & v1_funct_1(A) & v1_relat_1(A) -> v1_card_3(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) & v1_relat_1(k7_relat_1(A,B)))) # label(fc1_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3718 (all A all B k4_card_3(k2_funcop_1(A,B)) = k1_funct_2(A,B)) # label(t20_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3719 (all A k5_card_3(A,k1_xboole_0) = k1_xboole_0) # label(t24_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3720 $T # label(t1_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3721 (exists A (v1_relat_1(A) & v1_funct_1(A) & (all B (r2_hidden(B,f1_s4_card_3) -> (all C (r2_hidden(C,k1_funct_1(A,B)) <-> p1_s4_card_3(B,C) & r2_hidden(C,f2_s4_card_3(B)))))) & f1_s4_card_3 = k1_relat_1(A))) # label(s4_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3722 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) -> (r1_tarski(A,B) -> r1_tarski(k3_card_3(A),k3_card_3(B))))))) # label(t35_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3723 (all A (v1_relat_1(A) & v1_funct_1(A) -> (all B (v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) -> ((all C (r2_hidden(C,k1_relat_1(A)) -> k1_card_1(k1_funct_1(A,C)) = k1_funct_1(B,C))) & k1_relat_1(A) = k1_relat_1(B) <-> B = k1_card_3(A)))))) # label(d2_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3724 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) -> k1_card_1(k4_card_3(A)) = k7_card_3(A))) # label(d8_card_3) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3725 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k12_classes2(A,B,C) = k1_funct_2(B,C))) # label(redefinition_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3726 (all A all B (v1_classes1(A) & r2_hidden(B,A) & v1_ordinal1(B) -> r1_tarski(B,A))) # label(t8_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3727 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k5_classes2(A,B,C),A))) # label(dt_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3728 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k5_classes2(A,C,B) = k5_classes2(A,B,C))) # label(commutativity_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3729 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r1_tarski(k16_classes2(A),k16_classes2(B)) <-> r1_ordinal1(A,B)))))) # label(t82_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3730 (all A (v1_classes2(A) -> v2_classes1(A) & v1_classes1(A) & v1_ordinal1(A))) # label(cc2_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3731 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r2_hidden(k4_classes1(A),k1_classes1(B)) & r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))))))) # label(t27_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3732 (all A (v1_classes2(k15_classes2(A)) & -v1_xboole_0(k15_classes2(A)))) # label(dt_k15_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3733 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> -v1_xboole_0(k2_xboole_0(A,B)) & -v1_xboole_0(k3_xboole_0(A,B)) & v1_classes2(k3_xboole_0(A,B)) & v1_classes2(k2_xboole_0(A,B)))))) # label(t61_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3734 $T # label(t48_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3735 (all A (v2_classes1(A) -> r1_tarski(k4_classes1(k1_card_1(A)),A))) # label(t28_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3736 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(k1_classes1(B))) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))))))) # label(t34_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3737 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> k1_zfmisc_1(B) = k2_classes2(A,B))) # label(redefinition_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3738 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k5_xboole_0(B,C) = k10_classes2(A,B,C))) # label(redefinition_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3739 (all A (v3_ordinal1(A) -> v1_ordinal1(k16_classes2(A)) & v1_classes1(k16_classes2(A)) & v2_classes1(k16_classes2(A)) & v1_classes2(k16_classes2(A)) & -v1_xboole_0(k16_classes2(A)))) # label(fc8_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3740 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v4_ordinal1(k2_ordinal2(A)) & k1_xboole_0 != k2_ordinal2(A))) # label(t55_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3741 (all A (v2_classes1(A) -> k1_card_1(k4_classes1(k1_card_1(A))) = k1_card_1(A))) # label(t35_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3742 $T # label(t74_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3743 (all A all B -(r1_tarski(A,k4_classes1(k1_card_1(k1_classes1(B)))) & -r2_wellord2(A,k4_classes1(k1_card_1(k1_classes1(B)))) & -r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t38_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3744 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v3_ordinal1(k2_ordinal2(A)))) # label(t50_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3745 (all A (v3_ordinal1(A) -> v1_ordinal1(k4_classes1(A)))) # label(fc7_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3746 (all A all B all C (r2_hidden(C,A) & r2_hidden(B,A) & v2_classes1(A) -> r2_hidden(k4_tarski(B,C),A))) # label(t4_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3747 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k4_classes2(A,B) = k1_setfam_1(B))) # label(redefinition_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3748 (all A all B all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k4_tarski(A,B),C) & r2_hidden(k2_tarski(A,B),C)))) # label(t64_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3749 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> (all C (v1_classes2(C) & -v1_xboole_0(C) -> (r2_hidden(B,C) & r2_hidden(A,B) -> r2_hidden(A,C)))))))) # label(t59_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3750 $T # label(t2_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3751 (all A all B (v2_classes1(A) & v1_ordinal1(B) & r2_hidden(B,A) -> r2_hidden(B,k4_classes1(k1_card_1(A))))) # label(t43_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3752 (all A (v2_classes1(A) & v1_ordinal1(A) -> r1_tarski(A,k4_classes1(k1_card_1(A))))) # label(t31_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3753 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_ordinal1(A),k1_classes1(B)) & r1_tarski(A,k1_classes1(B)))))) # label(t7_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3754 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k8_classes2(A,B,B) = B)) # label(idempotence_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3755 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> r2_hidden(k1_zfmisc_1(A),B) & r2_hidden(k1_setfam_1(A),B) & r2_hidden(k3_tarski(A),B)))) # label(t65_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3756 $T # label(t60_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3757 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> k1_tarski(B) = k1_classes2(A,B))) # label(redefinition_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3758 $T # label(t68_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3759 (all A all B (r2_hidden(A,k1_classes1(B)) & v1_ordinal1(A) -> r1_tarski(A,k1_classes1(B)))) # label(t9_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3760 (all A k1_card_1(k1_classes1(A)) = k2_ordinal2(k1_classes1(A))) # label(t11_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3761 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (k16_classes2(B) = k16_classes2(A) -> A = B))))) # label(t81_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3762 (all A all B (m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k4_classes2(A,B),A))) # label(dt_k4_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3763 (all A all B (r2_hidden(B,k1_card_1(A)) & v2_classes1(A) -> r2_hidden(B,A))) # label(t14_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3764 (all A (v1_ordinal1(A) -> r1_classes1(A,k4_classes1(k1_card_1(k1_classes1(A)))))) # label(t45_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3765 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B (m1_subset_1(B,A) & -v1_xboole_0(B))))) # label(rc2_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3766 (all A (v1_classes2(A) <-> v2_classes1(A) & v1_ordinal1(A))) # label(d1_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3767 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> k4_xboole_0(B,C) = k9_classes2(A,B,C))) # label(redefinition_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3768 (all A all B (v1_classes2(B) & -v1_xboole_0(B) -> (r2_hidden(A,B) -> r2_hidden(k1_tarski(A),B)))) # label(t63_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3769 (all A (v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) -> ((all B (v3_ordinal1(B) -> (r2_hidden(B,k1_relat_1(A)) -> k1_funct_1(A,B) = k4_classes1(B)))) & v4_ordinal1(k1_relat_1(A)) -> k3_card_3(A) = k4_classes1(k1_relat_1(A))))) # label(t25_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3770 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k11_classes2(A,B,C) = k2_zfmisc_1(B,C))) # label(redefinition_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3771 (all A (v1_card_1(A) -> (all B (v2_classes1(B) & r2_hidden(A,B) -> r1_tarski(A,B))))) # label(t18_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3772 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k3_classes2(A,B),A))) # label(dt_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3773 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(A,C) & r2_hidden(B,C) -> r2_hidden(k2_zfmisc_1(A,B),C) & r2_hidden(k1_funct_2(A,B),C)))) # label(t67_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3774 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(C,A) & m1_subset_1(B,A) -> k2_tarski(B,C) = k5_classes2(A,B,C))) # label(redefinition_k5_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3775 $T # label(t73_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3776 (all A all B (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) -> k3_tarski(B) = k3_classes2(A,B))) # label(redefinition_k3_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3777 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k1_xboole_0,A))) # label(t62_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3778 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_ordinal1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc3_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3779 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_classes1(B)) -> r1_tarski(A,k1_classes1(B)))))) # label(t19_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3780 (all A (v3_ordinal1(A) -> (all B ((exists C (v1_funct_1(C) & B = k1_ordinal2(C) & k1_ordinal1(A) = k1_relat_1(C) & k13_classes2 = 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 | k1_funct_1(C,D) = k15_classes2(k3_card_3(k2_ordinal1(C,D)))))) & (all D (v3_ordinal1(D) -> (r2_hidden(k1_ordinal1(D),k1_ordinal1(A)) -> k1_funct_1(C,k1_ordinal1(D)) = k1_classes1(k1_funct_1(C,D))))) & v5_ordinal1(C) & v1_relat_1(C))) <-> k16_classes2(A) = B)))) # label(d5_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3781 (all A (np__0 != k1_card_1(k1_classes1(A)) & v4_ordinal1(k1_card_1(k1_classes1(A))) & k1_xboole_0 != k1_card_1(k1_classes1(A)))) # label(t22_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3782 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k7_classes2(A,B,C),A))) # label(dt_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3783 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> B = k7_classes2(A,B,B))) # label(idempotence_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3784 (all A all B -(-r2_wellord2(B,k4_classes1(k1_card_1(A))) & -r2_hidden(B,k4_classes1(k1_card_1(A))) & r1_tarski(B,k4_classes1(k1_card_1(A))) & v2_classes1(A))) # label(t37_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3785 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) -> k8_classes2(A,C,B) = k8_classes2(A,B,C))) # label(commutativity_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3786 (all A (v3_ordinal1(A) -> v1_ordinal1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(fc4_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3787 (all A all B (v1_classes1(A) & r2_hidden(B,A) -> -r2_wellord2(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A)))) # label(t1_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3788 (all A (v2_classes1(A) -> k1_card_1(A) = k2_ordinal2(A))) # label(t10_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3789 $T # label(t47_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3790 (all A (v2_classes1(A) -> k1_xboole_0 != k1_card_1(A) & v4_ordinal1(k1_card_1(A)) & np__0 != k1_card_1(A) | A = k1_xboole_0)) # label(t21_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3791 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> k4_tarski(B,C) = k6_classes2(A,B,C))) # label(redefinition_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3792 (all A all B (v2_classes1(A) -> r1_tarski(k1_funct_2(B,A),A) | -(r1_tarski(B,A) & r2_hidden(B,A)) & -(r2_hidden(k1_card_1(B),k1_card_1(A)) & r1_tarski(B,A)) & -(v1_ordinal1(A) & r2_hidden(B,A)))) # label(t23_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3793 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k9_classes2(A,B,C),A))) # label(dt_k9_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3794 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (v1_classes2(B) & -v1_xboole_0(B) -> r3_xboole_0(A,B))))) # label(t58_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3795 $T # label(t49_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3796 (all A (v3_ordinal1(A) -> (all B (v2_classes1(B) & r2_hidden(A,k2_ordinal2(B)) -> r1_tarski(k1_card_1(k4_classes1(A)),k1_card_1(B)))))) # label(t33_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3797 (all A (v2_classes1(A) -> v1_classes1(A))) # label(cc1_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3798 (all A (v1_ordinal1(A) & v2_classes1(A) -> k4_classes1(k1_card_1(A)) = A)) # label(t32_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3799 (all A all B (v1_classes2(A) & m1_subset_1(B,A) & -v1_xboole_0(A) -> m1_subset_1(k1_classes2(A,B),A))) # label(dt_k1_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3800 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,k2_ordinal2(B)) & v2_classes1(B) -> r2_hidden(k1_card_1(k4_classes1(A)),k1_card_1(B)) & r2_hidden(k4_classes1(A),B))))) # label(t26_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3801 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t51_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3802 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_classes2(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)))) # label(t52_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3803 (all A all B all C (-v1_xboole_0(C) & v1_classes2(C) -> (r2_hidden(B,C) & r2_hidden(A,C) -> r2_hidden(k4_xboole_0(A,B),C) & r2_hidden(k5_xboole_0(A,B),C) & r2_hidden(k3_xboole_0(A,B),C) & r2_hidden(k2_xboole_0(A,B),C)))) # label(t66_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3804 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k10_classes2(A,B,C) = k10_classes2(A,C,B))) # label(commutativity_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3805 (all A (-v1_xboole_0(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)))) # label(fc1_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3806 (all A all B (r2_hidden(A,k1_classes1(B)) -> r2_hidden(k1_card_1(A),k1_classes1(B)))) # label(t13_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3807 $T # label(dt_k16_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3808 (all A all B (v2_classes1(A) & r2_hidden(B,A) -> r2_hidden(k1_card_1(B),A))) # label(t12_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3809 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r1_tarski(k1_classes1(k1_xboole_0),A) & r1_tarski(k16_classes2(k1_xboole_0),A) & r1_tarski(k13_classes2,A))) # label(t79_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3810 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k10_classes2(A,B,C),A))) # label(dt_k10_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3811 (all A all B all C (v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & -v1_xboole_0(A) -> k8_classes2(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3812 (all A all B (v2_classes1(A) & v1_ordinal1(A) & r2_hidden(B,A) -> r2_hidden(k6_classes1(B),A))) # label(t30_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3813 (all A (v1_ordinal1(A) -> r1_tarski(k1_card_1(k6_classes1(A)),k1_card_1(A)))) # label(t42_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3814 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k2_classes2(A,B),A) & -v1_xboole_0(k2_classes2(A,B)))) # label(dt_k2_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3815 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k6_classes2(A,B,C),A))) # label(dt_k6_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3816 (all A v2_classes1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t40_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3817 $T # label(t72_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3818 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> m1_subset_1(k12_classes2(A,B,C),A))) # label(dt_k12_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3819 (all A (v3_ordinal1(A) -> k1_classes1(k16_classes2(A)) = k16_classes2(k1_ordinal1(A)))) # label(t76_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3820 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))))) # label(t17_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3821 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) -> k2_xboole_0(B,C) = k7_classes2(A,B,C))) # label(redefinition_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3822 (all A all B all C (v2_classes1(A) & r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k2_tarski(B,C),A) & r2_hidden(k1_tarski(B),A))) # label(t3_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3823 (all A (v3_ordinal1(A) -> v1_classes2(k1_classes1(A)))) # label(t53_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3824 (all A all B all C (m1_subset_1(C,A) & m1_subset_1(B,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k8_classes2(A,B,C),A))) # label(dt_k8_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3825 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> -(-r2_hidden(A,B) & A != B & -r2_hidden(B,A)))))) # label(t56_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3826 (all A all B (r2_hidden(A,k1_card_1(k1_classes1(B))) -> r2_hidden(A,k1_classes1(B)))) # label(t15_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3827 (all A (v1_ordinal1(A) -> k4_classes1(k1_card_1(k1_classes1(A))) = k1_classes1(A))) # label(t46_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3828 (all A r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A))) # label(t29_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3829 (all A all B (v1_ordinal1(A) & r2_hidden(A,k1_classes1(B)) -> r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))))) # label(t44_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3830 (all A (v1_ordinal1(A) -> v1_classes2(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & -v1_xboole_0(k1_classes1(A)) & v1_ordinal1(k1_classes1(A)))) # label(fc6_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3831 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v2_ordinal1(k2_ordinal2(A)) & v3_ordinal1(k2_ordinal2(A)) & v1_ordinal1(k2_ordinal2(A)))) # label(fc2_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3832 (all A (v3_ordinal1(A) -> (all B -(v1_ordinal1(B) & (all C -(r2_hidden(C,B) & A = k6_classes1(C))) & r2_hidden(A,k6_classes1(B)))))) # label(t41_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3833 (all A all B (-(-(r2_hidden(A,k1_classes1(B)) & v1_ordinal1(B)) & -(r2_hidden(k1_card_1(A),k1_card_1(k1_classes1(B))) & r1_tarski(A,k1_classes1(B))) & -(r1_tarski(A,k1_classes1(B)) & r2_hidden(A,k1_classes1(B)))) -> r1_tarski(k1_funct_2(A,k1_classes1(B)),k1_classes1(B)))) # label(t24_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3834 (all A (-v1_xboole_0(A) & v1_classes2(A) -> k4_classes1(k2_ordinal2(A)) = A)) # label(t54_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3835 (all A all B all C (-v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) -> k7_classes2(A,B,C) = k7_classes2(A,C,B))) # label(commutativity_k7_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3836 (all A (v3_ordinal1(A) -> (all B (v3_ordinal1(B) -> (r2_hidden(A,B) <-> r2_hidden(k16_classes2(A),k16_classes2(B))))))) # label(t80_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3837 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_classes2(B) -> r1_tarski(A,B) | r2_hidden(B,A))))) # label(t57_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3838 (all A (v1_ordinal1(A) & v2_classes1(A) -> v1_classes2(A))) # label(cc3_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3839 (all A (v2_classes1(A) -> v2_classes1(k4_classes1(k1_card_1(A))))) # label(t39_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3840 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> ((all C (v1_classes2(C) & -v1_xboole_0(C) -> (r1_tarski(A,C) -> r1_tarski(B,C)))) & r1_tarski(A,B) <-> k15_classes2(A) = B))) # label(d4_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3841 (all A (v2_classes1(A) -> v4_ordinal1(k1_card_1(A)))) # label(t20_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3842 (all A (v3_ordinal1(A) -> (all B (r2_hidden(A,B) & v2_classes1(B) -> r1_tarski(A,B) & r2_hidden(k1_ordinal1(A),B))))) # label(t6_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3843 (all A v1_ordinal1(k5_classes1(A))) # label(fc5_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3844 (all A all B all C (m1_subset_1(B,A) & m1_subset_1(C,A) & v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k11_classes2(A,B,C),A))) # label(dt_k11_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3845 (all A (v3_ordinal1(A) -> (all B (v5_ordinal1(B) & v1_funct_1(B) & v1_relat_1(B) -> (v4_ordinal1(A) & k1_relat_1(B) = A & (all C (v3_ordinal1(C) -> (r2_hidden(C,A) -> k1_funct_1(B,C) = k16_classes2(C)))) -> k15_classes2(k3_card_3(B)) = k16_classes2(A) | A = k1_xboole_0))))) # label(t78_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3846 (exists A (v1_ordinal1(A) & -v1_xboole_0(A) & v2_classes1(A) & v1_classes2(A) & v1_classes1(A))) # label(rc1_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3847 (all A (v1_card_1(A) -> (all B (r2_hidden(A,k1_card_1(B)) & v2_classes1(B) -> r2_hidden(A,B))))) # label(t16_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3848 (all A all B (v2_classes1(A) & r2_hidden(B,A) -> r1_tarski(k1_classes1(B),A))) # label(t5_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3849 (all A k1_card_1(k1_classes1(A)) = k1_card_1(k4_classes1(k1_card_1(k1_classes1(A))))) # label(t36_classes2) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3850 $T # label(t5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3851 $T # label(t7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3852 (all A (m1_subset_1(A,k5_numbers) -> -v1_xboole_0(k7_qc_lang1(A)))) # label(fc6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3853 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> np__0 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__3 & np__2 != k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) & k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) != np__1))) # label(t50_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3854 (all A (m1_subset_1(A,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k17_qc_lang1(A)))) & v3_qc_lang1(A)))) # label(t45_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3855 (all A (m1_subset_1(A,k8_qc_lang1) -> np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(k11_qc_lang1),np__1)) & (v3_qc_lang1(A) -> np__1 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & (v5_qc_lang1(A) -> np__3 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & (v4_qc_lang1(A) -> np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1))) & -(v2_qc_lang1(A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> -m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B))))))) # label(t49_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3856 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k24_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3857 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D (m2_subset_1(D,k5_qc_lang1,k7_qc_lang1(C)) & (exists E (k9_qc_lang1(D,E) = A & E = B & m1_qc_lang1(E,C))))))) <-> k16_qc_lang1(A) = B)))))) # label(d22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3858 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (k20_qc_lang1(A) = B <-> (exists C (A = k14_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))))))))) # label(d26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3859 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k18_qc_lang1(A)))) & -r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k19_qc_lang1(A))))))) # label(t46_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3860 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & k13_qc_lang1(B,C) = A))))))) # label(d19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3861 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (k6_qc_lang1(A) = k3_finseq_1(B) -> k7_finseq_1(k12_finseq_1(k5_qc_lang1,A),B) = k9_qc_lang1(A,B)))))) # label(d11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3862 $T # label(t42_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3863 $T # label(t11_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3864 (all A all B (m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists C (m1_subset_1(C,k5_qc_lang1) & C = A & B = k6_qc_lang1(C))) <-> r2_hidden(A,a_1_0_qc_lang1(B))))) # label(fraenkel_a_1_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3865 (exists A (m2_relset_1(A,k8_qc_lang1,f1_s3_qc_lang1) & k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k11_qc_lang1) = f2_s3_qc_lang1 & (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(B) -> f5_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k18_qc_lang1(B)),k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k19_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v5_qc_lang1(B) -> f6_s3_qc_lang1(B,k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k21_qc_lang1(B))) = k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B)) & (v3_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f4_s3_qc_lang1(k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,k17_qc_lang1(B)))) & (v2_qc_lang1(B) -> k8_funct_2(k8_qc_lang1,f1_s3_qc_lang1,A,B) = f3_s3_qc_lang1(B)))) & v1_funct_2(A,k8_qc_lang1,f1_s3_qc_lang1) & v1_funct_1(A))) # label(s3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3866 (all A (m1_subset_1(A,k8_qc_lang1) -> -(-v2_qc_lang1(A) & -v3_qc_lang1(A) & -v5_qc_lang1(A) & -v4_qc_lang1(A) & A != k11_qc_lang1))) # label(t33_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3867 $T # label(t20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3868 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> r1_tarski(k2_zfmisc_1(k1_tarski(C),B),k2_zfmisc_1(A,B)))))) # label(t1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3869 (all A (m1_subset_1(A,k5_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k6_qc_lang1(A) = B <-> k1_nat_1(np__7,B) = k1_mcart_1(A)))))) # label(d6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3870 $T # label(t26_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3871 $T # label(t38_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3872 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> k6_qc_lang1(B) = A)))) # label(t35_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3873 (all A (m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k23_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3874 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang1(A) = k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),k10_qc_lang1(A)))) # label(d14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3875 $T # label(t16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3876 $T # label(t24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3877 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k13_qc_lang1(A,B) = k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),k10_qc_lang1(A)),k10_qc_lang1(B)))))) # label(d15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3878 (all A (m1_subset_1(A,k8_qc_lang1) -> (v6_qc_lang1(A) <-> k24_qc_lang1(A) = k1_xboole_0))) # label(d30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3879 $T # label(t32_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3880 $T # label(t40_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3881 $T # label(t14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3882 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> a_1_0_qc_lang1(A) = k7_qc_lang1(A))) # label(d7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3883 (all A (m1_subset_1(A,k2_qc_lang1) -> k1_tarski(A) = k23_qc_lang1(A))) # label(redefinition_k23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3884 $T # label(t41_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3885 $T # label(t28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3886 $T # label(t3_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3887 $T # label(t17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3888 $T # label(dt_k1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3889 $T # label(t27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3890 (all A all B (m2_finseq_1(B,k1_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & r1_xreal_0(C,k3_finseq_1(B)) & r2_hidden(k1_funct_1(B,C),k2_qc_lang1) & r1_xreal_0(np__1,C) & A = k1_funct_1(B,C))) <-> r2_hidden(A,a_1_1_qc_lang1(B))))) # label(fraenkel_a_1_1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3891 $T # label(t30_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3892 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k15_qc_lang1(A),k5_qc_lang1))) # label(dt_k15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3893 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,A)),k10_qc_lang1(B)) = k14_qc_lang1(A,B))))) # label(d16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3894 (all A (m1_subset_1(A,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> m2_finseq_1(B,k1_qc_lang1))))) # label(dt_m1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3895 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_subset_1(k20_qc_lang1(A),k1_qc_lang1,k2_qc_lang1))) # label(dt_k20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3896 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> (all B (m1_subset_1(B,k5_qc_lang1) -> ((exists C (m2_subset_1(C,k1_numbers,k5_numbers) & (exists D ((exists E (k9_qc_lang1(E,D) = A & B = E & m2_subset_1(E,k5_qc_lang1,k7_qc_lang1(C)))) & m1_qc_lang1(D,C))))) <-> k15_qc_lang1(A) = B)))))) # label(d21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3897 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_finseq_1(B,k1_qc_lang1) -> (m1_qc_lang1(B,A) <-> k3_finseq_1(B) = A))))) # label(d8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3898 $T # label(t19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3899 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k14_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k14_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3900 $T # label(t43_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3901 (all A (m2_finseq_1(A,k1_qc_lang1) -> a_1_1_qc_lang1(A) = k22_qc_lang1(A))) # label(d28_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3902 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k21_qc_lang1(A),k8_qc_lang1))) # label(dt_k21_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.44 3903 (all A (m1_subset_1(A,k8_qc_lang1) -> r1_xreal_0(np__1,k3_finseq_1(k10_qc_lang1(A))))) # label(t34_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3904 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> np__0 != k1_mcart_1(B) & k1_mcart_1(B) != np__3 & k1_mcart_1(B) != np__2 & np__1 != k1_mcart_1(B))))) # label(t48_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3905 $T # label(t44_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3906 (all A ((exists B exists C (m2_subset_1(C,k1_numbers,k5_numbers) & k4_tarski(B,C) = A & r1_xreal_0(np__7,B) & m2_subset_1(B,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_0_0_qc_lang1))) # label(fraenkel_a_0_0_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3907 $T # label(t12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3908 (all A (-v1_xboole_0(A) -> (all B all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> r1_tarski(k2_zfmisc_1(k1_enumset1(C,D,E),B),k2_zfmisc_1(A,B)))))))))) # label(t2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3909 $T # label(t18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3910 $T # label(t15_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3911 (all A (m1_subset_1(A,k8_qc_lang1) -> -(v2_qc_lang1(A) & v3_qc_lang1(A)) & -(v4_qc_lang1(A) & v2_qc_lang1(A)) & -(v2_qc_lang1(A) & v5_qc_lang1(A)) & -(v3_qc_lang1(A) & v4_qc_lang1(A)) & -(v5_qc_lang1(A) & v4_qc_lang1(A)) & -(v5_qc_lang1(A) & v3_qc_lang1(A)))) # label(t51_qc_lang1_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3912 (all A (-v1_xboole_0(A) -> (v1_qc_lang1(A) & (all B (-v1_xboole_0(B) -> (v1_qc_lang1(B) -> r1_tarski(A,B)))) <-> k8_qc_lang1 = A))) # label(d10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3913 (all A (m1_subset_1(A,k8_qc_lang1) -> (np__2 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> v4_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__3 -> v5_qc_lang1(A)) & ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & m2_subset_1(k1_funct_1(k10_qc_lang1(A),np__1),k5_qc_lang1,k7_qc_lang1(B)))) -> v2_qc_lang1(A)) & (k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) = np__1 -> v3_qc_lang1(A)) & (np__0 = k1_mcart_1(k1_funct_1(k10_qc_lang1(A),np__1)) -> A = k11_qc_lang1))) # label(t36_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3914 (all A all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,a_1_2_qc_lang1(B)) <-> (exists C (k1_funct_1(k16_qc_lang1(B),C) = A & r1_xreal_0(np__1,C) & r1_xreal_0(C,k3_finseq_1(k16_qc_lang1(B))) & r2_hidden(k1_funct_1(k16_qc_lang1(B),C),k2_qc_lang1) & m2_subset_1(C,k1_numbers,k5_numbers)))))) # label(fraenkel_a_1_2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3915 $T # label(t29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3916 (all A (m1_subset_1(A,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(A)),k3_finseq_1(k10_qc_lang1(k21_qc_lang1(A)))) & v5_qc_lang1(A)))) # label(t47_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3917 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B = k18_qc_lang1(A) <-> (exists C (A = k13_qc_lang1(B,C) & m1_subset_1(C,k8_qc_lang1))))))))) # label(d24_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3918 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k21_qc_lang1(A) = B <-> (exists C (k14_qc_lang1(C,B) = A & m2_subset_1(C,k1_qc_lang1,k2_qc_lang1))))))))) # label(d27_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3919 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m2_subset_1(B,k1_numbers,k5_numbers) & (exists C ((exists D (m1_qc_lang1(D,B) & k9_qc_lang1(C,D) = A)) & m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)))))) <-> v2_qc_lang1(A)))) # label(d17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3920 $T # label(t39_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.24/23.45 3921 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k1_zfmisc_1(k2_qc_lang1)) -> (k24_qc_lang1(A) = B <-> (exists C (v1_funct_2(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & m2_relset_1(C,k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1)) & k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,A) = B & (all D (m1_subset_1(D,k8_qc_lang1) -> (v2_qc_lang1(D) -> a_1_2_qc_lang1(D) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v5_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = k6_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k21_qc_lang1(D)),k23_qc_lang1(k20_qc_lang1(D)))) & (v4_qc_lang1(D) -> k4_subset_1(k2_qc_lang1,k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k18_qc_lang1(D)),k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k19_qc_lang1(D))) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D)) & (v3_qc_lang1(D) -> k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,D) = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k17_qc_lang1(D))) & k1_xboole_0 = k8_funct_2(k8_qc_lang1,k1_zfmisc_1(k2_qc_lang1),C,k11_qc_lang1))) & v1_funct_1(C)))))))) # label(d29_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3922 $T # label(t6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3923 (all A all B (m1_subset_1(A,k5_qc_lang1) & m1_finseq_1(B,k1_qc_lang1) -> m1_subset_1(k9_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3924 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k12_qc_lang1(A),k8_qc_lang1))) # label(dt_k12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3925 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) <-> (exists B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & A = k14_qc_lang1(B,C)))))))) # label(d20_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3926 $T # label(t25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3927 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> ((exists C (k13_qc_lang1(C,B) = A & m1_subset_1(C,k8_qc_lang1))) <-> k19_qc_lang1(A) = B)))))) # label(d25_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3928 (all A (m1_finseq_1(A,k1_qc_lang1) -> m1_subset_1(k22_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1)))) # label(dt_k22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3929 $T # label(t31_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3930 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_finseq_1(k10_qc_lang1(A),k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) # label(dt_k10_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3931 $T # label(t8_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3932 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k17_qc_lang1(A),k8_qc_lang1))) # label(dt_k17_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3933 (all A (m1_subset_1(A,k5_numbers) -> m1_subset_1(k7_qc_lang1(A),k1_zfmisc_1(k5_qc_lang1)))) # label(dt_k7_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3934 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k18_qc_lang1(A),k8_qc_lang1))) # label(dt_k18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3935 (all A (m1_subset_1(A,k5_qc_lang1) -> m2_subset_1(k6_qc_lang1(A),k1_numbers,k5_numbers))) # label(dt_k6_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3936 (all A (m1_subset_1(A,k5_numbers) -> (exists B m1_qc_lang1(B,A)))) # label(existence_m1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3937 $T # label(t13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3938 $T # label(t9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3939 (all A (m1_subset_1(A,k8_qc_lang1) -> ((exists B (m1_subset_1(B,k8_qc_lang1) & k12_qc_lang1(B) = A)) <-> v3_qc_lang1(A)))) # label(d18_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3940 $T # label(t22_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.45 3941 (all A (m1_subset_1(A,k8_qc_lang1) -> (p1_s1_qc_lang1(A) -> p1_s1_qc_lang1(k12_qc_lang1(A))))) & (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(A) & p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k13_qc_lang1(A,B))))))) & (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (p1_s1_qc_lang1(B) -> p1_s1_qc_lang1(k14_qc_lang1(A,B))))))) & p1_s1_qc_lang1(k11_qc_lang1) & (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> p1_s1_qc_lang1(k9_qc_lang1(B,C)))))))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s1_qc_lang1(A))) # label(s1_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3942 (all A (m1_subset_1(A,k8_qc_lang1) -> m2_finseq_1(k16_qc_lang1(A),k1_qc_lang1))) # label(dt_k16_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3943 $T # label(dt_k5_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3944 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) -> (k7_finseq_1(k10_qc_lang1(B),C) = k10_qc_lang1(A) -> k10_qc_lang1(B) = k10_qc_lang1(A)))))))) # label(t37_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3945 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k19_qc_lang1(A),k8_qc_lang1))) # label(dt_k19_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3946 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k13_qc_lang1(A,B),k8_qc_lang1))) # label(dt_k13_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3947 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang1(A) -> p1_s2_qc_lang1(A)) & p1_s2_qc_lang1(k11_qc_lang1) & (p1_s2_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A) -> p1_s2_qc_lang1(A)) & (v4_qc_lang1(A) & p1_s2_qc_lang1(k18_qc_lang1(A)) & p1_s2_qc_lang1(k19_qc_lang1(A)) -> p1_s2_qc_lang1(A)) & (v5_qc_lang1(A) & p1_s2_qc_lang1(k21_qc_lang1(A)) -> p1_s2_qc_lang1(A)))) -> (all A (m1_subset_1(A,k8_qc_lang1) -> p1_s2_qc_lang1(A))) # label(s2_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3948 (all A (m1_subset_1(A,k8_qc_lang1) -> A = k10_qc_lang1(A))) # label(d12_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3949 (all A ((all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(B,A) & r2_hidden(C,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__2,np__0)),B),C),A)))))) & (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_finseq_1(C,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(C,A) -> r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(np__3,np__0)),k12_finseq_1(k2_qc_lang1,B)),C),A)))))) & (all B (m2_finseq_1(B,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)) -> (r2_hidden(B,A) -> r2_hidden(k7_finseq_1(k9_finseq_1(k4_tarski(np__1,np__0)),B),A)))) & r2_hidden(k9_finseq_1(k4_tarski(np__0,np__0)),A) & (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> r2_hidden(k7_finseq_1(k12_finseq_1(k7_qc_lang1(B),C),D),A))))))) & m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers)))) <-> v1_qc_lang1(A))) # label(d9_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3950 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k17_qc_lang1(A) = B <-> A = k12_qc_lang1(B))))))) # label(d23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3951 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k9_qc_lang1(B,C) = k7_finseq_1(k12_finseq_1(k7_qc_lang1(A),B),C))))))) # label(t23_qc_lang1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3952 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> k21_qc_lang1(A) = B)))))) # label(t67_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3953 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> A = k3_qc_lang2(k10_qc_lang2(A),k11_qc_lang2(A))))) # label(t53_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3954 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(A)))) # label(t50_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3955 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k6_qc_lang2(C,E,A) = k6_qc_lang2(D,F,B) -> D = C & E = F & A = B))))))))))))) # label(t21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3956 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k6_qc_lang2(A,B,C) = k14_qc_lang1(A,k14_qc_lang1(B,C)) & k7_qc_lang2(A,B,C) = k5_qc_lang2(A,k5_qc_lang2(B,C)))))))) # label(t20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3957 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(B,C) = k21_qc_lang1(k6_qc_lang2(A,B,C)) & A = k20_qc_lang1(k6_qc_lang2(A,B,C)) & v5_qc_lang1(k6_qc_lang2(A,B,C)))))))) # label(t25_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3958 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r1_qc_lang2(A,k13_qc_lang1(B,C)) <-> C = A | B = A))))))) # label(t62_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3959 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,k15_qc_lang2(B)) -> r2_qc_lang2(A,B)))))) # label(t103_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3960 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) <-> -(B != k12_qc_lang1(A) & (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> B != k14_qc_lang1(C,A))) & (all C (m1_subset_1(C,k8_qc_lang1) -> k13_qc_lang1(A,C) != B & B != k13_qc_lang1(C,A))))))))) # label(d20_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3961 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k14_qc_lang1(A,k14_qc_lang1(B,C)) = k6_qc_lang2(A,B,C))))))) # label(d6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3962 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> r2_qc_lang2(A,A))) # label(reflexivity_r2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3963 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> A = k5_qc_lang2(k20_qc_lang1(k17_qc_lang1(A)),k17_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))))))) # label(t56_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3964 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k5_qc_lang2(A,k5_qc_lang2(B,C)) = k7_qc_lang2(A,B,C))))))) # label(d7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3965 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k17_qc_lang1(k3_qc_lang2(A,B)) = k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)) & k11_qc_lang2(k3_qc_lang2(A,B)) = B & A = k10_qc_lang2(k3_qc_lang2(A,B)))))) # label(t45_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3966 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) <-> (exists C ((exists D (v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & r1_xreal_0(np__1,C) & k3_finseq_1(D) = C & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> -(-r1_xreal_0(C,E) & (all F (m1_subset_1(F,k8_qc_lang1) -> (all G (m1_subset_1(G,k8_qc_lang1) -> -(G = k1_funct_1(D,k1_nat_1(E,np__1)) & r1_qc_lang2(F,G) & F = k1_funct_1(D,E)))))) & r1_xreal_0(np__1,E)))) & B = k1_funct_1(D,C) & A = k1_funct_1(D,np__1))) & m2_subset_1(C,k1_numbers,k5_numbers)))))))) # label(d21_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3967 $T # label(t57_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3968 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) <-> (exists B ((exists C (m1_subset_1(C,k8_qc_lang1) & A = k5_qc_lang2(B,C))) & m2_subset_1(B,k1_qc_lang1,k2_qc_lang1)))))) # label(d13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3969 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> A = k4_qc_lang2(k13_qc_lang2(A),k14_qc_lang2(A))))) # label(t55_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3970 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r3_qc_lang2(A,B) <-> B != A & r2_qc_lang2(A,B)))))) # label(d22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3971 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> A = k13_qc_lang1(k18_qc_lang1(A),k19_qc_lang1(A))))) # label(t4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3972 $T # label(t43_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3973 $T # label(t70_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3974 (all A (m1_subset_1(A,k8_qc_lang1) -> -r3_qc_lang2(A,k11_qc_lang1))) # label(t84_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3975 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) -> v2_qc_lang2(k18_qc_lang1(A)) & v2_qc_lang2(k19_qc_lang1(A)) & v4_qc_lang1(A)))) # label(t51_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3976 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang2(k2_qc_lang2(A,B)) = A & k13_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k2_qc_lang2(A,B)) & B = k11_qc_lang2(k2_qc_lang2(A,B)))))) # label(t46_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3977 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang2(A) = k18_qc_lang1(k17_qc_lang1(A)))) # label(d16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3978 (all A all B all C all D (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(C,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k9_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3979 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k20_qc_lang1(k14_qc_lang1(A,B)) = A & B = k21_qc_lang1(k14_qc_lang1(A,B)))))) # label(t8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3980 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k10_qc_lang2(A),k8_qc_lang1))) # label(dt_k10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3981 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k2_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B))))))) # label(t113_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3982 (all A (m1_subset_1(A,k8_qc_lang1) -> -r1_qc_lang2(A,k11_qc_lang1))) # label(t58_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3983 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> k18_qc_lang1(A) = B | k19_qc_lang1(A) = B)))))) # label(t66_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3984 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(k14_qc_lang1(C,A),B) -> r3_qc_lang2(A,B)))))))) # label(t92_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3985 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(A,k2_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k2_qc_lang2(A,B)) & r3_qc_lang2(B,k2_qc_lang2(A,B)) & r3_qc_lang2(k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B)))))) # label(t93_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.46 3986 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(A,B,C,D) = k7_qc_lang2(F,G,E) -> F = A & B = G & k5_qc_lang2(C,D) = E))))))))))))))) # label(t32_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3987 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k14_qc_lang1(A,k12_qc_lang1(B)) = k17_qc_lang1(k5_qc_lang2(A,B)))))) # label(t48_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3988 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> r3_qc_lang2(k17_qc_lang1(A),A)))) # label(t96_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3989 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(B,C) & r2_qc_lang2(A,B) -> r2_qc_lang2(A,C)))))))) # label(t77_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3990 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r3_qc_lang2(A,B) & r3_qc_lang2(B,C) -> r3_qc_lang2(A,C)))))))) # label(t76_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3991 $T # label(t41_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3992 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (B = A <-> r1_qc_lang2(A,k12_qc_lang1(B))))))) # label(t60_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3993 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k14_qc_lang1(B,D) = k14_qc_lang1(A,C) -> B = A & C = D))))))))) # label(t6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3994 $T # label(dt_k15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3995 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> k15_qc_lang2(k9_qc_lang1(B,C)) = k1_tarski(k9_qc_lang1(B,C)))))))) # label(t108_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3996 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(D,F,H,B) = k9_qc_lang2(C,E,G,A) -> D = C & A = B & G = H & F = E))))))))))))))))) # label(t30_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3997 $T # label(t44_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3998 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k9_qc_lang2(A,B,C,D) = k5_qc_lang2(A,k7_qc_lang2(B,C,D)) & k14_qc_lang1(A,k6_qc_lang2(B,C,D)) = k8_qc_lang2(A,B,C,D))))))))) # label(t26_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 3999 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (k6_qc_lang2(F,G,E) = k8_qc_lang2(A,B,C,D) -> F = A & G = B & E = k14_qc_lang1(C,D)))))))))))))))) # label(t29_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4000 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) -> r3_qc_lang2(A,B)))))) # label(t73_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4001 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(k13_qc_lang1(A,B),C) -> r3_qc_lang2(A,C) & r3_qc_lang2(B,C)))))))) # label(t90_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4002 $T # label(t102_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4003 $T # label(t40_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4004 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(v2_qc_lang1(A) & r1_qc_lang2(B,A)))))) # label(t64_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4005 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (-(-(r3_qc_lang2(A,B) & r2_qc_lang2(B,C)) & -(r2_qc_lang2(A,B) & r3_qc_lang2(B,C)) & -(r2_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r3_qc_lang2(A,B) & r1_qc_lang2(B,C)) & -(r3_qc_lang2(B,C) & r1_qc_lang2(A,B)) & -(r2_qc_lang2(B,C) & r1_qc_lang2(A,B))) -> r3_qc_lang2(A,C)))))))) # label(t83_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4006 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k2_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4007 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k13_qc_lang2(A),k8_qc_lang1))) # label(dt_k13_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4008 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k2_qc_lang2(A,B) = k2_qc_lang2(C,D) -> D = B & C = A))))))))) # label(t17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4009 (all A (m1_subset_1(A,k8_qc_lang1) -> (A = k1_qc_lang2 | k11_qc_lang1 = A <-> r2_qc_lang2(A,k1_qc_lang2)))) # label(t101_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4010 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k14_qc_lang2(A),k8_qc_lang1))) # label(dt_k14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4011 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(A,B,C,D) = k14_qc_lang1(F,E) -> k6_qc_lang2(B,C,D) = E & F = A))))))))))))) # label(t28_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4012 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k19_qc_lang1(k13_qc_lang1(A,B)) = B & k18_qc_lang1(k13_qc_lang1(A,B)) = A)))) # label(t5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4013 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> -r3_qc_lang2(A,k9_qc_lang1(C,D)))))))))) # label(t85_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4014 $T # label(t68_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4015 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) -> v3_qc_lang1(A) & v4_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))) & v3_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))) & v2_qc_lang2(A)))) # label(t49_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4016 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_hidden(A,k15_qc_lang2(B)) -> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B))))))) # label(t105_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4017 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang2(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (k4_qc_lang2(B,C) = A & m1_subset_1(C,k8_qc_lang1)))))))) # label(d12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4018 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(B,A) & r2_qc_lang2(A,B)))))) # label(t81_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4019 (all A (m1_subset_1(A,k8_qc_lang1) -> (A = k11_qc_lang1 <-> r1_qc_lang2(A,k1_qc_lang2)))) # label(t61_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4020 (all A (m1_subset_1(A,k8_qc_lang1) -> (r2_qc_lang2(A,k11_qc_lang1) <-> r3_qc_lang2(A,k1_qc_lang2)))) # label(t88_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4021 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> -r3_qc_lang2(A,A))) # label(irreflexivity_r3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4022 $T # label(t11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4023 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t82_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4024 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k5_qc_lang2(B,D) = k5_qc_lang2(A,C) -> C = D & B = A))))))))) # label(t19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4025 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B))) = k3_qc_lang2(A,B))))) # label(d3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4026 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k4_qc_lang2(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k5_enumset1(k12_qc_lang1(B),k13_qc_lang1(A,k12_qc_lang1(B)),k2_qc_lang2(A,B),k12_qc_lang1(A),k13_qc_lang1(B,k12_qc_lang1(A)),k2_qc_lang2(B,A),k4_qc_lang2(A,B))))))) # label(t115_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4027 $T # label(t34_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4028 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> r3_qc_lang2(k21_qc_lang1(A),A)))) # label(t98_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4029 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_hidden(B,k15_qc_lang2(C)) -> r2_hidden(A,k15_qc_lang2(C)) | -r1_qc_lang2(A,B) & -r3_qc_lang2(A,B) & -r2_qc_lang2(A,B)))))))) # label(t120_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4030 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k15_qc_lang2(k13_qc_lang1(A,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k1_tarski(k13_qc_lang1(A,B))))))) # label(t111_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4031 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k5_qc_lang2(C,E) = k7_qc_lang2(A,B,D) -> A = C & E = k5_qc_lang2(B,D)))))))))))) # label(t24_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4032 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k3_qc_lang2(A,B) = k2_qc_lang2(k12_qc_lang1(A),B))))) # label(t14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4033 $T # label(t12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4034 $T # label(t15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4035 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (B = k15_qc_lang2(A) <-> (all C (r2_hidden(C,B) <-> (exists D (D = C & r2_qc_lang2(D,A) & m1_subset_1(D,k8_qc_lang1))))))))) # label(d23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4036 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k8_qc_lang2(A,B,C,D) = k14_qc_lang1(A,k6_qc_lang2(B,C,D)))))))))) # label(d8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4037 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k14_qc_lang1(C,B))))))))) # label(t91_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4038 $T # label(t35_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4039 (all A (m1_subset_1(A,k8_qc_lang1) -> k11_qc_lang2(k18_qc_lang1(A)) = k14_qc_lang2(A))) # label(d19_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4040 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & (all C (m1_subset_1(C,k8_qc_lang1) -> -r1_qc_lang2(C,B)))))))) # label(t75_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4041 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> r3_qc_lang2(k18_qc_lang1(A),A) & r3_qc_lang2(k19_qc_lang1(A),A)))) # label(t97_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4042 $T # label(t69_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4043 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> v4_qc_lang2(k9_qc_lang2(A,B,C,D)) & v4_qc_lang2(k7_qc_lang2(A,B,D)))))))))) # label(t38_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4044 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(B,A) & r2_qc_lang2(A,B) -> B = A))))) # label(t78_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4045 $T # label(t36_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4046 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (r2_qc_lang2(A,B) | r2_qc_lang2(A,C) <-> r3_qc_lang2(A,k13_qc_lang1(B,C))))))))) # label(t89_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4047 (all A all B (m1_subset_1(B,k8_qc_lang1) & m1_subset_1(A,k2_qc_lang1) -> m1_subset_1(k5_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4048 $T # label(t106_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4049 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(A) -> (r1_qc_lang2(B,A) <-> B = k17_qc_lang1(A))))))) # label(t65_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4050 (all A (m1_subset_1(A,k8_qc_lang1) -> k10_qc_lang2(A) = k17_qc_lang1(k18_qc_lang1(k17_qc_lang1(A))))) # label(d14_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4051 (all A (m1_subset_1(A,k8_qc_lang1) -> k17_qc_lang1(k12_qc_lang1(A)) = A)) # label(t2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4052 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> -r1_qc_lang2(A,k9_qc_lang1(C,D)))))))))) # label(t59_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4053 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k11_qc_lang2(A),k8_qc_lang1))) # label(dt_k11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4054 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(A,B) & r2_qc_lang2(B,A)))))) # label(t79_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4055 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang2(A) -> v3_qc_lang1(k21_qc_lang1(k17_qc_lang1(A))) & v5_qc_lang1(k17_qc_lang1(A)) & v3_qc_lang1(A)))) # label(t52_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4056 (all A (m1_subset_1(A,k8_qc_lang1) -> (k1_tarski(A) = k15_qc_lang2(A) <-> v2_qc_lang1(A) | k11_qc_lang1 = A))) # label(t116_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4057 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_qc_lang2(A,B) = k12_qc_lang1(k13_qc_lang1(A,k12_qc_lang1(B))))))) # label(d2_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4058 $T # label(t10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4059 (all A (m1_subset_1(A,k8_qc_lang1) -> (v1_qc_lang2(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (m1_subset_1(C,k8_qc_lang1) & A = k3_qc_lang2(B,C)))))))) # label(d10_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4060 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k7_qc_lang2(D,F,B) = k7_qc_lang2(C,E,A) -> E = F & B = A & C = D))))))))))))) # label(t23_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4061 $T # label(t9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4062 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k4_qc_lang2(A,B) = k4_qc_lang2(C,D) -> B = D & C = A))))))))) # label(t18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4063 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k14_qc_lang1(k20_qc_lang1(A),k21_qc_lang1(A)) = A))) # label(t7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4064 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k2_xboole_0(k2_xboole_0(k15_qc_lang2(A),k15_qc_lang2(B)),k2_enumset1(k12_qc_lang1(B),k12_qc_lang1(A),k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B))) = k15_qc_lang2(k3_qc_lang2(A,B)))))) # label(t114_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4065 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(k12_qc_lang1(A),B) -> r3_qc_lang2(A,B)))))) # label(t87_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4066 $T # label(d17_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4067 $T # label(t37_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4068 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> r3_qc_lang2(k13_qc_lang1(k12_qc_lang1(A),k12_qc_lang1(B)),k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(A),k3_qc_lang2(A,B)) & r3_qc_lang2(A,k3_qc_lang2(A,B)) & r3_qc_lang2(B,k3_qc_lang2(A,B)) & r3_qc_lang2(k12_qc_lang1(B),k3_qc_lang2(A,B)))))) # label(t94_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4069 (all A (m1_subset_1(A,k8_qc_lang1) -> k11_qc_lang2(A) = k17_qc_lang1(k19_qc_lang1(k17_qc_lang1(A))))) # label(d15_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4070 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r3_qc_lang2(B,A) & r3_qc_lang2(A,B)))))) # label(t80_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4071 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k14_qc_lang1(A,k12_qc_lang1(B))) = k5_qc_lang2(A,B))))) # label(d5_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4072 (all A (m1_subset_1(A,k8_qc_lang1) -> (v5_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k15_qc_lang2(k21_qc_lang1(A)),k1_tarski(A))))) # label(t119_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4073 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) & r1_qc_lang2(A,B)))))) # label(t71_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4074 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (k9_qc_lang2(A,B,C,D) = k5_qc_lang2(F,E) -> E = k7_qc_lang2(B,C,D) & A = F))))))))))))) # label(t31_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4075 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) -> r1_tarski(k15_qc_lang2(A),k15_qc_lang2(B))))))) # label(t104_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4076 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> k5_qc_lang2(A,k7_qc_lang2(B,C,D)) = k9_qc_lang2(A,B,C,D))))))))) # label(d9_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4077 (all A all B all C (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(C,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> m1_subset_1(k7_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k7_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4078 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k4_qc_lang2(A,B) = k13_qc_lang1(k2_qc_lang2(A,B),k2_qc_lang2(B,A)))))) # label(d4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4079 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k3_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4080 (all A (m1_subset_1(A,k8_qc_lang1) -> k2_xboole_0(k15_qc_lang2(A),k1_tarski(k12_qc_lang1(A))) = k15_qc_lang2(k12_qc_lang1(A)))) # label(t110_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4081 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_qc_lang1,k2_qc_lang1) -> (all H (m2_subset_1(H,k1_qc_lang1,k2_qc_lang1) -> (k8_qc_lang2(C,E,G,A) = k8_qc_lang2(D,F,H,B) -> D = C & A = B & G = H & E = F))))))))))))))))) # label(t27_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4082 (all A (m1_subset_1(A,k8_qc_lang1) -> (k11_qc_lang1 = A <-> r2_qc_lang2(A,k11_qc_lang1)))) # label(t99_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4083 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) -> k2_qc_lang2(k12_qc_lang2(A),k11_qc_lang2(A)) = A))) # label(t54_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4084 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (all E (m1_subset_1(E,k8_qc_lang1) -> (k6_qc_lang2(A,B,D) = k14_qc_lang1(C,E) -> C = A & k14_qc_lang1(B,D) = E))))))))))) # label(t22_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4085 $T # label(t39_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4086 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(r1_xreal_0(k3_finseq_1(k10_qc_lang1(B)),k3_finseq_1(k10_qc_lang1(A))) & r3_qc_lang2(A,B)))))) # label(t74_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4087 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r1_qc_lang2(A,B) -> r2_qc_lang2(A,B)))))) # label(t72_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4088 (all A (m1_subset_1(A,k8_qc_lang1) -> k12_qc_lang2(k18_qc_lang1(A)) = k13_qc_lang2(A))) # label(d18_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4089 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> -(v2_qc_lang1(A) & r3_qc_lang2(B,A)))))) # label(t95_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4090 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (r2_qc_lang2(A,B) <-> r3_qc_lang2(A,k12_qc_lang1(B))))))) # label(t86_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4091 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k13_qc_lang1(A,B) = k13_qc_lang1(C,D) -> C = A & D = B))))))))) # label(t3_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4092 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> A = k13_qc_lang2(k4_qc_lang2(A,B)) & k18_qc_lang1(k4_qc_lang2(A,B)) = k2_qc_lang2(A,B) & k2_qc_lang2(B,A) = k19_qc_lang1(k4_qc_lang2(A,B)) & k14_qc_lang2(k4_qc_lang2(A,B)) = B)))) # label(t47_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4093 (all A all B all C (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(B,k2_qc_lang1) & m1_subset_1(C,k8_qc_lang1) -> m1_subset_1(k6_qc_lang2(A,B,C),k8_qc_lang1))) # label(dt_k6_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4094 (all A (m1_subset_1(A,k8_qc_lang1) -> (v3_qc_lang1(A) -> k2_xboole_0(k15_qc_lang2(k17_qc_lang1(A)),k1_tarski(A)) = k15_qc_lang2(A)))) # label(t117_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4095 (all A (m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k12_qc_lang2(A),k8_qc_lang1))) # label(dt_k12_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4096 (all A (m1_subset_1(A,k8_qc_lang1) -> (v2_qc_lang2(A) <-> (exists B (m1_subset_1(B,k8_qc_lang1) & (exists C (A = k2_qc_lang2(B,C) & m1_subset_1(C,k8_qc_lang1)))))))) # label(d11_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4097 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> (k3_qc_lang2(A,B) = k3_qc_lang2(C,D) -> B = D & C = A))))))))) # label(t16_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4098 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> k2_xboole_0(k15_qc_lang2(A),k1_tarski(k14_qc_lang1(B,A))) = k15_qc_lang2(k14_qc_lang1(B,A)))))) # label(t112_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4099 (all A (m1_subset_1(A,k8_qc_lang1) -> (v4_qc_lang1(A) -> k15_qc_lang2(A) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(k18_qc_lang1(A)),k15_qc_lang2(k19_qc_lang1(A))),k1_tarski(A))))) # label(t118_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4100 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m1_subset_1(D,k8_qc_lang1) -> A = k20_qc_lang1(k8_qc_lang2(A,B,C,D)) & k6_qc_lang2(B,C,D) = k21_qc_lang1(k8_qc_lang2(A,B,C,D)) & v5_qc_lang1(k8_qc_lang2(A,B,C,D)))))))))) # label(t33_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4101 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k12_qc_lang1(B) = k12_qc_lang1(A) -> B = A))))) # label(t1_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4102 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(B)) -> (all D (m1_qc_lang1(D,B) -> (k9_qc_lang1(C,D) = A <-> r2_qc_lang2(A,k9_qc_lang1(C,D))))))))))) # label(t100_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4103 (all A all B (m1_subset_1(A,k8_qc_lang1) & m1_subset_1(B,k8_qc_lang1) -> m1_subset_1(k4_qc_lang2(A,B),k8_qc_lang1))) # label(dt_k4_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4104 $T # label(t42_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4105 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (r1_qc_lang2(A,k14_qc_lang1(C,B)) <-> B = A))))))) # label(t63_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4106 (all A all B all C all D (m1_subset_1(A,k2_qc_lang1) & m1_subset_1(C,k2_qc_lang1) & m1_subset_1(D,k8_qc_lang1) & m1_subset_1(B,k2_qc_lang1) -> m1_subset_1(k8_qc_lang2(A,B,C,D),k8_qc_lang1))) # label(dt_k8_qc_lang2) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4107 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k12_cqc_lang(A,B) = k2_qc_lang2(A,B))) # label(redefinition_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4108 $T # label(t9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4109 $T # label(t1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4110 $T # label(t14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4111 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s6_cqc_lang) -> (f3_s6_cqc_lang(A) = B <-> (exists C (B = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,A) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f8_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k10_cqc_lang(D)) & f9_s6_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k11_cqc_lang(D,E)) & f10_s6_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k15_cqc_lang(F,D)) & k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s6_cqc_lang(G,I,H))))))))))))) & f2_s6_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s6_cqc_lang,C,k9_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s6_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s6_cqc_lang) & v1_funct_1(C)))))))) -> f4_s6_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang) = f3_s6_cqc_lang(k8_cqc_lang(f5_s6_cqc_lang,f6_s6_cqc_lang,f7_s6_cqc_lang)) # label(s6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4112 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> m2_subset_1(k16_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4113 (all A (-(-r2_hidden(A,k2_qc_lang1) & -r2_hidden(A,k4_qc_lang1) & -r2_hidden(A,k3_qc_lang1)) <-> r2_hidden(A,k1_qc_lang1))) # label(t7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4114 (all A (m2_finseq_1(A,k1_qc_lang1) -> (all B (v1_funct_1(B) & m2_relset_1(B,k4_qc_lang1,k1_qc_lang1) -> (all C (m2_finseq_1(C,k1_qc_lang1) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r1_xreal_0(np__1,D) & r1_xreal_0(D,k3_finseq_1(A)) -> (r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D))) & (-r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) -> k1_funct_1(A,D) = k1_funct_1(C,D))))) & k3_finseq_1(C) = k3_finseq_1(A) <-> C = k4_cqc_lang(A,B)))))))) # label(d3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4115 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (v1_cqc_lang(B,A) & m1_qc_lang1(B,A) <-> a_2_1_cqc_lang(A,B) = k1_xboole_0 & k1_xboole_0 = a_2_0_cqc_lang(A,B)))))) # label(t15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4116 $T # label(t8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4117 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k4_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t22_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4118 $T # label(dt_k3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4119 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s7_cqc_lang) -> (f2_s7_cqc_lang(A) = B <-> (exists C (v1_funct_1(C) & m2_relset_1(C,k7_cqc_lang,f1_s7_cqc_lang) & f3_s7_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k10_cqc_lang(D)) = f5_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) & f8_s7_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k15_cqc_lang(F,D)) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k11_cqc_lang(D,E)) = f7_s7_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,E)) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s7_cqc_lang(G,I,H))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s7_cqc_lang,C,A) = B & v1_funct_2(C,k7_cqc_lang,f1_s7_cqc_lang)))))))) -> f5_s7_cqc_lang(f2_s7_cqc_lang(f6_s7_cqc_lang)) = f2_s7_cqc_lang(k10_cqc_lang(f6_s7_cqc_lang)) # label(s7_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.47 4120 (all A all B (v1_relat_1(k3_cqc_lang(A,B)) & v1_funct_1(k3_cqc_lang(A,B)))) # label(fc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4121 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m1_qc_lang1(B,A) -> (r1_tarski(k2_relat_1(B),k2_qc_lang1) <-> v1_cqc_lang(B,A)))))) # label(d5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4122 (all A (m1_subset_1(A,f1_s4_cqc_lang) -> (all B (m1_subset_1(B,f1_s4_cqc_lang) -> -((exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) & f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) & f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)) = f4_s4_cqc_lang(G,I,H))))))))))))) & f3_s4_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = B)) & A != B & (exists C (v1_funct_2(C,k7_cqc_lang,f1_s4_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (v1_cqc_lang(H,G) & m1_qc_lang1(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k10_cqc_lang(D)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,E)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s4_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,D)) & f4_s4_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,k9_cqc_lang) = f3_s4_cqc_lang & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,C,f2_s4_cqc_lang) = A & m2_relset_1(C,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_1(C)))))))) # label(s4_cqc_lang_AndLHS) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4123 (exists A ((exists B (v1_funct_1(B) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k9_cqc_lang) = f3_s4_cqc_lang & (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k1_qc_lang1,k2_qc_lang1) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (m1_qc_lang1(G,F) & v1_cqc_lang(G,F) -> (all H (m2_subset_1(H,k5_qc_lang1,k7_qc_lang1(F)) -> f4_s4_cqc_lang(F,H,G) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k8_cqc_lang(F,H,G)) & k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k11_cqc_lang(C,D)) = f6_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C),k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,D)) & f7_s4_cqc_lang(E,k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k15_cqc_lang(E,C)) & f5_s4_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,C)) = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,k10_cqc_lang(C)))))))))))))) & A = k8_funct_2(k7_cqc_lang,f1_s4_cqc_lang,B,f2_s4_cqc_lang) & m2_relset_1(B,k7_cqc_lang,f1_s4_cqc_lang) & v1_funct_2(B,k7_cqc_lang,f1_s4_cqc_lang))) & m1_subset_1(A,f1_s4_cqc_lang))) # label(s4_cqc_lang_AndRHS) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4124 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> k9_cqc_lang = k17_cqc_lang(k9_cqc_lang,A))) # label(t28_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4125 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> v1_funct_1(k6_cqc_lang(A,B)) & m2_relset_1(k6_cqc_lang(A,B),k4_qc_lang1,k1_qc_lang1))) # label(dt_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4126 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> m2_subset_1(k14_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4127 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v4_qc_lang1(B) -> k13_qc_lang1(k17_cqc_lang(k18_qc_lang1(B),A),k17_cqc_lang(k19_qc_lang1(B),A)) = k17_cqc_lang(B,A)))))) # label(t33_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4128 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v5_qc_lang1(B) -> k17_cqc_lang(B,A) = k14_qc_lang1(k20_qc_lang1(B),k17_cqc_lang(k21_qc_lang1(B),A)) | k20_qc_lang1(B) = A))))) # label(t36_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4129 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (k1_xboole_0 = k5_qc_lang3(B) -> k17_cqc_lang(B,A) = B))))) # label(t39_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4130 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k1_qc_lang1,k4_qc_lang1) -> (all D (m2_finseq_1(D,k1_qc_lang1) -> (all E (m2_finseq_1(E,k1_qc_lang1) -> (all F (m2_relset_1(F,k4_qc_lang1,k1_qc_lang1) & v1_funct_1(F) -> (k4_cqc_lang(E,F) = D & r1_xreal_0(np__1,A) & r1_xreal_0(A,k3_finseq_1(E)) & k6_cqc_lang(C,B) = F -> (k1_funct_1(E,A) = C -> k1_funct_1(D,A) = B) & (k1_funct_1(E,A) != C -> k1_funct_1(E,A) = k1_funct_1(D,A))))))))))))))) # label(t11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4131 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s8_cqc_lang) -> ((exists C (v1_funct_1(C) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> f9_s8_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k15_cqc_lang(F,D)) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,E)) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k10_cqc_lang(D)) = f5_s8_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,D)) & f4_s8_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & f3_s8_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,k9_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s8_cqc_lang,C,A) = B & m2_relset_1(C,k7_cqc_lang,f1_s8_cqc_lang) & v1_funct_2(C,k7_cqc_lang,f1_s8_cqc_lang))) <-> B = f2_s8_cqc_lang(A)))))) -> f6_s8_cqc_lang(f2_s8_cqc_lang(f7_s8_cqc_lang),f2_s8_cqc_lang(f8_s8_cqc_lang)) = f2_s8_cqc_lang(k11_cqc_lang(f7_s8_cqc_lang,f8_s8_cqc_lang)) # label(s8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4132 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k5_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t24_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4133 (all A (m1_subset_1(A,k8_qc_lang1) -> (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(k12_qc_lang1(A),k8_qc_lang1,k7_cqc_lang)))) # label(t18_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4134 $T # label(t12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4135 $T # label(t2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4136 (all A all B all C (m1_subset_1(A,k5_numbers) & m1_subset_1(B,k7_qc_lang1(A)) & m1_qc_lang1(C,A) & v1_cqc_lang(C,A) -> k8_cqc_lang(A,B,C) = k9_qc_lang1(B,C))) # label(redefinition_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4137 (all A (m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k10_cqc_lang(A),k8_qc_lang1,k7_cqc_lang))) # label(dt_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4138 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_qc_lang1(E,D) & v1_cqc_lang(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> f5_s3_cqc_lang(D,F,E) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k8_cqc_lang(D,F,E)) & f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k15_cqc_lang(C,A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k11_cqc_lang(A,B)) = f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,B)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,A)))))))))))))) & (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_qc_lang1(E,D) & v1_cqc_lang(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k11_cqc_lang(A,B)) = f7_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A),k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,B)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k15_cqc_lang(C,A)) = f8_s3_cqc_lang(C,k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k10_cqc_lang(A)) = f6_s3_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,A)) & f5_s3_cqc_lang(D,F,E) = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k8_cqc_lang(D,F,E)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f3_s3_cqc_lang,k9_cqc_lang) = f4_s3_cqc_lang & f4_s3_cqc_lang = k8_funct_2(k7_cqc_lang,f1_s3_cqc_lang,f2_s3_cqc_lang,k9_cqc_lang) -> f2_s3_cqc_lang = f3_s3_cqc_lang # label(s3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4139 (all A all B all C (m1_subset_1(A,k5_numbers) & v1_funct_1(C) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & m1_qc_lang1(B,A) -> k4_cqc_lang(B,C) = k5_cqc_lang(A,B,C))) # label(redefinition_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4140 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> k17_cqc_lang(k13_qc_lang1(B,C),A) = k13_qc_lang1(k17_cqc_lang(B,A),k17_cqc_lang(C,A)))))))) # label(t34_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4141 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (B != A -> k17_cqc_lang(k14_qc_lang1(A,C),B) = k14_qc_lang1(A,k17_cqc_lang(C,B))))))))) # label(t38_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4142 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s9_cqc_lang) -> ((exists C (v1_funct_1(C) & v1_funct_2(C,k7_cqc_lang,f1_s9_cqc_lang) & m2_relset_1(C,k7_cqc_lang,f1_s9_cqc_lang) & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,E)) & f7_s9_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k15_cqc_lang(F,D)) & f5_s9_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,D)) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k10_cqc_lang(D)) & f4_s9_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,k9_cqc_lang) = f3_s9_cqc_lang & B = k8_funct_2(k7_cqc_lang,f1_s9_cqc_lang,C,A))) <-> B = f2_s9_cqc_lang(A)))))) -> f7_s9_cqc_lang(f8_s9_cqc_lang,f2_s9_cqc_lang(f9_s9_cqc_lang)) = f2_s9_cqc_lang(k15_cqc_lang(f8_s9_cqc_lang,f9_s9_cqc_lang)) # label(s9_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4143 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k3_qc_lang2(A,B) = k13_cqc_lang(A,B))) # label(redefinition_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4144 (all A all B (m1_finseq_1(A,k1_qc_lang1) & v1_funct_1(B) & m1_relset_1(B,k4_qc_lang1,k1_qc_lang1) -> m2_finseq_1(k4_cqc_lang(A,B),k1_qc_lang1))) # label(dt_k4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4145 $T # label(t25_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4146 (all A all B all C (m1_qc_lang1(C,B) & m2_subset_1(B,k1_numbers,k5_numbers) -> ((exists D (m2_subset_1(D,k1_numbers,k5_numbers) & r1_xreal_0(np__1,D) & r2_hidden(k1_funct_1(C,D),k4_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)) & k1_funct_1(C,D) = A)) <-> r2_hidden(A,a_2_0_cqc_lang(B,C))))) # label(fraenkel_a_2_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4147 (all A all B (m1_subset_1(A,k7_cqc_lang) & m1_subset_1(B,k7_cqc_lang) -> k14_cqc_lang(A,B) = k4_qc_lang2(A,B))) # label(redefinition_k14_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4148 (all A (m1_subset_1(A,k8_qc_lang1) -> (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) <-> k5_qc_lang3(A) = k1_xboole_0 & k1_xboole_0 = k6_qc_lang3(A)))) # label(t13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4149 $T # label(t3_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4150 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k3_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t21_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4151 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(k14_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang)))))) # label(t23_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4152 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k1_qc_lang1,k2_qc_lang1) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (v1_cqc_lang(E,D) & m1_qc_lang1(E,D) -> (all F (m2_subset_1(F,k5_qc_lang1,k7_qc_lang1(D)) -> p1_s1_cqc_lang(k9_cqc_lang) & (p1_s1_cqc_lang(A) & p1_s1_cqc_lang(B) -> p1_s1_cqc_lang(k11_cqc_lang(A,B))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k15_cqc_lang(C,A))) & (p1_s1_cqc_lang(A) -> p1_s1_cqc_lang(k10_cqc_lang(A))) & p1_s1_cqc_lang(k8_cqc_lang(D,F,E)))))))))))))) -> (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> p1_s1_cqc_lang(A))) # label(s1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4153 $T # label(t4_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4154 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> k11_cqc_lang(A,B) = k13_qc_lang1(A,B))) # label(redefinition_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4155 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> k2_cqc_lang(A,B,C,D,E) = k1_cqc_lang(B,C,D,E))) # label(redefinition_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4156 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m2_subset_1(C,k5_qc_lang1,k7_qc_lang1(A)) -> (all D (m1_qc_lang1(D,A) -> k9_qc_lang1(C,k5_cqc_lang(A,D,k6_cqc_lang(k3_qc_lang3(np__0),B))) = k17_cqc_lang(k9_qc_lang1(C,D),B))))))))) # label(t30_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4157 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k8_qc_lang1) -> m1_subset_1(k17_cqc_lang(A,B),k8_qc_lang1))) # label(dt_k17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4158 (all A all B all C k3_cqc_lang(k4_tarski(A,B),C) = k9_funct_2(A,B,C)) # label(t42_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4159 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> k14_qc_lang1(A,B) = k15_cqc_lang(A,B))) # label(redefinition_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4160 (all A all B (k1_relat_1(k3_cqc_lang(A,B)) = k1_tarski(A) & k1_tarski(B) = k2_relat_1(k3_cqc_lang(A,B)))) # label(t5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4161 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k5_qc_lang1,k7_qc_lang1(A)) -> (all C (m1_qc_lang1(C,A) -> (k1_xboole_0 = a_2_1_cqc_lang(A,C) & k1_xboole_0 = a_2_0_cqc_lang(A,C) <-> m2_subset_1(k9_qc_lang1(B,C),k8_qc_lang1,k7_cqc_lang)))))))) # label(t17_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4162 (exists A (m2_relset_1(A,k7_cqc_lang,f1_s2_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k9_cqc_lang) = f2_s2_cqc_lang & (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> (all C (m2_subset_1(C,k8_qc_lang1,k7_cqc_lang) -> (all D (m2_subset_1(D,k1_qc_lang1,k2_qc_lang1) -> (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (v1_cqc_lang(F,E) & m1_qc_lang1(F,E) -> (all G (m2_subset_1(G,k5_qc_lang1,k7_qc_lang1(E)) -> f4_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k10_cqc_lang(B)) & k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k11_cqc_lang(B,C)) = f5_s2_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B),k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,C)) & f6_s2_cqc_lang(D,k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,B)) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k15_cqc_lang(D,B)) & f3_s2_cqc_lang(E,G,F) = k8_funct_2(k7_cqc_lang,f1_s2_cqc_lang,A,k8_cqc_lang(E,G,F)))))))))))))) & v1_funct_2(A,k7_cqc_lang,f1_s2_cqc_lang) & v1_funct_1(A))) # label(s2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4163 (all A all B k2_funcop_1(k1_tarski(A),B) = k3_cqc_lang(A,B)) # label(d2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4164 (all A all B all C (v1_cqc_lang(C,A) & m1_qc_lang1(C,A) & m1_subset_1(B,k7_qc_lang1(A)) & m1_subset_1(A,k5_numbers) -> m2_subset_1(k8_cqc_lang(A,B,C),k8_qc_lang1,k7_cqc_lang))) # label(dt_k8_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4165 (all A all B all C (m2_subset_1(B,k1_numbers,k5_numbers) & m1_qc_lang1(C,B) -> ((exists D (A = k1_funct_1(C,D) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1) & r1_xreal_0(D,k3_finseq_1(C)) & r1_xreal_0(np__1,D) & m2_subset_1(D,k1_numbers,k5_numbers))) <-> r2_hidden(A,a_2_1_cqc_lang(B,C))))) # label(fraenkel_a_2_1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4166 $T # label(dt_k1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4167 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m1_subset_1(B,f1_s5_cqc_lang) -> (B = f2_s5_cqc_lang(A) <-> (exists C (m2_relset_1(C,k7_cqc_lang,f1_s5_cqc_lang) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,A) = B & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k9_cqc_lang) = f3_s5_cqc_lang & (all D (m2_subset_1(D,k8_qc_lang1,k7_cqc_lang) -> (all E (m2_subset_1(E,k8_qc_lang1,k7_cqc_lang) -> (all F (m2_subset_1(F,k1_qc_lang1,k2_qc_lang1) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (m1_qc_lang1(H,G) & v1_cqc_lang(H,G) -> (all I (m2_subset_1(I,k5_qc_lang1,k7_qc_lang1(G)) -> k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k10_cqc_lang(D)) = f5_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k11_cqc_lang(D,E)) = f6_s5_cqc_lang(k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D),k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,E)) & k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k15_cqc_lang(F,D)) = f7_s5_cqc_lang(F,k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,D)) & f4_s5_cqc_lang(G,I,H) = k8_funct_2(k7_cqc_lang,f1_s5_cqc_lang,C,k8_cqc_lang(G,I,H)))))))))))))) & v1_funct_2(C,k7_cqc_lang,f1_s5_cqc_lang) & v1_funct_1(C)))))))) -> f2_s5_cqc_lang(k9_cqc_lang) = f3_s5_cqc_lang # label(s5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4168 (all A all B k1_funct_1(k3_cqc_lang(A,B),A) = B) # label(t6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4169 (all A all B all C C = k1_binop_1(k9_funct_2(A,B,C),A,B)) # label(t43_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4170 (all A all B (m1_subset_1(B,k2_qc_lang1) & m1_subset_1(A,k4_qc_lang1) -> k6_cqc_lang(A,B) = k3_cqc_lang(A,B))) # label(redefinition_k6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4171 (all A (m1_subset_1(A,k7_cqc_lang) -> k10_cqc_lang(A) = k12_qc_lang1(A))) # label(redefinition_k10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4172 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> B = k17_cqc_lang(B,A))))) # label(t40_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4173 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> m2_subset_1(k15_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k15_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4174 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k6_qc_lang3(k17_cqc_lang(B,A)) = k6_qc_lang3(B))))) # label(t41_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4175 (all A (m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) -> (all B (m2_subset_1(B,k8_qc_lang1,k7_cqc_lang) -> m2_subset_1(k2_qc_lang2(A,B),k8_qc_lang1,k7_cqc_lang))))) # label(t20_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4176 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k14_qc_lang1(A,B) = k17_cqc_lang(k14_qc_lang1(A,B),A))))) # label(t37_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4177 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v3_qc_lang1(B) -> k12_qc_lang1(k17_cqc_lang(k17_qc_lang1(B),A)) = k17_cqc_lang(B,A)))))) # label(t31_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4178 (all A all B all C (m1_qc_lang1(B,A) & v1_funct_1(C) & m1_relset_1(C,k4_qc_lang1,k1_qc_lang1) & m1_subset_1(A,k5_numbers) -> m1_qc_lang1(k5_cqc_lang(A,B,C),A))) # label(dt_k5_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4179 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k4_qc_lang1) -> v1_funct_1(k3_cqc_lang(B,A)) & m2_relset_1(k3_cqc_lang(B,A),k4_qc_lang1,k1_qc_lang1))))) # label(t10_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4180 (all A (r2_hidden(A,a_0_0_cqc_lang) <-> (exists B (k1_xboole_0 = k6_qc_lang3(B) & k5_qc_lang3(B) = k1_xboole_0 & B = A & m1_subset_1(B,k8_qc_lang1))))) # label(fraenkel_a_0_0_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4181 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k13_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k13_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4182 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (v2_qc_lang1(B) -> k17_cqc_lang(B,A) = k9_qc_lang1(k15_qc_lang1(B),k4_cqc_lang(k16_qc_lang1(B),k6_cqc_lang(k3_qc_lang3(np__0),A)))))))) # label(t29_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4183 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> k12_qc_lang1(k17_cqc_lang(B,A)) = k17_cqc_lang(k12_qc_lang1(B),A))))) # label(t32_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4184 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (m2_subset_1(k13_qc_lang1(A,B),k8_qc_lang1,k7_cqc_lang) <-> m2_subset_1(A,k8_qc_lang1,k7_cqc_lang) & m2_subset_1(B,k8_qc_lang1,k7_cqc_lang)))))) # label(t19_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4185 $T # label(t27_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4186 (all A (m1_subset_1(A,k8_qc_lang1) -> (all B (m2_subset_1(B,k1_qc_lang1,k2_qc_lang1) -> (all C (m1_subset_1(C,k8_qc_lang1) -> (k17_cqc_lang(A,B) = C <-> (exists D (v1_funct_2(D,k8_qc_lang1,k8_qc_lang1) & m2_relset_1(D,k8_qc_lang1,k8_qc_lang1) & (all E (m1_subset_1(E,k8_qc_lang1) -> (v2_qc_lang1(E) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k9_qc_lang1(k15_qc_lang1(E),k4_cqc_lang(k16_qc_lang1(E),k6_cqc_lang(k3_qc_lang3(np__0),B)))) & (v5_qc_lang1(E) -> k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E) = k2_cqc_lang(k8_qc_lang1,k20_qc_lang1(E),B,E,k14_qc_lang1(k20_qc_lang1(E),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k21_qc_lang1(E))))) & (v4_qc_lang1(E) -> k13_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k18_qc_lang1(E)),k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k19_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & (v3_qc_lang1(E) -> k12_qc_lang1(k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k17_qc_lang1(E))) = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,E)) & k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,k9_cqc_lang) = k9_cqc_lang)) & C = k8_funct_2(k8_qc_lang1,k8_qc_lang1,D,A) & v1_funct_1(D)))))))))) # label(d6_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4187 (all A (m2_subset_1(A,k1_qc_lang1,k2_qc_lang1) -> (all B (m1_subset_1(B,k8_qc_lang1) -> (A = k20_qc_lang1(B) & v5_qc_lang1(B) -> k17_cqc_lang(B,A) = B))))) # label(t35_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4188 (all A (m1_subset_1(A,k5_numbers) -> (exists B (v1_relat_1(B) & v1_finseq_1(B) & v1_cqc_lang(B,A) & v1_funct_1(B) & m1_qc_lang1(B,A))))) # label(rc1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4189 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k12_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k12_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4190 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k7_cqc_lang) -> m2_subset_1(k11_cqc_lang(A,B),k8_qc_lang1,k7_cqc_lang))) # label(dt_k11_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4191 (all A all B all C all D all E (m1_subset_1(E,A) & m1_subset_1(D,A) & -v1_xboole_0(A) -> m1_subset_1(k2_cqc_lang(A,B,C,D,E),A))) # label(dt_k2_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4192 $T # label(t26_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4193 (all A all B all C all D ((A = B -> k1_cqc_lang(A,B,C,D) = C) & (A != B -> D = k1_cqc_lang(A,B,C,D)))) # label(d1_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4194 (all A all B (m1_subset_1(B,k7_cqc_lang) & m1_subset_1(A,k2_qc_lang1) -> k16_cqc_lang(A,B) = k5_qc_lang2(A,B))) # label(redefinition_k16_cqc_lang) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4195 (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]. 22.30/23.48 4196 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,B,k2_pboole(A,B,C)),k2_pboole(A,B,C)) & r6_pboole(A,k2_pboole(A,k2_pboole(A,B,C),C),k2_pboole(A,B,C)))))) # label(t47_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4197 (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]. 22.30/23.48 4198 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,k3_pboole(A,C,B),k1_pboole(A)) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))) # label(t57_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4199 (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]. 22.30/23.48 4200 (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]. 22.30/23.48 4201 (all A exists B m1_pboole(B,A)) # label(existence_m1_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4202 (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]. 22.30/23.48 4203 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,k3_pboole(A,B,D),k1_pboole(A)) & r2_pboole(A,B,k2_pboole(A,C,D)) -> r2_pboole(A,B,C)))))))) # label(t56_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4204 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> 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,k2_pboole(A,B,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]. 22.30/23.48 4205 (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]. 22.30/23.48 4206 (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]. 22.30/23.48 4207 (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) & v2_relat_1(D) & v1_funct_2(C,A,B) -> k5_relat_1(C,D) = k8_pboole(A,B,C,D))) # label(redefinition_k8_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4208 (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]. 22.30/23.48 4209 (all A exists B (v1_funcop_1(B) & v1_funct_1(B) & v1_relat_1(B) & m1_pboole(B,A))) # label(rc4_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4210 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r4_pboole(A,B,C) -> r4_pboole(A,C,B)))) # label(symmetry_r4_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4211 (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]. 22.30/23.48 4212 $T # label(t125_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4213 (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) & r5_pboole(A,C,D) & r2_pboole(A,B,D) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t123_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4214 (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,D,C) -> r2_pboole(A,k2_pboole(A,B,D),C)))))))) # label(t18_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4215 $T # label(t32_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4216 (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]. 22.30/23.48 4217 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k2_pboole(A,k3_pboole(A,C,D),B),k3_pboole(A,k2_pboole(A,C,B),k2_pboole(A,D,B))) & r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),k2_pboole(A,B,D))))))))) # label(t39_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4218 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B all C k2_finseq_2(A,C) = k5_relat_1(k2_finseq_2(A,B),k2_funcop_1(k1_tarski(B),C))))) # label(t152_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4219 (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]. 22.30/23.48 4220 (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]. 22.30/23.48 4221 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E))) <-> D = k12_pboole(A,B,C)))))))) # label(d22_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4222 (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]. 22.30/23.48 4223 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (all E (m1_pboole(E,A) -> (r6_pboole(A,k2_pboole(A,B,C),k2_pboole(A,D,E)) & r5_pboole(A,D,B) & r5_pboole(A,E,C) -> r6_pboole(A,D,C) & r6_pboole(A,E,B)))))))))) # label(t124_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4224 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (m3_pboole(D,A,B,C) <-> (all E (r2_hidden(E,A) -> v1_funct_1(k1_funct_1(D,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E))))))))))) # label(d18_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4225 (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]. 22.30/23.48 4226 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r6_pboole(A,B,C) <-> r2_pboole(A,C,B) & r2_pboole(A,B,C)))))) # label(d13_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4227 (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]. 22.30/23.48 4228 (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]. 22.30/23.48 4229 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r6_pboole(A,k3_pboole(A,C,D),k1_pboole(A)) & r2_pboole(A,B,C) -> r6_pboole(A,B,k1_pboole(A))))))))) # label(t51_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4230 (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]. 22.30/23.48 4231 (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]. 22.30/23.48 4232 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> r7_pboole(A,B,B))) # label(reflexivity_r7_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4233 (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]. 22.30/23.48 4234 (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]. 22.30/23.48 4235 (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,D) & r2_pboole(A,E,C) -> r2_pboole(A,E,B)))) <-> r6_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t29_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4236 (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]. 22.30/23.48 4237 $T # label(d2_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4238 (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]. 22.30/23.48 4239 $T # label(d1_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.48 4240 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k2_pboole(A,k1_pboole(A),B),B) & r6_pboole(A,k2_pboole(A,B,k1_pboole(A)),B))) # label(t53_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4241 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k4_pboole(A,C,B),D) & r2_pboole(A,k4_pboole(A,B,C),D) -> r2_pboole(A,k5_pboole(A,B,C),D)))))))) # label(t99_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4242 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,k3_finseq_2(A)) -> ((all D (m2_finseq_2(D,A,k3_finseq_2(A)) -> k4_card_3(k5_relat_1(D,B)) = k1_funct_1(C,D))) <-> k6_pboole(A,B) = C))))) # label(d19_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4243 (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]. 22.30/23.49 4244 (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]. 22.30/23.49 4245 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r2_pboole(A,B,k2_pboole(A,B,C)) & r2_pboole(A,C,k2_pboole(A,B,C)))))) # label(t16_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4246 (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]. 22.30/23.49 4247 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> (all C (r2_hidden(C,A) -> v1_xboole_0(k1_funct_1(B,C))))))) # label(d15_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4248 (all A all B (v2_relat_1(B) & m1_pboole(B,A) -> 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]. 22.30/23.49 4249 (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]. 22.30/23.49 4250 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k2_pboole(A,k4_pboole(A,C,B),B),k2_pboole(A,C,B)) & r6_pboole(A,k2_pboole(A,B,k4_pboole(A,C,B)),k2_pboole(A,B,C)))))) # label(t73_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4251 (all A all B k1_xboole_0 = k1_funct_1(k1_pboole(B),A)) # label(t5_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4252 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k2_pboole(A,B,B) = B)) # label(idempotence_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4253 (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]. 22.30/23.49 4254 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,k2_pboole(A,B,C),D) -> r2_pboole(A,B,D) & r2_pboole(A,C,D)))))))) # label(t43_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4255 (all A k1_pboole(A) = k2_funcop_1(A,k1_xboole_0)) # label(d6_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4256 (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]. 22.30/23.49 4257 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> v1_pboole(B,A)))) # label(redefinition_v1_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4258 $T # label(t131_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4259 (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]. 22.30/23.49 4260 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)))) <-> r2_pboole(A,B,C)))))) # label(d5_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4261 (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]. 22.30/23.49 4262 (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]. 22.30/23.49 4263 $T # label(t13_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4264 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> -((all D (m1_pboole(D,A) -> -(r1_pboole(A,D,C) & r1_pboole(A,D,B)))) & r4_pboole(A,B,C)))))) # label(t11_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4265 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> r6_pboole(A,k3_pboole(A,C,k4_pboole(A,B,C)),k1_pboole(A)) & r6_pboole(A,k3_pboole(A,k4_pboole(A,B,C),C),k1_pboole(A)))))) # label(t69_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4266 (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]. 22.30/23.49 4267 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D)))) <-> m2_pboole(C,A,B)))))) # label(d17_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4268 $T # label(t117_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4269 (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]. 22.30/23.49 4270 (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]. 22.30/23.49 4271 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> ((all D (r2_hidden(D,A) -> r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D)))) <-> r1_pboole(A,B,C)))))) # label(d4_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4272 (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]. 22.30/23.49 4273 (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]. 22.30/23.49 4274 (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]. 22.30/23.49 4275 (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]. 22.30/23.49 4276 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r6_pboole(A,B,k2_pboole(A,C,D)) <-> r2_pboole(A,C,B) & r2_pboole(A,D,B) & (all E (m1_pboole(E,A) -> (r2_pboole(A,C,E) & r2_pboole(A,D,E) -> r2_pboole(A,B,E))))))))))) # label(t28_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4277 (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]. 22.30/23.49 4278 (all A all B (m1_pboole(B,A) -> (v3_relat_1(B) <-> r6_pboole(A,B,k1_pboole(A))))) # label(t141_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4279 (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]. 22.30/23.49 4280 (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]. 22.30/23.49 4281 (all A all B all C all D (m1_pboole(D,B) & v2_relat_1(D) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) & 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]. 22.30/23.49 4282 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r4_pboole(A,B,D) | r4_pboole(A,B,C) -> r4_pboole(A,B,k2_pboole(A,C,D))))))))) # label(t106_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4283 (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]. 22.30/23.49 4284 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & m1_pboole(D,B) & m1_relset_1(C,A,B) & v1_funct_2(C,A,B) -> m1_pboole(k7_pboole(A,B,C,D),A))) # label(dt_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4285 (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]. 22.30/23.49 4286 (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]. 22.30/23.49 4287 $T # label(t31_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4288 (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]. 22.30/23.49 4289 (all A all B (m1_pboole(B,A) -> (v2_relat_1(B) <-> v2_pboole(B,A)))) # label(redefinition_v2_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4290 (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]. 22.30/23.49 4291 (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]. 22.30/23.49 4292 (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]. 22.30/23.49 4293 (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]. 22.30/23.49 4294 (all A all B k2_funcop_1(A,B) = k10_pboole(A,B)) # label(redefinition_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4295 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k5_pboole(A,B,C),A))) # label(dt_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4296 (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]. 22.30/23.49 4297 (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]. 22.30/23.49 4298 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> -(B = k1_pboole(A) & r4_pboole(A,B,B)))))) # label(t140_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4299 (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]. 22.30/23.49 4300 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> (r3_pboole(A,B,C) -> -r3_pboole(A,C,B)))) # label(antisymmetry_r3_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4301 (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]. 22.30/23.49 4302 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,C) -> r2_pboole(A,k2_pboole(A,B,D),k2_pboole(A,C,D)) & r2_pboole(A,k2_pboole(A,D,B),k2_pboole(A,D,C))))))))) # label(t20_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4303 (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]. 22.30/23.49 4304 (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]. 22.30/23.49 4305 (all A all B (m1_pboole(B,A) -> r2_pboole(A,k1_pboole(A),B))) # label(t49_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4306 (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]. 22.30/23.49 4307 (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]. 22.30/23.49 4308 (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]. 22.30/23.49 4309 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r1_pboole(A,B,k3_pboole(A,C,D)) <-> r1_pboole(A,B,D) & r1_pboole(A,B,C)))))))) # label(t8_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4310 (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]. 22.30/23.49 4311 (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]. 22.30/23.49 4312 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (all D (m3_pboole(D,A,B,C) -> m1_pboole(D,A))))) # label(dt_m3_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4313 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r4_pboole(A,B,C) -> r4_pboole(A,B,k3_pboole(A,C,D))))))))) # label(t112_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4314 (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]. 22.30/23.49 4315 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> -(r3_pboole(A,B,D) & k1_pboole(A) = k3_pboole(A,C,D) & r3_pboole(A,B,C)))))))))) # label(t137_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4316 (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]. 22.30/23.49 4317 (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]. 22.30/23.49 4318 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> (r6_pboole(A,B,C) <-> C = B))) # label(redefinition_r6_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4319 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k4_pboole(A,B,C) = D <-> (all E (r2_hidden(E,A) -> k4_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) = k1_funct_1(D,E)))))))))) # label(d9_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4320 (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]. 22.30/23.49 4321 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (r2_pboole(A,B,D) & r4_pboole(A,B,C) -> r4_pboole(A,D,C)))))))) # label(t109_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4322 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (m4_pboole(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v2_relat_1(C))))) # label(rc5_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4323 (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]. 22.30/23.49 4324 (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]. 22.30/23.49 4325 (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]. 22.30/23.49 4326 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> k5_pboole(A,B,C) = k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B)))))) # label(d12_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4327 (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]. 22.30/23.49 4328 (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]. 22.30/23.49 4329 $T # label(t107_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4330 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,C,B) & v3_relat_1(B) -> v3_relat_1(C)))))) # label(t142_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4331 (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]. 22.30/23.49 4332 (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]. 22.30/23.49 4333 (all A -((all B -p1_s3_pboole(A,B)) & r2_hidden(A,f1_s3_pboole))) -> (exists A (m1_pboole(A,f1_s3_pboole) & (all B (r2_hidden(B,f1_s3_pboole) -> p1_s3_pboole(B,k1_funct_1(A,B)))))) # label(s3_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4334 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r4_pboole(A,B,C) <-> (all D -(r2_hidden(D,A) & r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d10_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4335 (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]. 22.30/23.49 4336 (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]. 22.30/23.49 4337 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r5_pboole(A,B,C) <-> (all D (r2_hidden(D,A) -> r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D))))))))) # label(d11_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4338 (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]. 22.30/23.49 4339 (all A (m1_pboole(A,k1_xboole_0) -> A = k1_xboole_0)) # label(t134_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4340 (all A all B (m1_pboole(B,A) -> ((all C (r2_hidden(C,A) -> k1_xboole_0 = k1_funct_1(B,C))) -> k1_pboole(A) = B))) # label(t6_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4341 (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]. 22.30/23.49 4342 (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]. 22.30/23.49 4343 (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]. 22.30/23.49 4344 (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]. 22.30/23.49 4345 (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]. 22.30/23.49 4346 (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]. 22.30/23.49 4347 (all A all B (v1_funct_1(k10_pboole(A,B)) & v1_funct_2(k10_pboole(A,B),A,k1_tarski(B)) & m2_relset_1(k10_pboole(A,B),A,k1_tarski(B)))) # label(dt_k10_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4348 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)))) <-> k2_pboole(A,B,C) = D))))))) # label(d7_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4349 (all A all B (m1_pboole(B,A) -> ((all C -(r2_hidden(C,A) & v1_xboole_0(k1_funct_1(B,C)))) <-> v2_relat_1(B)))) # label(d16_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4350 (all A (-v1_xboole_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C all D (m1_pboole(D,k1_tarski(C)) -> (D = k2_funcop_1(k1_tarski(C),A) -> k1_funct_1(k7_pboole(k5_numbers,k3_finseq_2(k1_tarski(C)),k9_pboole(C),k6_pboole(k1_tarski(C),D)),B) = k1_funct_2(k2_finseq_1(B),A)))))))) # label(t153_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4351 (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]. 22.30/23.49 4352 (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]. 22.30/23.49 4353 (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]. 22.30/23.49 4354 $T # label(t33_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4355 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)))) <-> D = k11_pboole(A,B,C)))))))) # label(d21_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4356 (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]. 22.30/23.49 4357 (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]. 22.30/23.49 4358 (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]. 22.30/23.49 4359 (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]. 22.30/23.49 4360 (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]. 22.30/23.49 4361 (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]. 22.30/23.49 4362 (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]. 22.30/23.49 4363 (all A all B (v1_funct_1(B) & v1_funct_2(B,k5_numbers,k3_finseq_2(k1_tarski(A))) & m2_relset_1(B,k5_numbers,k3_finseq_2(k1_tarski(A))) -> (k9_pboole(A) = 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)))))) # label(d20_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4364 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (v2_relat_1(D) & m1_pboole(D,A) -> ((all E (m1_pboole(E,A) -> (r1_pboole(A,E,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]. 22.30/23.49 4365 (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]. 22.30/23.49 4366 (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]. 22.30/23.49 4367 (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]. 22.30/23.49 4368 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_relat_1(A) -> v1_setfam_1(k2_relat_1(A))))) # label(t1_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4369 (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]. 22.30/23.49 4370 (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]. 22.30/23.49 4371 (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]. 22.30/23.49 4372 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (r2_hidden(D,A) -> k1_funct_1(k5_pboole(A,B,C),D) = k5_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)))))))) # label(t4_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4373 (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]. 22.30/23.49 4374 (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]. 22.30/23.49 4375 $T # label(t30_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4376 (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]. 22.30/23.49 4377 $T # label(t14_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4378 (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]. 22.30/23.49 4379 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> (r5_pboole(A,B,C) -> r5_pboole(A,C,B)))) # label(symmetry_r5_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4380 (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]. 22.30/23.49 4381 (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]. 22.30/23.49 4382 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k2_pboole(A,B,C),A))) # label(dt_k2_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4383 (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]. 22.30/23.49 4384 (all A all B (m1_pboole(B,A) -> r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B) & r6_pboole(A,k5_pboole(A,k1_pboole(A),B),B))) # label(t91_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4385 (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]. 22.30/23.49 4386 (exists A (m1_pboole(A,f1_s2_pboole) & (all B (r2_hidden(B,f1_s2_pboole) -> (all C (r2_hidden(C,k1_funct_1(A,B)) <-> r2_hidden(C,k1_funct_1(f2_s2_pboole,B)) & p1_s2_pboole(B,C))))))) # label(s2_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4387 (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]. 22.30/23.49 4388 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) -> k3_pboole(A,B,B) = B)) # label(idempotence_k3_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4389 (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]. 22.30/23.49 4390 (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]. 22.30/23.49 4391 (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]. 22.30/23.49 4392 (all A all B (m1_pboole(B,A) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (D = k14_pboole(A,B,C) <-> (all E (r2_hidden(E,A) -> k9_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) = k1_funct_1(D,E)))))))))) # label(d25_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4393 (all A m1_pboole(k1_pboole(A),A)) # label(dt_k1_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4394 (all A (v3_relat_1(k1_pboole(A)) & v1_funct_1(k1_pboole(A)) & v1_relat_1(k1_pboole(A)))) # label(fc3_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4395 (all A all B all C (m1_subset_1(C,A) & m1_pboole(B,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]. 22.30/23.49 4396 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v3_relat_1(A) <-> k1_tarski(k1_xboole_0) = k2_relat_1(A) | k1_xboole_0 = A))) # label(t2_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4397 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> ((all E (r2_hidden(E,A) -> k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)))) <-> D = k3_pboole(A,B,C)))))))) # label(d8_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4398 (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,k3_pboole(A,B,D),k3_pboole(A,C,E))))))))))) # label(t23_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4399 (all A all B all C all D (-v1_xboole_0(B) & m1_relset_1(C,A,B) & m1_pboole(D,B) & v1_funct_2(C,A,B) & v1_funct_1(C) -> k7_pboole(A,B,C,D) = k5_relat_1(C,D))) # label(redefinition_k7_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4400 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r2_pboole(A,B,C) -> r6_pboole(A,k2_pboole(A,B,C),C) & r6_pboole(A,k2_pboole(A,C,B),C)))))) # label(t24_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4401 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) -> (all B (v1_relat_1(B) & v1_funcop_1(B) & v1_funct_1(B) -> (all C (v1_funcop_1(C) & v1_funct_1(C) & v1_relat_1(C) -> (C = k13_pboole(A,B) <-> (all D (r2_hidden(D,k1_relat_1(C)) -> k5_relat_1(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D))) & k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))))))))) # label(d24_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4402 (exists A (v1_funct_1(A) & v3_relat_1(A) & v1_relat_1(A))) # label(rc1_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4403 (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]. 22.30/23.49 4404 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k11_pboole(A,B,C),A))) # label(dt_k11_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4405 (all A all B (v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funcop_1(B) & v1_funct_1(B) & v1_relat_1(A) -> v1_relat_1(k13_pboole(A,B)) & v1_funcop_1(k13_pboole(A,B)) & v1_funct_1(k13_pboole(A,B)))) # label(dt_k13_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4406 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> (exists C (r1_pboole(A,C,B) & m1_pboole(C,A))))) # label(t146_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4407 (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]. 22.30/23.49 4408 (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]. 22.30/23.49 4409 (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]. 22.30/23.49 4410 (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]. 22.30/23.49 4411 (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]. 22.30/23.49 4412 (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]. 22.30/23.49 4413 (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,B,D),k3_pboole(A,C,D)) & r2_pboole(A,k3_pboole(A,D,B),k3_pboole(A,D,C))))))))) # label(t21_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.49 4414 (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]. 22.30/23.50 4415 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> r6_pboole(A,k3_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D))) & r6_pboole(A,k3_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k3_pboole(A,B,D),k3_pboole(A,C,D))))))))) # label(t46_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4416 $T # label(t93_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4417 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) & v2_relat_1(B) -> v2_relat_1(C)))))) # label(t145_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4418 (all A -(k1_xboole_0 = f2_s1_pboole(A) & r2_hidden(A,f1_s1_pboole))) -> (exists A ((all B (r2_hidden(B,f1_s1_pboole) -> r2_hidden(k1_funct_1(A,B),f2_s1_pboole(B)))) & m1_pboole(A,f1_s1_pboole))) # label(s1_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4419 (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]. 22.30/23.50 4420 (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]. 22.30/23.50 4421 (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]. 22.30/23.50 4422 (all A all B (m1_pboole(B,A) & v2_relat_1(B) -> -r2_hidden(k1_xboole_0,k2_relat_1(B)))) # label(t149_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4423 (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]. 22.30/23.50 4424 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (r7_pboole(A,B,C) <-> (all D (m1_pboole(D,A) -> (r1_pboole(A,D,B) -> r1_pboole(A,D,C))))))))) # label(d14_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4425 (all A all B all C (m1_pboole(B,A) & m1_pboole(C,A) -> k5_pboole(A,C,B) = k5_pboole(A,B,C))) # label(commutativity_k5_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4426 (all A all B (v1_relat_1(B) & v1_funct_1(B) -> (k1_relat_1(B) = A <-> m1_pboole(B,A)))) # label(d3_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4427 (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]. 22.30/23.50 4428 $T # label(t90_pboole) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4429 (all A all B all C all D all E all F all G all H (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(F,A) & m1_subset_1(G,B) & m1_subset_1(H,C) & -v1_xboole_0(D) & -v1_xboole_0(A) -> k1_multop_1(E,F,G,H) = k2_multop_1(A,B,C,D,E,F,G,H))) # label(redefinition_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4430 $T # label(t5_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4431 (exists A (v1_funct_1(A) & m2_relset_1(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1) & (all B (m1_subset_1(B,f1_s3_multop_1) -> (all C (m1_subset_1(C,f2_s3_multop_1) -> (all D (m1_subset_1(D,f3_s3_multop_1) -> f5_s3_multop_1(B,C,D) = k8_funct_2(k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1,A,k4_domain_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1,B,C,D)))))))) & v1_funct_2(A,k3_zfmisc_1(f1_s3_multop_1,f2_s3_multop_1,f3_s3_multop_1),f4_s3_multop_1))) # label(s3_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4432 (all A (m1_subset_1(A,f1_s2_multop_1) -> (all B (m1_subset_1(B,f1_s2_multop_1) -> (all C (m1_subset_1(C,f1_s2_multop_1) -> (exists D (m1_subset_1(D,f1_s2_multop_1) & p1_s2_multop_1(A,B,C,D))))))))) -> (exists A (v1_funct_1(A) & m2_relset_1(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1) & (all B (m1_subset_1(B,f1_s2_multop_1) -> (all C (m1_subset_1(C,f1_s2_multop_1) -> (all D (m1_subset_1(D,f1_s2_multop_1) -> p1_s2_multop_1(B,C,D,k2_multop_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1,A,B,C,D)))))))) & v1_funct_2(A,k3_zfmisc_1(f1_s2_multop_1,f1_s2_multop_1,f1_s2_multop_1),f1_s2_multop_1))) # label(s2_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4433 $T # label(dt_k3_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4434 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m2_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k3_zfmisc_1(A,B,C),D) & m2_relset_1(F,k3_zfmisc_1(A,B,C),D) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> k2_multop_1(A,B,C,D,E,G,H,I) = k2_multop_1(A,B,C,D,F,G,H,I))))))) -> E = F))))))))))))) # label(t4_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4435 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,k3_zfmisc_1(A,B,C),D) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & v1_funct_1(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k3_zfmisc_1(A,B,C),D) & m2_relset_1(F,k3_zfmisc_1(A,B,C),D) -> ((all G (m1_subset_1(G,A) -> (all H (m1_subset_1(H,B) -> (all I (m1_subset_1(I,C) -> k8_funct_2(k3_zfmisc_1(A,B,C),D,F,k4_domain_1(A,B,C,G,H,I)) = k8_funct_2(k3_zfmisc_1(A,B,C),D,E,k4_domain_1(A,B,C,G,H,I)))))))) -> F = E))))))))))))) # label(t3_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4436 (all A (m1_subset_1(A,f1_s6_multop_1) -> (all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (exists E (p1_s6_multop_1(A,B,C,D,E) & m1_subset_1(E,f1_s6_multop_1))))))))))) -> (exists A (v1_funct_2(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1) & m2_relset_1(A,k4_zfmisc_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1),f1_s6_multop_1) & (all B (m1_subset_1(B,f1_s6_multop_1) -> (all C (m1_subset_1(C,f1_s6_multop_1) -> (all D (m1_subset_1(D,f1_s6_multop_1) -> (all E (m1_subset_1(E,f1_s6_multop_1) -> p1_s6_multop_1(B,C,D,E,k4_multop_1(f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,f1_s6_multop_1,A,B,C,D,E)))))))))) & v1_funct_1(A))) # label(s6_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4437 (all A (m1_subset_1(A,f1_s1_multop_1) -> (all B (m1_subset_1(B,f2_s1_multop_1) -> (all C (m1_subset_1(C,f3_s1_multop_1) -> (exists D (m1_subset_1(D,f4_s1_multop_1) & p1_s1_multop_1(A,B,C,D))))))))) -> (exists A ((all B (m1_subset_1(B,f1_s1_multop_1) -> (all C (m1_subset_1(C,f2_s1_multop_1) -> (all D (m1_subset_1(D,f3_s1_multop_1) -> p1_s1_multop_1(B,C,D,k8_funct_2(k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1,A,k4_domain_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1,B,C,D))))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & v1_funct_2(A,k3_zfmisc_1(f1_s1_multop_1,f2_s1_multop_1,f3_s1_multop_1),f4_s1_multop_1) & v1_funct_1(A))) # label(s1_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4438 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) -> (all G (v1_funct_1(G) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) & v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k4_multop_1(A,B,C,D,E,G,H,I,J,K) = k4_multop_1(A,B,C,D,E,F,H,I,J,K))))))))) -> G = F))))))))))))))) # label(t8_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4439 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (-v1_xboole_0(D) -> (all E (-v1_xboole_0(E) -> (all F (v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(F) -> (all G (v1_funct_2(G,k4_zfmisc_1(A,B,C,D),E) & m2_relset_1(G,k4_zfmisc_1(A,B,C,D),E) & v1_funct_1(G) -> ((all H (m1_subset_1(H,A) -> (all I (m1_subset_1(I,B) -> (all J (m1_subset_1(J,C) -> (all K (m1_subset_1(K,D) -> k8_funct_2(k4_zfmisc_1(A,B,C,D),E,F,k5_domain_1(A,B,C,D,H,I,J,K)) = k8_funct_2(k4_zfmisc_1(A,B,C,D),E,G,k5_domain_1(A,B,C,D,H,I,J,K)))))))))) -> F = G))))))))))))))) # label(t7_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4440 $T # label(t1_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4441 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D all E k3_multop_1(A,B,C,D,E) = k1_funct_1(A,k4_mcart_1(B,C,D,E))))) # label(d2_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4442 (all A (-v1_xboole_0(A) -> (all B all C all D all E all F (v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(B,C,D,E),A) & m2_relset_1(F,k4_zfmisc_1(B,C,D,E),A) -> (all G (m2_relset_1(G,k4_zfmisc_1(B,C,D,E),A) & v1_funct_2(G,k4_zfmisc_1(B,C,D,E),A) & v1_funct_1(G) -> ((all H all I all J all K (r2_hidden(H,B) & r2_hidden(I,C) & r2_hidden(K,E) & r2_hidden(J,D) -> k1_funct_1(F,k4_mcart_1(H,I,J,K)) = k1_funct_1(G,k4_mcart_1(H,I,J,K)))) -> F = G))))))) # label(t6_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4443 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(B) & -v1_xboole_0(D) & -v1_xboole_0(E) & v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(H,B) & m1_subset_1(J,D) & m1_subset_1(I,C) & m1_subset_1(G,A) & -v1_xboole_0(C) & -v1_xboole_0(A) -> m1_subset_1(k4_multop_1(A,B,C,D,E,F,G,H,I,J),E))) # label(dt_k4_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4444 (all A (-v1_xboole_0(A) -> (all B all C all D all E (v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(B,C,D),A) & m2_relset_1(E,k3_zfmisc_1(B,C,D),A) -> (all F (v1_funct_1(F) & v1_funct_2(F,k3_zfmisc_1(B,C,D),A) & m2_relset_1(F,k3_zfmisc_1(B,C,D),A) -> ((all G all H all I (r2_hidden(H,C) & r2_hidden(I,D) & r2_hidden(G,B) -> k1_funct_1(E,k3_mcart_1(G,H,I)) = k1_funct_1(F,k3_mcart_1(G,H,I)))) -> E = F))))))) # label(t2_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4445 (exists A (m2_relset_1(A,k4_zfmisc_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1),f1_s8_multop_1) & (all B (m1_subset_1(B,f1_s8_multop_1) -> (all C (m1_subset_1(C,f1_s8_multop_1) -> (all D (m1_subset_1(D,f1_s8_multop_1) -> (all E (m1_subset_1(E,f1_s8_multop_1) -> f2_s8_multop_1(B,C,D,E) = k4_multop_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,A,B,C,D,E))))))))) & v1_funct_2(A,k4_zfmisc_1(f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1,f1_s8_multop_1),f1_s8_multop_1) & v1_funct_1(A))) # label(s8_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4446 (exists A (v1_funct_1(A) & v1_funct_2(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1) & (all B (m1_subset_1(B,f1_s4_multop_1) -> (all C (m1_subset_1(C,f2_s4_multop_1) -> (all D (m1_subset_1(D,f3_s4_multop_1) -> f5_s4_multop_1(B,C,D) = k2_multop_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1,f4_s4_multop_1,A,B,C,D))))))) & m2_relset_1(A,k3_zfmisc_1(f1_s4_multop_1,f2_s4_multop_1,f3_s4_multop_1),f4_s4_multop_1))) # label(s4_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4447 (all A (v1_funct_1(A) & v1_relat_1(A) -> (all B all C all D k1_funct_1(A,k3_mcart_1(B,C,D)) = k1_multop_1(A,B,C,D)))) # label(d1_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4448 (all A (m1_subset_1(A,f1_s5_multop_1) -> (all B (m1_subset_1(B,f2_s5_multop_1) -> (all C (m1_subset_1(C,f3_s5_multop_1) -> (all D (m1_subset_1(D,f4_s5_multop_1) -> (exists E (p1_s5_multop_1(A,B,C,D,E) & m1_subset_1(E,f5_s5_multop_1))))))))))) -> (exists A (v1_funct_1(A) & v1_funct_2(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & m2_relset_1(A,k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1) & (all B (m1_subset_1(B,f1_s5_multop_1) -> (all C (m1_subset_1(C,f2_s5_multop_1) -> (all D (m1_subset_1(D,f3_s5_multop_1) -> (all E (m1_subset_1(E,f4_s5_multop_1) -> p1_s5_multop_1(B,C,D,E,k8_funct_2(k4_zfmisc_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1),f5_s5_multop_1,A,k5_domain_1(f1_s5_multop_1,f2_s5_multop_1,f3_s5_multop_1,f4_s5_multop_1,B,C,D,E))))))))))))) # label(s5_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4449 (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) & -v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,k3_zfmisc_1(A,B,C),D) & m1_relset_1(E,k3_zfmisc_1(A,B,C),D) & m1_subset_1(G,B) & m1_subset_1(H,C) & m1_subset_1(F,A) -> m1_subset_1(k2_multop_1(A,B,C,D,E,F,G,H),D))) # label(dt_k2_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4450 (all A all B all C all D all E all F all G all H all I all J (-v1_xboole_0(A) & -v1_xboole_0(C) & -v1_xboole_0(D) & v1_funct_1(F) & v1_funct_2(F,k4_zfmisc_1(A,B,C,D),E) & m1_relset_1(F,k4_zfmisc_1(A,B,C,D),E) & m1_subset_1(I,C) & m1_subset_1(J,D) & m1_subset_1(H,B) & m1_subset_1(G,A) & -v1_xboole_0(E) & -v1_xboole_0(B) -> k4_multop_1(A,B,C,D,E,F,G,H,I,J) = k3_multop_1(F,G,H,I,J))) # label(redefinition_k4_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4451 $T # label(dt_k1_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4452 (exists A (v1_funct_1(A) & (all B (m1_subset_1(B,f1_s7_multop_1) -> (all C (m1_subset_1(C,f2_s7_multop_1) -> (all D (m1_subset_1(D,f3_s7_multop_1) -> (all E (m1_subset_1(E,f4_s7_multop_1) -> k8_funct_2(k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1,A,k5_domain_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1,B,C,D,E)) = f6_s7_multop_1(B,C,D,E))))))))) & m2_relset_1(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1) & v1_funct_2(A,k4_zfmisc_1(f1_s7_multop_1,f2_s7_multop_1,f3_s7_multop_1,f4_s7_multop_1),f5_s7_multop_1))) # label(s7_multop_1) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4453 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4454 (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]. 22.30/23.50 4455 (exists A l1_struct_0(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4456 (all A all B (m1_subset_1(B,A) -> l2_struct_0(g2_struct_0(A,B)) & v2_struct_0(g2_struct_0(A,B)))) # label(dt_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4457 (all A (-v3_struct_0(A) & l1_struct_0(A) -> -v1_xboole_0(u1_struct_0(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4458 (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]. 22.30/23.50 4459 (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]. 22.30/23.50 4460 (all A (l1_struct_0(A) -> (v1_struct_0(A) -> A = g1_struct_0(u1_struct_0(A))))) # label(abstractness_v1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4461 (all A (l2_struct_0(A) -> l1_struct_0(A))) # label(dt_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.30/23.50 4462 (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]. 22.30/23.50 4463 (all A all B (l1_struct_0(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v3_struct_0(A) -> (exists C m1_struct_0(C,A,B)))) # label(existence_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4464 (all A (l2_struct_0(A) -> (v2_struct_0(A) -> g2_struct_0(u1_struct_0(A),u2_struct_0(A)) = A))) # label(abstractness_v2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4465 (exists A (l1_struct_0(A) & v1_struct_0(A))) # label(rc1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4466 (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]. 22.39/23.61 4467 (all A all B all C (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> 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]. 22.39/23.61 4468 (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_subset_1(C,B) <-> m1_struct_0(C,A,B))))) # label(redefinition_m1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4469 (exists A (-v3_struct_0(A) & l2_struct_0(A))) # label(rc4_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4470 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k2_struct_0(A,B,C) = k2_tarski(B,C))) # label(redefinition_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4471 (all A all B (m1_subset_1(B,A) -> (all C all D (g2_struct_0(C,D) = g2_struct_0(A,B) -> A = C & D = B)))) # label(free_g2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4472 (exists A l2_struct_0(A)) # label(existence_l2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4473 (exists A (l2_struct_0(A) & v2_struct_0(A))) # label(rc2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4474 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> k2_struct_0(A,B,C) = k2_struct_0(A,C,B))) # label(commutativity_k2_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4475 (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]. 22.39/23.61 4476 (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]. 22.39/23.61 4477 (exists A (l1_struct_0(A) & -v3_struct_0(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4478 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4479 (all A (l1_struct_0(A) -> (v3_struct_0(A) <-> v1_xboole_0(u1_struct_0(A))))) # label(d1_struct_0) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4480 $T # label(t72_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4481 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> C = k10_cat_1(A,B)))))))) # label(t87_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4482 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> (exists C m2_cat_1(C,A,B)))) # label(existence_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4483 (all A all B k3_cqc_lang(A,B) = k7_cat_1(A,B)) # label(redefinition_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4484 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(F,A) & v5_cat_1(E,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | v5_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k6_cat_1(A,C,D) = k1_xboole_0))))))))))))) # label(t75_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4485 $T # label(t130_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4486 (all A (l1_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k2_cat_1(A,k4_cat_1(A,B,C)) = k2_cat_1(A,B) & k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C)))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_cat_1(A,k5_cat_1(A,B)) = B & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k2_cat_1(A,C) -> k4_cat_1(A,k5_cat_1(A,B),C) = C))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k3_cat_1(A,C) -> k4_cat_1(A,C,k5_cat_1(A,B)) = C))) & B = k2_cat_1(A,k5_cat_1(A,B)))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) & k3_cat_1(A,C) = k2_cat_1(A,D) -> k4_cat_1(A,k4_cat_1(A,B,C),D) = k4_cat_1(A,B,k4_cat_1(A,C,D))))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) <-> k2_cat_1(A,C) = k3_cat_1(A,B)))))) -> v2_cat_1(A)))) # label(t29_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4487 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (r1_cat_1(A,C,D) & r1_cat_1(A,B,C) -> r1_cat_1(A,B,D)))))))))) # label(t93_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4488 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(B,A) & r1_cat_1(A,B,C) -> v7_cat_1(C,A)))))))) # label(t85_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4489 $T # label(t14_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4490 (all A (v2_cat_1(A) & l1_cat_1(A) -> k6_partfun1(u1_cat_1(A)) = k12_cat_1(A,A,k15_cat_1(A)))) # label(t117_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4491 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (k6_cat_1(A,C,B) = k1_tarski(D) & m1_cat_1(D,A,C,B)))))))))) # label(t86_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4492 $T # label(t20_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4493 (all A (l1_cat_1(A) -> v1_funct_1(u4_cat_1(A)) & v1_funct_2(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & m2_relset_1(u4_cat_1(A),u2_cat_1(A),u1_cat_1(A)))) # label(dt_u4_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4494 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> (all G (m1_cat_1(G,A,D,E) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) -> G = F)))))))))) <-> v10_cat_1(C,A,B)))))))) # label(d24_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4495 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v9_cat_1(D,A,B) & v9_cat_1(E,B,C) -> v9_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t127_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4496 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k1_xboole_0 != k6_cat_1(A,D,E) -> (all F (m1_cat_1(F,A,D,E) -> r2_hidden(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))))))))))))))) # label(t124_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4497 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) & l1_cat_1(B) & v2_cat_1(B) -> m1_subset_1(k13_cat_1(A,B,C,D),u1_cat_1(B)))) # label(dt_k13_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4498 (all A all B g1_cat_1(k1_tarski(A),k1_tarski(B),k7_cat_1(B,A),k7_cat_1(B,A),k1_cat_1(B,B,B),k7_cat_1(A,B)) = k8_cat_1(A,B)) # label(d9_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4499 (all A all B m1_subset_1(A,u2_cat_1(k8_cat_1(B,A)))) # label(t33_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.61 4500 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> m2_cat_1(k7_funct_2(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,C))))))))))) # label(t110_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4501 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v5_cat_1(k10_cat_1(A,B),A))))) # label(t74_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4502 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> B = k8_funct_2(u2_cat_1(A),u2_cat_1(A),k15_cat_1(A),B))))) # label(t115_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4503 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k2_cat_1(A,E) = k3_cat_1(A,D) -> k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E))))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))) = k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) -> m2_cat_1(C,A,B)))))))) # label(t96_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4504 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> D = k9_cat_1(A,B,B,C,k10_cat_1(A,B),D)))))))))) # label(t58_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4505 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> v4_cat_1(F,A) | k1_xboole_0 = k6_cat_1(A,C,D) | k1_xboole_0 = k6_cat_1(A,B,C)))))))))))))) # label(t67_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4506 (all A (l1_cat_1(A) -> v1_funct_1(u5_cat_1(A)) & m2_relset_1(u5_cat_1(A),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(A)),u2_cat_1(A)))) # label(dt_u5_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4507 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (r2_hidden(D,k6_cat_1(A,B,C)) -> m1_cat_1(D,A,B,C))))))))) # label(t21_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4508 $T # label(t15_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4509 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (v3_cat_1(B,A) <-> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,C) = k2_cat_1(A,B) & k4_cat_1(A,C,B) = k4_cat_1(A,D,B) & k3_cat_1(A,D) = k2_cat_1(A,B) & k2_cat_1(A,D) = k2_cat_1(A,C) -> C = D)))))))))) # label(d10_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4510 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k3_cat_1(A,D) = k3_cat_1(A,C) & k4_cat_1(A,B,C) = k4_cat_1(A,B,D) & k3_cat_1(A,B) = k2_cat_1(A,D) & k3_cat_1(A,B) = k2_cat_1(A,C) -> C = D))))) <-> v4_cat_1(B,A)))))) # label(d11_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4511 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(A),k12_cat_1(A,A,k15_cat_1(A)),B) = B)))) # label(t116_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4512 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> k1_xboole_0 != k6_cat_1(k8_cat_1(A,B),C,D))))) # label(t38_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4513 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k2_cat_1(A,B) = k2_cat_1(A,k4_cat_1(A,B,C)) & k3_cat_1(A,k4_cat_1(A,B,C)) = k3_cat_1(A,C)))))))) # label(t42_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4514 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r2_hidden(k5_cat_1(A,B),k6_cat_1(A,B,B)))))) # label(t55_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4515 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> m1_cat_1(B,A,k2_cat_1(A,B),k3_cat_1(A,B)))))) # label(t22_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4516 (all A (l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k6_partfun1(u2_cat_1(A)),A,A))) # label(t111_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4517 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> D = k9_cat_1(A,B,C,C,D,k10_cat_1(A,C))))))))))) # label(t57_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4518 $T # label(t13_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4519 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k6_cat_1(A,B,B) != k1_xboole_0)))) # label(t56_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4520 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k13_cat_1(B,C,E,k13_cat_1(A,B,D,F)) = k13_cat_1(A,C,k14_cat_1(A,B,C,D,E),F))))))))))))) # label(t113_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4521 $T # label(t101_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4522 (all A all B all C (m1_subset_1(B,u2_cat_1(A)) & m1_subset_1(C,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k4_cat_1(A,B,C),u2_cat_1(A)))) # label(dt_k4_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4523 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> ((exists C (m1_subset_1(C,u2_cat_1(A)) & k2_cat_1(A,C) = k3_cat_1(A,B) & k5_cat_1(A,k2_cat_1(A,B)) = k4_cat_1(A,B,C) & k5_cat_1(A,k3_cat_1(A,B)) = k4_cat_1(A,C,B) & k3_cat_1(A,C) = k2_cat_1(A,B))) <-> v5_cat_1(B,A)))))) # label(d12_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4524 $T # label(t2_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4525 $T # label(t53_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4526 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,C,D) -> (all H (m1_cat_1(H,A,D,E) -> -(k6_cat_1(A,D,E) != k1_xboole_0 & k9_cat_1(A,B,C,E,F,k9_cat_1(A,C,D,E,G,H)) != k9_cat_1(A,B,D,E,k9_cat_1(A,B,C,D,F,G),H) & k6_cat_1(A,C,D) != k1_xboole_0 & k6_cat_1(A,B,C) != k1_xboole_0))))))))))))))))) # label(t54_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4527 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) -> (exists D m1_cat_1(D,A,B,C)))) # label(existence_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4528 (all A (l1_cat_1(A) -> (v1_cat_1(A) -> g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) = A))) # label(abstractness_v1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4529 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k2_relat_1(k16_cat_1(A,B,C,D,E)) = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)))))) <-> v9_cat_1(C,A,B)))))))) # label(t132_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.39/23.62 4530 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) <-> (exists D (m1_cat_1(D,A,B,C) & v5_cat_1(D,A))) & k6_cat_1(A,B,C) != k1_xboole_0))))))) # label(d17_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4531 $T # label(t3_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4532 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> r1_cat_1(A,B,B))))) # label(t91_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4533 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (m1_cat_1(D,A,B,C) <-> r2_hidden(D,k6_cat_1(A,B,C)))))))))))) # label(d7_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4534 $T # label(t16_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4535 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v8_cat_1(C,A,B) <-> k2_relat_1(C) = u2_cat_1(B) & u1_cat_1(B) = k2_relat_1(k12_cat_1(A,B,C)) & v2_funct_1(C)))))))) # label(d22_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4536 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> -((exists E (m1_cat_1(E,A,C,B) & (exists F (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) & F != E & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,F) & m1_cat_1(F,A,C,B))))) & k1_xboole_0 != k6_cat_1(A,C,B) & k1_xboole_0 != k6_cat_1(A,B,C)))))))))) # label(t71_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4537 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v6_cat_1(B,A) & v6_cat_1(C,A) -> r1_cat_1(A,B,C)))))))) # label(t88_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4538 (exists A (v2_cat_1(A) & l1_cat_1(A))) # label(rc2_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4539 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> -(k1_xboole_0 = k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) & k1_xboole_0 != k6_cat_1(A,D,E)))))))))))) # label(t126_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4540 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | v5_cat_1(k11_cat_1(A,B,C,D),A)))))))))) # label(t76_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4541 (all A all B all C k1_cat_1(A,B,C) = k3_cqc_lang(k4_tarski(A,B),C)) # label(d1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4542 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))) # label(t104_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4543 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k14_cat_1(A,B,C,D,E)),F) = k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,E),k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F)))))))))))))) # label(t112_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4544 (all A (l1_cat_1(A) -> -v1_xboole_0(u2_cat_1(A)))) # label(dt_u2_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4545 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k3_cat_1(A,D)) & k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k13_cat_1(A,B,C,k2_cat_1(A,D)))))))))) # label(t109_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4546 (all A (l1_cat_1(A) -> ((all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) <-> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B)))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) -> k1_funct_1(u4_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B))) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B) = k1_funct_1(u3_cat_1(A),k1_funct_1(u5_cat_1(A),k4_tarski(C,B)))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D) -> k1_funct_1(u5_cat_1(A),k4_tarski(k1_funct_1(u5_cat_1(A),k4_tarski(D,C)),B)) = k1_funct_1(u5_cat_1(A),k4_tarski(D,k1_funct_1(u5_cat_1(A),k4_tarski(C,B))))))))))) & (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) -> k1_funct_1(u5_cat_1(A),k4_tarski(k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),C)) = C))) & (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) -> C = k1_funct_1(u5_cat_1(A),k4_tarski(C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)))))) & k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) = B)) <-> v2_cat_1(A)))) # label(d8_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4547 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (k2_cat_1(A,C) = k3_cat_1(A,B) & k2_cat_1(A,D) = k3_cat_1(A,C) -> k4_cat_1(A,B,k4_cat_1(A,C,D)) = k4_cat_1(A,k4_cat_1(A,B,C),D)))))))))) # label(t43_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4548 (all A all B all C all D (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u1_cat_1(A)) & m1_cat_1(D,A,B,C) -> m1_cat_1(k11_cat_1(A,B,C,D),A,C,B))) # label(dt_k11_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4549 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) -> E = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D)))))))))))) # label(t103_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4550 $T # label(dt_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4551 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(F,A) & v3_cat_1(E,A) -> v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) | k1_xboole_0 = k6_cat_1(A,C,D) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))) # label(t61_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4552 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v4_cat_1(E,A) & v4_cat_1(F,A) -> k6_cat_1(A,B,C) = k1_xboole_0 | k6_cat_1(A,C,D) = k1_xboole_0 | v4_cat_1(k9_cat_1(A,B,C,D,E,F),A)))))))))))))) # label(t66_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4553 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (k5_cat_1(A,B) = k5_cat_1(A,C) -> B = C))))))) # label(t45_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4554 (all A (l1_cat_1(A) -> -v1_xboole_0(u1_cat_1(A)))) # label(dt_u1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4555 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) -> E = k13_cat_1(A,B,C,D)))))))))))) # label(t107_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4556 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u2_cat_1(k8_cat_1(A,B))) -> r2_hidden(E,k6_cat_1(k8_cat_1(A,B),C,D)))))))) # label(t36_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4557 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) = k1_tarski(D) -> (all E (m1_cat_1(E,A,B,C) -> D = E))))))))))) # label(t25_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4558 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u2_cat_1(k8_cat_1(A,B))) -> m1_cat_1(E,k8_cat_1(A,B),C,D))))))) # label(t37_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4559 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & m1_subset_1(E,u1_cat_1(A)) & m1_subset_1(D,u1_cat_1(A)) & m2_cat_1(C,A,B) & v2_cat_1(B) -> v1_funct_1(k16_cat_1(A,B,C,D,E)) & v1_funct_2(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))) & m2_relset_1(k16_cat_1(A,B,C,D,E),k6_cat_1(A,D,E),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))) # label(dt_k16_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4560 (all A all B (v1_funct_1(k7_cat_1(A,B)) & v1_funct_2(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)) & m2_relset_1(k7_cat_1(A,B),k1_tarski(A),k1_tarski(B)))) # label(dt_k7_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4561 (all A all B all C (l1_cat_1(A) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> m1_subset_1(D,u2_cat_1(A)))))) # label(dt_m1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4562 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,k2_cat_1(A,B),k3_cat_1(A,B)))))) # label(t19_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4563 $T # label(t31_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4564 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) = k5_cat_1(A,B))))) # label(d5_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4565 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> m1_cat_1(k10_cat_1(A,B),A,B,B))) # label(dt_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4566 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (C = k3_cat_1(A,D) & B = k2_cat_1(A,D) <-> r2_hidden(D,k6_cat_1(A,B,C))))))))))) # label(t18_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4567 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> (v4_cat_1(D,A) <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,C,E) -> (all G (m1_cat_1(G,A,C,E) -> (k9_cat_1(A,B,C,E,D,F) = k9_cat_1(A,B,C,E,D,G) -> F = G | k1_xboole_0 = k6_cat_1(A,C,E)))))))))))))))))) # label(t65_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4568 (all A all B all C (v2_cat_1(A) & l1_cat_1(B) & v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m1_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v2_cat_1(B) & l1_cat_1(A) -> v1_funct_1(k12_cat_1(A,B,C)) & v1_funct_2(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(k12_cat_1(A,B,C),u1_cat_1(A),u1_cat_1(B)))) # label(dt_k12_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4569 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) -> (all C (m1_cat_1(C,A,B,B) -> C = k10_cat_1(A,B)))))))) # label(t83_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4570 (all A all B all C all D (m1_subset_1(D,k1_tarski(A)) -> (all E (m1_subset_1(E,k1_tarski(B)) -> k1_funct_1(k1_cat_1(A,B,C),k4_tarski(D,E)) = C)))) # label(t9_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4571 (all A (l1_cat_1(A) & v2_cat_1(A) -> k15_cat_1(A) = k6_partfun1(u2_cat_1(A)))) # label(d21_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4572 $T # label(t114_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4573 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k2_cat_1(A,B),u1_cat_1(A)))) # label(dt_k2_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4574 $T # label(t30_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4575 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v3_cat_1(k10_cat_1(A,B),A))))) # label(t64_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4576 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> k1_funct_1(k16_cat_1(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F)))))))))))))) # label(t131_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4577 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k6_cat_1(A,B,C) != k1_xboole_0 -> B = k2_cat_1(A,D) & k3_cat_1(A,D) = C))))))))) # label(t23_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4578 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> ((all E (m1_cat_1(E,A,B,C) -> D = E)) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_tarski(D) = k6_cat_1(A,B,C)))))))))) # label(t26_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4579 $T # label(t80_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4580 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> (v5_cat_1(D,A) <-> k6_cat_1(A,C,B) != k1_xboole_0 & (exists E (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E) & m1_cat_1(E,A,C,B))))))))))))) # label(t70_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4581 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> v4_cat_1(D,A) & v3_cat_1(D,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t73_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4582 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,B,C) & l1_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> m2_cat_1(k14_cat_1(A,B,C,D,E),A,C))) # label(dt_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4583 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,B) = k3_cat_1(A,C) -> k1_funct_1(u5_cat_1(A),k4_tarski(B,C)) = k4_cat_1(A,C,B)))))))) # label(t41_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4584 $T # label(t120_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4585 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(A),k4_tarski(C,B)) = k4_cat_1(A,B,C)))))))) # label(d4_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4586 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k5_cat_1(A,B),u2_cat_1(A)))) # label(dt_k5_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4587 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> ((all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (k1_tarski(D) = k6_cat_1(A,B,C) & m1_cat_1(D,A,B,C))))) <-> v7_cat_1(B,A)))))) # label(t82_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4588 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (r2_hidden(F,k6_cat_1(A,D,E)) -> r2_hidden(k1_funct_1(C,F),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t123_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4589 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(D,B,A) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & m1_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) & v1_funct_1(E) & v1_funct_2(D,B,A) & v1_funct_1(D) & m1_relset_1(C,B,A) & v1_funct_2(C,B,A) -> l1_cat_1(g1_cat_1(A,B,C,D,E,F)) & v1_cat_1(g1_cat_1(A,B,C,D,E,F)))) # label(dt_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4590 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) <-> (exists D (m1_cat_1(D,A,B,C) & (exists E (m1_cat_1(E,A,C,B) & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) & k10_cat_1(A,B) = k9_cat_1(A,B,C,B,D,E))))) & k6_cat_1(A,C,B) != k1_xboole_0 & k1_xboole_0 != k6_cat_1(A,B,C)))))))) # label(t81_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4591 $T # label(t79_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4592 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> (all C (m2_cat_1(C,A,B) -> v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C))))) # label(dt_m2_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4593 (all A all B all C all D (-v1_xboole_0(D) -> (all E (m2_relset_1(E,A,D) & v1_funct_2(E,A,D) & v1_funct_1(E) -> (r1_tarski(k2_funct_2(A,D,E,B),C) & r1_tarski(B,A) -> v1_funct_1(k2_partfun1(A,D,E,B)) & m2_relset_1(k2_partfun1(A,D,E,B),B,C) & v1_funct_2(k2_partfun1(A,D,E,B),B,C)))))) # label(t4_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4594 (all A all B all C (m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k6_cat_1(A,B,C),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k6_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4595 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v5_cat_1(D,A) -> k6_cat_1(A,B,C) = k1_xboole_0 | (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,B,C,B,D,E) = k10_cat_1(A,B) & k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) <-> E = k11_cat_1(A,B,C,D))))))))))))) # label(d14_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4596 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k1_xboole_0 = k6_cat_1(A,B,D) & k6_cat_1(A,C,D) != k1_xboole_0))))))))) # label(t52_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4597 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (v6_cat_1(B,A) -> v3_cat_1(D,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))) # label(t90_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4598 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) & m1_subset_1(E,u1_cat_1(B)))))))))))) # label(t97_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4599 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,B,C) -> r1_cat_1(A,C,B)))))))) # label(t92_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4600 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k2_cat_1(A,D)) & k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),k3_cat_1(A,D)) = k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)))))))))) # label(t105_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4601 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u2_cat_1(A)) -> k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u3_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),D))) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),D))) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),k8_funct_2(u2_cat_1(B),u1_cat_1(B),u4_cat_1(B),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))))) & (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (r2_hidden(k4_tarski(E,D),k1_relat_1(u5_cat_1(A))) -> k1_funct_1(u5_cat_1(B),k4_tarski(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k1_funct_1(C,k1_funct_1(u5_cat_1(A),k4_tarski(E,D)))))))) & (all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)))))) <-> m2_cat_1(C,A,B)))))))) # label(d18_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4602 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k9_cat_1(A,C,B,C,E,D) = k10_cat_1(A,C) -> k6_cat_1(A,C,B) = k1_xboole_0 | v3_cat_1(E,A) | k6_cat_1(A,B,C) = k1_xboole_0))))))))))) # label(t63_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4603 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (k1_xboole_0 != k6_cat_1(A,B,C) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,E,B) -> (all G (m1_cat_1(G,A,E,B) -> (k9_cat_1(A,E,B,C,G,D) = k9_cat_1(A,E,B,C,F,D) -> k1_xboole_0 = k6_cat_1(A,E,B) | G = F))))))) <-> v3_cat_1(D,A))))))))))) # label(t60_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4604 $T # label(t5_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4605 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (v9_cat_1(C,A,B) <-> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) != k1_xboole_0 -> (all F (m1_cat_1(F,B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E)) -> (exists G (F = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,G) & m1_cat_1(G,A,D,E))) & k1_xboole_0 != k6_cat_1(A,D,E))))))))))))))) # label(d23_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4606 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(u5_cat_1(A))) <-> k2_cat_1(A,B) = k3_cat_1(A,C)))))))) # label(t40_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4607 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> (all D (m1_subset_1(D,u1_cat_1(k8_cat_1(A,B))) -> (all E (m1_subset_1(E,u1_cat_1(k8_cat_1(A,B))) -> (all F (m1_subset_1(F,u1_cat_1(k8_cat_1(A,B))) -> (all G (m1_cat_1(G,k8_cat_1(A,B),C,D) -> (all H (m1_cat_1(H,k8_cat_1(A,B),E,F) -> H = G)))))))))))) # label(t39_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4608 (all A all B (l1_cat_1(k8_cat_1(A,B)) & v2_cat_1(k8_cat_1(A,B)) & v1_cat_1(k8_cat_1(A,B)))) # label(dt_k8_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4609 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & -r2_hidden(k4_cat_1(A,E,F),k6_cat_1(A,B,D)) & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))) # label(t51_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4610 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (k6_cat_1(A,D,E) != k1_xboole_0 -> (all F (m1_cat_1(F,A,D,E) -> m1_cat_1(k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F),B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))))) # label(t125_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4611 $T # label(t17_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4612 $T # label(t10_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4613 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (m1_subset_1(E,u1_cat_1(B)) & k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),D)) = k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),E))))) -> (all D (v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(D) -> (k12_cat_1(A,B,C) = D <-> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (k8_funct_2(u1_cat_1(B),u2_cat_1(B),u6_cat_1(B),F) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k8_funct_2(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),E)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E) = F))))))))))))))) # label(d19_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4614 $T # label(t121_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4615 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v3_cat_1(k9_cat_1(A,B,C,D,E,F),A) -> k1_xboole_0 = k6_cat_1(A,B,C) | v3_cat_1(E,A) | k6_cat_1(A,C,D) = k1_xboole_0))))))))))))) # label(t62_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4616 $T # label(t95_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4617 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> a_3_0_cat_1(A,B,C) = k6_cat_1(A,B,C))))))) # label(d6_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4618 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k13_cat_1(A,B,C,D) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D))))))))) # label(d20_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4619 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> v2_funct_1(k16_cat_1(A,B,C,D,E)))))) <-> v10_cat_1(C,A,B)))))))) # label(t133_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4620 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k10_cat_1(A,B) = k9_cat_1(A,B,B,B,k10_cat_1(A,B),k10_cat_1(A,B)))))) # label(t59_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4621 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,k13_cat_1(A,B,C,D)))))))))) # label(t108_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4622 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k2_cat_1(A,B) = k8_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),B))))) # label(d2_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4623 $T # label(t119_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.90 4624 (all A all B (v2_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) -> k10_cat_1(A,B) = k5_cat_1(A,B))) # label(redefinition_k10_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4625 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & v1_funct_1(C) -> (all D (v1_funct_2(D,u1_cat_1(A),u1_cat_1(B)) & m2_relset_1(D,u1_cat_1(A),u1_cat_1(B)) & v1_funct_1(D) -> ((all E (m1_subset_1(E,u1_cat_1(A)) -> k10_cat_1(B,k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,E)))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k2_cat_1(A,F) = k3_cat_1(A,E) -> k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,E,F)) = k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,F))))))) & (all E (m1_subset_1(E,u2_cat_1(A)) -> k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k2_cat_1(A,E)) & k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u1_cat_1(A),u1_cat_1(B),D,k3_cat_1(A,E)))) -> m2_cat_1(C,A,B)))))))))) # label(t100_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4626 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(E,B,C) & m2_cat_1(D,A,B) -> k14_cat_1(A,B,C,D,E) = k5_relat_1(D,E))) # label(redefinition_k14_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4627 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v6_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> k1_xboole_0 != k6_cat_1(A,C,B) & (exists D ((all E (m1_cat_1(E,A,C,B) -> D = E)) & m1_cat_1(D,A,C,B)))))))))) # label(d15_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4628 $T # label(t49_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4629 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> -(k6_cat_1(A,B,C) = k1_tarski(F) & (all G (m1_cat_1(G,A,D,E) -> k1_tarski(G) != k6_cat_1(A,D,E))) & r2_tarski(k6_cat_1(A,B,C),k6_cat_1(A,D,E))))))))))))))) # label(t27_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4630 (all A all B all C (v1_funct_1(k1_cat_1(A,B,C)) & m2_relset_1(k1_cat_1(A,B,C),k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k1_tarski(C)))) # label(dt_k1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4631 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (r1_cat_1(A,C,B) & v6_cat_1(B,A) -> v6_cat_1(C,A)))))))) # label(t89_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4632 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,B,A) & v1_funct_1(D) & v1_funct_1(E) & m1_relset_1(F,A,B) & v1_funct_2(F,A,B) & v1_funct_1(F) & m1_relset_1(E,k2_zfmisc_1(B,B),B) & m1_relset_1(D,B,A) & v1_funct_2(D,B,A) & v1_funct_2(C,B,A) -> (all G all H all I all J all K all L (g1_cat_1(A,B,C,D,E,F) = g1_cat_1(G,H,I,J,K,L) -> A = G & L = F & E = K & J = D & C = I & H = B)))) # label(free_g1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4633 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,B,C) -> (v10_cat_1(D,A,B) & v10_cat_1(E,B,C) -> v10_cat_1(k14_cat_1(A,B,C,D,E),A,C)))))))))))) # label(t128_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4634 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (v7_cat_1(B,A) <-> (all C (m1_subset_1(C,u1_cat_1(A)) -> (exists D (m1_cat_1(D,A,B,C) & (all E (m1_cat_1(E,A,B,C) -> E = D)))) & k6_cat_1(A,B,C) != k1_xboole_0))))))) # label(d16_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4635 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v4_cat_1(k10_cat_1(A,B),A))))) # label(t69_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4636 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> r1_tarski(k2_funct_2(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)),k6_cat_1(B,k13_cat_1(A,B,C,D),k13_cat_1(A,B,C,E))))))))))))) # label(t129_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4637 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_cat_1(F,A,B,C) -> (all G (m1_cat_1(G,A,D,E) -> (F = G -> k6_cat_1(A,D,E) = k1_xboole_0 | E = C & D = B | k6_cat_1(A,B,C) = k1_xboole_0))))))))))))))) # label(t24_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4638 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k2_cat_1(A,C) -> C = k4_cat_1(A,k5_cat_1(A,B),C)))))))) # label(t47_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4639 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k16_cat_1(A,B,C,D,E) = k2_partfun1(u2_cat_1(A),u2_cat_1(B),C,k6_cat_1(A,D,E)))))))))))) # label(d25_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4640 $T # label(t6_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4641 $T # label(t106_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4642 (all A (l1_cat_1(A) -> m2_relset_1(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) & v1_funct_2(u6_cat_1(A),u1_cat_1(A),u2_cat_1(A)) & v1_funct_1(u6_cat_1(A)))) # label(dt_u6_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4643 (all A all B all C k1_funct_1(k1_cat_1(A,B,C),k4_tarski(A,B)) = C) # label(t8_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4644 $T # label(t12_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4645 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k3_cat_1(A,k5_cat_1(A,B)) & k2_cat_1(A,k5_cat_1(A,B)) = B)))) # label(t44_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4646 (all A all B m1_subset_1(A,u1_cat_1(k8_cat_1(A,B)))) # label(t32_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4647 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (B = k3_cat_1(A,C) -> C = k4_cat_1(A,C,k5_cat_1(A,B))))))))) # label(t46_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4648 (all A all B all C (k1_relat_1(k1_cat_1(A,B,C)) = k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) & k1_tarski(k4_tarski(A,B)) = k1_relat_1(k1_cat_1(A,B,C)))) # label(t7_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4649 (exists A (l1_cat_1(A) & v2_cat_1(A) & v1_cat_1(A))) # label(rc3_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4650 $T # label(t1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4651 (all A (l1_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),B) = k3_cat_1(A,B))))) # label(d3_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4652 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u2_cat_1(A),u2_cat_1(B)) & m2_relset_1(C,u2_cat_1(A),u2_cat_1(B)) -> ((all D (m1_subset_1(D,u1_cat_1(A)) -> (exists E (k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) = k10_cat_1(B,E) & m1_subset_1(E,u1_cat_1(B)))))) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (k10_cat_1(B,E) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,D)) -> k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,C),D) = E)))))))))))) # label(t102_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4653 $T # label(t78_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4654 (all A all B (m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m1_subset_1(k3_cat_1(A,B),u1_cat_1(A)))) # label(dt_k3_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4655 (all A (l1_cat_1(A) & v2_cat_1(A) -> m2_cat_1(k15_cat_1(A),A,A))) # label(dt_k15_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4656 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k13_cat_1(A,A,k15_cat_1(A),B))))) # label(t118_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4657 $T # label(t11_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4658 (all A all B all C (m1_subset_1(C,u2_cat_1(k8_cat_1(A,B))) -> B = C)) # label(t35_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4659 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_cat_1(D,A,B,C) -> (all E (m1_cat_1(E,A,C,B) -> (k10_cat_1(A,C) = k9_cat_1(A,C,B,C,E,D) -> k6_cat_1(A,B,C) = k1_xboole_0 | v4_cat_1(D,A) | k6_cat_1(A,C,B) = k1_xboole_0))))))))))) # label(t68_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4660 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> (v5_cat_1(E,A) & v5_cat_1(F,A) -> k1_xboole_0 = k6_cat_1(A,B,C) | k1_xboole_0 = k6_cat_1(A,C,D) | k11_cat_1(A,B,D,k9_cat_1(A,B,C,D,E,F)) = k9_cat_1(A,D,C,B,k11_cat_1(A,C,D,F),k11_cat_1(A,B,C,E))))))))))))))) # label(t77_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4661 (all A all B all C all D all E all F (m1_subset_1(D,u1_cat_1(A)) & m1_cat_1(F,A,C,D) & m1_cat_1(E,A,B,C) & m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> m1_cat_1(k9_cat_1(A,B,C,D,E,F),A,B,D))) # label(dt_k9_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4662 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (v7_cat_1(C,A) & v7_cat_1(B,A) -> r1_cat_1(A,B,C)))))))) # label(t84_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4663 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,B,C) -> (all F (m1_cat_1(F,A,C,D) -> -(k1_xboole_0 != k6_cat_1(A,B,C) & k4_cat_1(A,E,F) != k9_cat_1(A,B,C,D,E,F) & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))) # label(d13_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4664 $T # label(t28_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4665 (all A all B all C all D (l1_cat_1(B) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(B)) -> ((exists E (m1_subset_1(E,u2_cat_1(B)) & k2_cat_1(B,E) = C & D = k3_cat_1(B,E) & A = E)) <-> r2_hidden(A,a_3_0_cat_1(B,C,D))))) # label(fraenkel_a_3_0_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4666 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> k10_cat_1(B,k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k3_cat_1(A,D))) & k10_cat_1(B,k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D))) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k10_cat_1(A,k2_cat_1(A,D))))))))))) # label(t98_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4667 (all A all B all C (m1_subset_1(C,u1_cat_1(k8_cat_1(A,B))) -> C = A)) # label(t34_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4668 $T # label(t50_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4669 $T # label(t94_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4670 (all A (l1_cat_1(A) & v2_cat_1(A) -> v8_cat_1(k15_cat_1(A),A,A))) # label(t122_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4671 (exists A (v1_cat_1(A) & l1_cat_1(A))) # label(rc1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4672 (exists A l1_cat_1(A)) # label(existence_l1_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4673 (all A (l1_cat_1(A) -> m2_relset_1(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_2(u3_cat_1(A),u2_cat_1(A),u1_cat_1(A)) & v1_funct_1(u3_cat_1(A)))) # label(dt_u3_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4674 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (k3_cat_1(A,D) = k2_cat_1(A,E) -> k3_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D)) = k2_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) & k4_cat_1(B,k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,D),k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,E)) = k8_funct_2(u2_cat_1(A),u2_cat_1(B),C,k4_cat_1(A,D,E))))))))))))) # label(t99_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4675 $T # label(t48_cat_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4676 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v8_lattices(A) & v7_lattices(A) & v9_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) <-> v10_lattices(A)))) # label(d10_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4677 $T # label(t28_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4678 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v11_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k3_lattices(A,B,D) = k3_lattices(A,B,C) & k4_lattices(A,B,C) = k4_lattices(A,B,D) -> D = C))))))))) # label(t32_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4679 (all A (-v3_struct_0(A) & l1_lattices(A) -> (v7_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_lattices(A,k2_lattices(A,B,C),D) = k2_lattices(A,B,k2_lattices(A,C,D))))))))))) # label(d7_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4680 (all A (v8_lattices(A) & l3_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k4_lattices(A,B,C),B))))))) # label(t23_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4681 (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) = k2_lattices(A,B,C))) # label(redefinition_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4682 (exists A l3_lattices(A)) # label(existence_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4683 (all A (l2_lattices(A) -> (v2_lattices(A) -> A = g2_lattices(u1_struct_0(A),u2_lattices(A))))) # label(abstractness_v2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4684 $T # label(t9_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4685 (all A all B all C (v6_lattices(A) & l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> k4_lattices(A,C,B) = k4_lattices(A,B,C))) # label(commutativity_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4686 (all A (l2_lattices(A) -> v1_funct_1(u2_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)))) # label(dt_u2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4687 $T # label(t20_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4688 $T # label(t24_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4689 $T # label(t36_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4690 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v9_lattices(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))))))))) # label(d9_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4691 (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,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)))))))))) # label(t34_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4692 (all A (v10_lattices(A) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> 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]. 22.69/23.91 4693 (all A (v4_lattices(A) & l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,C,B) & r1_lattices(A,B,C) -> C = B))))))) # label(t26_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4694 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k7_lattices(A,B),u1_struct_0(A)))) # label(dt_k7_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4695 (exists A (l2_lattices(A) & -v3_struct_0(A) & v2_lattices(A) & v4_lattices(A) & v5_lattices(A))) # label(rc7_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4696 (all A all B all C (l1_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_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]. 22.69/23.91 4697 (all A (-v3_struct_0(A) & l1_lattices(A) -> (v13_lattices(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,C,B) & B = k2_lattices(A,B,C))) <-> B = k5_lattices(A))))))) # label(d16_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4698 (exists A (l1_lattices(A) & -v3_struct_0(A) & v1_lattices(A) & v6_lattices(A) & v7_lattices(A))) # label(rc8_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4699 $T # label(t33_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4700 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v12_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,D) -> k1_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,k1_lattices(A,B,C),D))))))))))) # label(d12_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4701 $T # label(t12_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4702 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v17_lattices(A) -> v11_lattices(A) & v15_lattices(A) & v16_lattices(A) & v14_lattices(A) & v13_lattices(A) & -v3_struct_0(A)))) # label(cc5_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4703 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v14_lattices(A) & v13_lattices(A) -> v15_lattices(A) & -v3_struct_0(A)))) # label(cc3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4704 (all A (l3_lattices(A) -> (v11_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v9_lattices(A) & v10_lattices(A) & v12_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc7_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4705 $T # label(t6_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4706 (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) -> v2_lattices(g2_lattices(A,B)) & l2_lattices(g2_lattices(A,B)))) # label(dt_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4707 (all A (l3_lattices(A) -> l2_lattices(A) & l1_lattices(A))) # label(dt_l3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4708 (all A (v5_lattices(A) & l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,C,D) & r1_lattices(A,B,C) -> r1_lattices(A,B,D)))))))))) # label(t25_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4709 (all A all B all C (v1_funct_1(B) & m1_relset_1(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) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l3_lattices(g3_lattices(A,B,C)) & v3_lattices(g3_lattices(A,B,C)))) # label(dt_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4710 (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)) -> k3_lattices(A,k5_lattices(A),B) = B)))) # label(t39_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4711 (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 (g2_lattices(A,B) = g2_lattices(C,D) -> D = B & C = A)))) # label(free_g2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4712 (exists A (-v3_struct_0(A) & v1_lattices(A) & l1_lattices(A))) # label(rc5_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4713 (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_xboole_0(A) -> v2_lattices(g2_lattices(A,B)) & -v3_struct_0(g2_lattices(A,B)))) # label(fc1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4714 (all A all B (-v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> -v3_struct_0(g1_lattices(A,B)) & v1_lattices(g1_lattices(A,B)))) # label(fc2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4715 (all A (-v3_struct_0(A) & v9_lattices(A) & l3_lattices(A) & v8_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r1_lattices(A,B,C) <-> B = k2_lattices(A,B,C)))))))) # label(t21_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4716 (all A (-v3_struct_0(A) & l3_lattices(A) & v13_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattices(A,k5_lattices(A),B) = k5_lattices(A))))) # label(t40_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4717 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> l1_lattices(g1_lattices(A,B)) & v1_lattices(g1_lattices(A,B)))) # label(dt_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4718 (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)) -> (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]. 22.69/23.91 4719 (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]. 22.69/23.91 4720 (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) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> r3_lattices(A,B,B))) # label(reflexivity_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4721 (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]. 22.69/23.91 4722 $T # label(t42_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4723 (exists A (l3_lattices(A) & -v3_struct_0(A) & v3_lattices(A))) # label(rc6_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4724 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v11_lattices(A) & v16_lattices(A) & v15_lattices(A) <-> v17_lattices(A)))) # label(d20_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4725 (all A (l1_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_lattices(A,B,C) = k2_lattices(A,C,B))))) <-> v6_lattices(A)))) # label(d6_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4726 (all A all B all C (-v3_struct_0(A) & v4_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l2_lattices(A) -> k3_lattices(A,B,C) = k1_lattices(A,B,C))) # label(redefinition_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4727 $T # label(t10_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4728 (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)) -> (r2_lattices(A,B,C) <-> k1_lattices(A,C,B) = k6_lattices(A) & k5_lattices(A) = k2_lattices(A,C,B) & k5_lattices(A) = k2_lattices(A,B,C) & k1_lattices(A,B,C) = k6_lattices(A)))))))) # label(d18_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4729 (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) -> k3_lattices(A,B,C) = k3_lattices(A,C,B))) # label(commutativity_k3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4730 (all A (l3_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (r2_lattices(A,C,B) & m1_subset_1(C,u1_struct_0(A)))))) <-> v16_lattices(A)))) # label(d19_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4731 (exists A (v2_lattices(A) & l2_lattices(A))) # label(rc2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4732 $T # label(t11_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4733 (exists A l2_lattices(A)) # label(existence_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4734 (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)) -> k7_lattices(A,k3_lattices(A,B,C)) = k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))))))) # label(t51_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4735 (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)) -> k1_lattices(A,k2_lattices(A,B,C),k2_lattices(A,B,D)) = k2_lattices(A,B,k1_lattices(A,C,D)))))))) <-> v11_lattices(A)))) # label(d11_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4736 (all A (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k4_lattices(A,k6_lattices(A),B))))) # label(t43_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4737 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v10_lattices(A) -> v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v9_lattices(A) & v8_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4738 (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)) -> k4_lattices(A,B,k3_lattices(A,C,D)) = k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,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]. 22.69/23.91 4739 $T # label(t16_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4740 (all A (-v3_struct_0(A) & l1_lattices(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k2_lattices(A,C,B) & k2_lattices(A,B,C) = B)) & m1_subset_1(B,u1_struct_0(A)))) <-> v13_lattices(A)))) # label(d13_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4741 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) & v14_lattices(A) <-> v15_lattices(A)))) # label(d15_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4742 (all A (l2_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_lattices(A),B,C) = k1_lattices(A,B,C))))))) # label(d1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4743 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v11_lattices(A) & l3_lattices(A) & v16_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_lattices(A,C,B) <-> C = k7_lattices(A,B))))))))) # label(d21_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4744 (exists A (l3_lattices(A) & -v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v17_lattices(A) & v16_lattices(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v5_lattices(A))) # label(rc13_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4745 $T # label(t2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4746 (exists A (l2_lattices(A) & v2_lattices(A) & -v3_struct_0(A))) # label(rc4_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4747 (all A (l2_lattices(A) -> l1_struct_0(A))) # label(dt_l2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4748 (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)) -> k5_lattices(A) = k4_lattices(A,k7_lattices(A,B),B))))) # label(t47_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4749 $T # label(t46_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4750 (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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,k1_lattices(A,B,C),D))))))) <-> v5_lattices(A)))) # label(d5_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4751 (all A (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r3_lattices(A,B,k6_lattices(A)))))) # label(t45_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4752 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v15_lattices(A) -> -v3_struct_0(A) & v13_lattices(A) & v14_lattices(A)))) # label(cc4_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4753 (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)) -> k3_lattices(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,C,D)),k4_lattices(A,D,B)) = k4_lattices(A,k4_lattices(A,k3_lattices(A,B,C),k3_lattices(A,C,D)),k3_lattices(A,D,B)))))))) -> v11_lattices(A)))) # label(t29_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4754 $T # label(t14_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4755 (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)) -> k6_lattices(A) = k3_lattices(A,k7_lattices(A,B),B))))) # label(t48_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4756 (all A (l1_lattices(A) -> l1_struct_0(A))) # label(dt_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4757 (exists A (v3_lattices(A) & v5_lattices(A) & v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v8_lattices(A) & v6_lattices(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc11_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4758 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v5_lattices(A) & v8_lattices(A) & v9_lattices(A) & v7_lattices(A) & v6_lattices(A) & v4_lattices(A) -> -v3_struct_0(A) & v10_lattices(A)))) # label(cc2_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.91 4759 (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]. 22.69/23.91 4760 (all A (v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & v7_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r1_lattices(A,B,C) -> r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D))))))))))) # label(t27_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4761 $T # label(t4_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4762 (all A all B all C (v6_lattices(A) & v9_lattices(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_lattices(A) & v8_lattices(A) & -v3_struct_0(A) -> (r3_lattices(A,B,C) <-> r1_lattices(A,B,C)))) # label(redefinition_r3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4763 (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]. 22.69/23.92 4764 (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]. 22.69/23.92 4765 $T # label(t15_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4766 (exists A (l3_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A))) # label(rc9_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4767 (all A (l2_lattices(A) & -v3_struct_0(A) -> ((exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_lattices(A,B,C) & B = k1_lattices(A,C,B))))) <-> v14_lattices(A)))) # label(d14_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4768 (all A (-v3_struct_0(A) & l2_lattices(A) -> m1_subset_1(k6_lattices(A),u1_struct_0(A)))) # label(dt_k6_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4769 (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]. 22.69/23.92 4770 (all A (v6_lattices(A) & v9_lattices(A) & l3_lattices(A) & v8_lattices(A) & -v3_struct_0(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]. 22.69/23.92 4771 $T # label(t7_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4772 (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 (g1_lattices(A,B) = g1_lattices(C,D) -> C = A & B = D)))) # label(free_g1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4773 $T # label(t38_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4774 (all A (-v3_struct_0(A) & l2_lattices(A) -> (v14_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_lattices(A,C,B) & k1_lattices(A,B,C) = B)) <-> k6_lattices(A) = B)))))) # label(d17_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4775 (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)) -> k7_lattices(A,k7_lattices(A,B)) = B)))) # label(t49_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4776 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> (all D all E all F (g3_lattices(A,B,C) = g3_lattices(D,E,F) -> F = C & B = E & A = D)))) # label(free_g3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4777 (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) = C <-> r1_lattices(A,B,C)))))))) # label(d3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4778 (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]. 22.69/23.92 4779 (exists A (v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & v3_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc12_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4780 (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]. 22.69/23.92 4781 $T # label(t30_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4782 (all A (v8_lattices(A) & l3_lattices(A) & v9_lattices(A) & v6_lattices(A) & -v3_struct_0(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]. 22.69/23.92 4783 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> -v3_struct_0(g3_lattices(A,B,C)) & v3_lattices(g3_lattices(A,B,C)))) # label(fc3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4784 (all A (v14_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_lattices(A,k6_lattices(A),B) = k6_lattices(A))))) # label(t44_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4785 $T # label(t37_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4786 (all A (l2_lattices(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,B,C) = k1_lattices(A,C,B))))) <-> v4_lattices(A)))) # label(d4_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4787 (all A (-v3_struct_0(A) & v17_lattices(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k7_lattices(A,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]. 22.69/23.92 4788 $T # label(t8_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4789 $T # label(t35_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4790 $T # label(t13_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4791 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_lattices(A) & v6_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_lattices(A,B,C),u1_struct_0(A)))) # label(dt_k4_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4792 (all A (l3_lattices(A) & v9_lattices(A) & v8_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]. 22.69/23.92 4793 (exists A (v3_lattices(A) & v7_lattices(A) & v9_lattices(A) & v10_lattices(A) & v14_lattices(A) & v13_lattices(A) & v12_lattices(A) & v11_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc10_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4794 (exists A l1_lattices(A)) # label(existence_l1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4795 $T # label(t5_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4796 (exists A (l1_lattices(A) & v1_lattices(A))) # label(rc1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4797 $T # label(t1_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4798 (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]. 22.69/23.92 4799 $T # label(t3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4800 (all A (-v3_struct_0(A) & l3_lattices(A) -> (v8_lattices(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_lattices(A,k2_lattices(A,B,C),C) = C))))))) # label(d8_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4801 (exists A (l3_lattices(A) & v3_lattices(A))) # label(rc3_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4802 (all A (l3_lattices(A) -> (v16_lattices(A) & v15_lattices(A) & v11_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v17_lattices(A)))) # label(cc6_lattices) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4803 $T # label(t26_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4804 (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]. 22.69/23.92 4805 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & k4_subset_1(u1_struct_0(A),B,C) = k2_pre_topc(A) -> C = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B)))))))) # label(t25_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4806 (all A all B all C all D (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) & l1_struct_0(A) -> m1_subset_1(k5_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4807 $T # label(t34_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4808 $T # label(d7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4809 (exists A (-v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & l1_pre_topc(A))) # label(rc2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4810 (all A (l1_struct_0(A) -> k1_xboole_0 = k1_pre_topc(A))) # label(d2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4811 $T # label(t40_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4812 (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]. 22.69/23.92 4813 $T # label(t9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4814 (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) & (v2_pre_topc(A) & k6_pre_topc(A,B) = B -> v4_pre_topc(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4815 (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]. 22.69/23.92 4816 (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]. 22.69/23.92 4817 (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)) -> (r2_hidden(D,C) <-> (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))))))) <-> C = k6_pre_topc(A,B)))))))) # label(d13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4818 (all A (l1_struct_0(A) -> k2_pre_topc(A) = k3_subset_1(u1_struct_0(A),k1_pre_topc(A)))) # label(t27_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4819 $T # label(t28_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4820 $T # label(t10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4821 (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) -> k9_relat_1(C,D) = k4_pre_topc(A,B,C,D))) # label(redefinition_k4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4822 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),B,k3_subset_1(u1_struct_0(A),B)) = k2_pre_topc(A))))) # label(t18_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4823 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & k6_pre_topc(A,B) = k6_setfam_1(u1_struct_0(A),C) & (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]. 22.69/23.92 4824 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C all D (g1_pre_topc(C,D) = g1_pre_topc(A,B) -> D = B & C = A)))) # label(free_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4825 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (exists B (v1_pre_topc(B) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4826 $T # label(t38_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4827 (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]. 22.69/23.92 4828 $T # label(t8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4829 $T # label(t37_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4830 (all A (l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v1_pre_topc(B))))) # label(rc3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4831 (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]. 22.69/23.92 4832 (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 (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = k3_xboole_0(D,k2_pre_topc(B)) & r2_hidden(D,u1_pre_topc(A)))))))))))) # label(d9_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4833 $T # label(t19_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4834 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & -v3_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]. 22.69/23.92 4835 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4836 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> -v3_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))))))))))) # label(t54_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4837 (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]. 22.69/23.92 4838 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,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)) = 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]. 22.69/23.92 4839 $T # label(t1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4840 (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]. 22.69/23.92 4841 (all A (l1_struct_0(A) -> k2_pre_topc(A) = u1_struct_0(A))) # label(d3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4842 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4843 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) = k3_subset_1(u1_struct_0(A),B))))) # label(t17_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4844 (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]. 22.69/23.92 4845 $T # label(t21_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4846 (all A (l1_struct_0(A) -> v1_xboole_0(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)))) # label(fc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4847 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & v4_pre_topc(B,A))))) # label(rc7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4848 (all A (l1_pre_topc(A) -> (exists B m1_pre_topc(B,A)))) # label(existence_m1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4849 (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_1(C) & l1_struct_0(B) & l1_struct_0(A) -> 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]. 22.69/23.92 4850 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> v2_pre_topc(B))))) # label(cc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4851 $T # label(t3_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4852 (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))) -> (C = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t24_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4853 (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]. 22.69/23.92 4854 $T # label(t35_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4855 (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]. 22.69/23.92 4856 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & k3_xboole_0(D,k2_pre_topc(B)) = C & v4_pre_topc(D,A))) <-> v4_pre_topc(C,B)))))))) # label(t43_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4857 $T # label(t11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4858 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(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]. 22.69/23.92 4859 (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]. 22.69/23.92 4860 $T # label(t6_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4861 $T # label(t4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4862 $T # label(d4_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4863 $T # label(t32_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4864 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t49_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4865 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k2_pre_topc(A)))))) # label(t13_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4866 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> l1_pre_topc(g1_pre_topc(A,B)) & v1_pre_topc(g1_pre_topc(A,B)))) # label(dt_g1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4867 $T # label(t2_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4868 (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]. 22.69/23.92 4869 (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) -> k5_pre_topc(A,B,C,D) = k10_relat_1(C,D))) # label(redefinition_k5_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4870 (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) <-> k3_pre_topc(A,B) = C))))))) # label(d10_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4871 $T # label(t20_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4872 (all A (l1_struct_0(A) -> k2_pre_topc(A) = u1_struct_0(A))) # label(t12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4873 $T # label(t31_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4874 (exists A (v1_pre_topc(A) & l1_pre_topc(A))) # label(rc1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4875 (all A (l1_pre_topc(A) -> l1_struct_0(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4876 $T # label(t36_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4877 (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]. 22.69/23.92 4878 $T # label(d11_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4879 (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]. 22.69/23.92 4880 (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]. 22.69/23.92 4881 (all A (l1_pre_topc(A) -> (v2_pre_topc(A) <-> r2_hidden(u1_struct_0(A),u1_pre_topc(A)) & (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,u1_pre_topc(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),u1_pre_topc(A))))) & (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)))))))))) # label(d1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4882 $T # label(t7_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4883 (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]. 22.69/23.92 4884 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) & k2_pre_topc(A) = B) & -(k1_xboole_0 = k6_subset_1(u1_struct_0(A),k2_pre_topc(A),B) & k2_pre_topc(A) != B))))) # label(t23_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4885 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> 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]. 22.69/23.92 4886 (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]. 22.69/23.92 4887 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v4_pre_topc(D,B) -> v4_pre_topc(k5_pre_topc(A,B,C,D),A)))) <-> v5_pre_topc(C,A,B)))))))) # label(d12_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4888 $T # label(t29_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4889 (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]. 22.69/23.92 4890 (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]. 22.69/23.92 4891 (exists A l1_pre_topc(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4892 $T # label(t30_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4893 (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]. 22.69/23.92 4894 (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) <-> k5_setfam_1(u1_struct_0(A),B) = k2_pre_topc(A)))))) # label(d8_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4895 (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]. 22.69/23.92 4896 (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]. 22.69/23.92 4897 $T # label(t33_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4898 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> k6_pre_topc(B,D) = k3_xboole_0(k6_pre_topc(A,C),k2_pre_topc(B))))))))))) # label(t47_pre_topc) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4899 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> k1_xboole_0 = k1_tops_1(A,B)))))) # label(t84_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4900 $T # label(t98_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4901 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,k6_subset_1(u1_struct_0(A),B,C)),k6_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t50_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4902 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t36_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4903 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k6_pre_topc(A,k1_tops_1(A,B))) & r1_tarski(k1_tops_1(A,k6_pre_topc(A,B)),B) <-> v4_tops_1(B,A)))))) # label(d6_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4904 $T # label(t15_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4905 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) <-> B = k1_tops_1(A,k6_pre_topc(A,B))))))) # label(d8_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4906 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(C,A) & v5_tops_1(B,A) -> v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t108_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4907 $T # label(t3_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4908 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(C,A) & v2_tops_1(C,A) -> v2_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t85_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4909 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (C = k1_tops_1(A,C) -> v3_pre_topc(C,A)) & (v3_pre_topc(D,B) -> D = k1_tops_1(B,D)))))))))) # label(t55_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4910 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))) = k2_tops_1(A,B))))) # label(d2_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4911 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_tops_1(B,A) -> v2_tops_1(B,A) & v3_tops_1(B,A)))))) # label(cc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4912 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v4_pre_topc(k2_pre_topc(A),A) & v3_pre_topc(k2_pre_topc(A),A))) # label(fc8_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4913 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,k1_tops_1(A,B)) = k1_tops_1(A,B))))) # label(t45_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4914 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) <-> k6_subset_1(u1_struct_0(A),B,k1_tops_1(A,B)) = k2_tops_1(A,B)))))) # label(t77_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4915 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & v3_pre_topc(B,A))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4916 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & r1_xboole_0(B,C) & k1_xboole_0 != C))) <-> v1_tops_1(B,A)))))) # label(t80_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4917 $T # label(t19_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4918 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v4_pre_topc(k6_pre_topc(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4919 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t103_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4920 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v3_pre_topc(B,A) -> (v6_tops_1(B,A) <-> v5_tops_1(B,A))))))) # label(t105_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4921 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & l1_pre_topc(A) & v2_pre_topc(A) -> v3_tops_1(k2_tops_1(A,B),A) & v2_tops_1(k2_tops_1(A,B),A))) # label(fc12_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4922 $T # label(t7_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4923 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,B) = k4_subset_1(u1_struct_0(A),k5_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)),B),k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t64_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4924 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (v4_pre_topc(B,A) & v3_pre_topc(B,A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4925 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> (all C (r2_hidden(C,B) <-> (exists D (r1_tarski(D,B) & r2_hidden(C,D) & v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t57_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4926 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k1_pre_topc(A),A))) # label(t52_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4927 $T # label(t12_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4928 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> v4_tops_1(k6_pre_topc(A,B),A) & v4_tops_1(k1_tops_1(A,B),A)))))) # label(t111_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4929 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k1_tops_1(A,B),B))))) # label(t44_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4930 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k2_tops_1(A,B))))) # label(t62_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4931 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_tops_1(C,A) -> v3_pre_topc(C,A) & v4_tops_1(C,A)) & (v4_tops_1(D,B) & v3_pre_topc(D,B) -> v6_tops_1(D,B)))))))))) # label(t107_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4932 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) -> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4933 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)))))))))) # label(t41_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4934 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> B = k1_xboole_0))))) # label(t97_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4935 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> k2_pre_topc(A) = k1_tops_1(A,k2_pre_topc(A)))) # label(t43_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4936 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> v4_pre_topc(k1_pre_topc(A),A))) # label(t22_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4937 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) <-> v5_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t101_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4938 (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))) -> (v3_pre_topc(B,A) & r1_tarski(B,C) -> r1_tarski(B,k1_tops_1(A,C))))))))) # label(t56_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4939 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> m1_subset_1(k2_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k2_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4940 $T # label(t33_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4941 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v2_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v5_membered(B) & v4_membered(B) & v3_membered(B) & v1_membered(B) & v4_pre_topc(B,A) & v1_xboole_0(B))))) # label(rc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4942 (all A (l1_pre_topc(A) -> k1_pre_topc(A) = k1_tops_1(A,k1_pre_topc(A)))) # label(t47_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4943 $T # label(t16_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4944 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k1_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t71_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4945 (all A (l1_pre_topc(A) -> v1_tops_1(k2_pre_topc(A),A))) # label(fc9_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4946 $T # label(t25_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4947 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) <-> v4_pre_topc(B,A)))))) # label(t29_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4948 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k2_tops_1(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) & r2_hidden(C,D) -> -r1_xboole_0(k3_subset_1(u1_struct_0(A),B),D) & -r1_xboole_0(B,D))))))))))) # label(t61_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4949 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(B,A) -> k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B) = k2_tops_1(A,k6_pre_topc(A,B)) & k2_tops_1(A,B) = k2_tops_1(A,k6_pre_topc(A,B))))))) # label(t104_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4950 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t96_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4951 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4952 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,k1_tops_1(A,B)) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,k1_tops_1(A,B)))))))) # label(t58_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4953 $T # label(t83_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4954 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & v3_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A))) # label(fc11_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4955 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> v4_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t35_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4956 (all A all B (v2_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v1_membered(k1_tops_1(A,B)) & v2_membered(k1_tops_1(A,B)) & v3_membered(k1_tops_1(A,B)) & v5_membered(k1_tops_1(A,B)) & v2_tops_1(k1_tops_1(A,B),A) & v4_membered(k1_tops_1(A,B)) & v1_xboole_0(k1_tops_1(A,B)))) # label(fc10_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.92 4957 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & v1_tops_1(C,A) & v3_pre_topc(C,A) -> v1_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t82_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4958 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v3_tops_1(B,A)))))) # label(cc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4959 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,k2_tops_1(A,B)) <-> v2_tops_1(B,A)))))) # label(t88_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4960 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> (v3_tops_1(B,A) <-> B = k2_tops_1(A,B))))))) # label(t94_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4961 $T # label(t13_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4962 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(k6_pre_topc(A,B),A) <-> v3_tops_1(B,A)))))) # label(d5_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4963 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C))),k5_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))) = k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C)))))))) # label(t70_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4964 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) & r1_tarski(B,C) -> v1_tops_1(C,A)))))))) # label(t79_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4965 $T # label(t1_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4966 (all A all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4967 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),C,B)) = k6_pre_topc(A,C))))))))) # label(t81_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4968 (all A (l1_pre_topc(A) -> v1_xboole_0(k1_tops_1(A,k1_pre_topc(A))) & v3_membered(k1_tops_1(A,k1_pre_topc(A))) & v4_membered(k1_tops_1(A,k1_pre_topc(A))) & v5_membered(k1_tops_1(A,k1_pre_topc(A))) & v2_membered(k1_tops_1(A,k1_pre_topc(A))) & v1_membered(k1_tops_1(A,k1_pre_topc(A))))) # label(fc5_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4969 (all A all B (l1_pre_topc(A) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4970 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_xboole_0(k1_tops_1(A,B),k2_tops_1(A,B)))))) # label(t73_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4971 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v4_pre_topc(B,A) & v3_pre_topc(B,A)))))) # label(cc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4972 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(B,A) <-> k2_pre_topc(A) = k6_pre_topc(A,B)))))) # label(d3_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4973 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k6_pre_topc(A,k6_pre_topc(A,B)))))) # label(t26_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4974 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(cc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4975 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v2_tops_1(B,A)))))) # label(t92_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4976 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v3_tops_1(k2_tops_1(A,B),A)))))) # label(t95_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4977 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C) -> C = B))))))) # label(t21_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4978 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t66_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4979 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_tops_1(k3_subset_1(u1_struct_0(A),B),A) <-> v2_tops_1(B,A)))))) # label(d4_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4980 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> k2_tops_1(A,B) = k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),B)))))) # label(t76_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4981 $T # label(t6_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4982 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t38_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4983 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v1_membered(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A) & v1_xboole_0(k1_pre_topc(A)))) # label(fc1_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4984 (all A (l1_pre_topc(A) -> (exists B (v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_membered(B) & v2_membered(B) & v1_membered(B) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))))))) # label(rc4_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4985 $T # label(t100_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4986 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> k6_pre_topc(A,B) = k6_pre_topc(A,k1_tops_1(A,k6_pre_topc(A,B)))))))) # label(t59_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4987 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_hidden(C,k6_pre_topc(A,B)) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(C,D) & r1_xboole_0(B,D) & v3_pre_topc(D,A))))))))))) # label(t39_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4988 $T # label(t11_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4989 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) <-> k6_pre_topc(A,k1_tops_1(A,B)) = B))))) # label(d7_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4990 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k6_pre_topc(A,B)),k2_tops_1(A,B)))))) # label(t72_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4991 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) & v3_tops_1(C,A) -> v3_tops_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t90_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4992 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> v3_pre_topc(k1_tops_1(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4993 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k4_subset_1(u1_struct_0(A),B,C)),k4_subset_1(u1_struct_0(A),k2_tops_1(A,B),k2_tops_1(A,C))))))))) # label(t67_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4994 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) & v4_pre_topc(B,A) -> v3_tops_1(B,A)))))) # label(t93_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4995 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v5_tops_1(B,A) -> k2_tops_1(A,B) = k2_tops_1(A,k1_tops_1(A,B))))))) # label(t102_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4996 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k6_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C)),k6_pre_topc(A,k6_subset_1(u1_struct_0(A),B,C))))))))) # label(t32_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4997 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,k3_subset_1(u1_struct_0(A),C)) <-> r1_tarski(B,C)))))))) # label(t20_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4998 $T # label(t5_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 4999 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k4_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)),k1_tops_1(A,k4_subset_1(u1_struct_0(A),B,C))))))))) # label(t49_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5000 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_tops_1(A,k2_tops_1(A,B)) = k2_tops_1(A,k2_tops_1(A,k2_tops_1(A,B))))))) # label(t75_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5001 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,B),k6_pre_topc(A,B)))))) # label(t63_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5002 $T # label(t14_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5003 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(k2_tops_1(A,k2_tops_1(A,B)),k2_tops_1(A,B)))))) # label(t68_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5004 $T # label(t23_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5005 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> r1_tarski(k5_subset_1(u1_struct_0(A),B,k6_pre_topc(A,C)),k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)))))))))) # label(t40_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5006 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 != C & v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & r1_xboole_0(B,D) & D != k1_xboole_0 & r1_tarski(D,C))))))) <-> v2_tops_1(B,A))))))) # label(t87_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5007 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) <-> v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t30_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5008 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v2_membered(k1_pre_topc(A)) & v3_membered(k1_pre_topc(A)) & v5_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v1_membered(k1_pre_topc(A)) & v4_pre_topc(k1_pre_topc(A),A) & v3_pre_topc(k1_pre_topc(A),A) & v1_xboole_0(k1_pre_topc(A)))) # label(fc7_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5009 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> ((exists D (v3_pre_topc(D,A) & r1_tarski(D,C) & r2_hidden(B,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_hidden(B,k1_tops_1(A,C))))))) # label(t54_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5010 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k2_pre_topc(A) = k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A)))))) # label(t2_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5011 (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))) -> k1_tops_1(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k1_tops_1(A,B),k1_tops_1(A,C)))))))) # label(t46_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5012 $T # label(t60_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5013 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) -> r1_tarski(k2_tops_1(A,B),B)))))) # label(t69_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5014 $T # label(t4_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5015 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)) = k1_tops_1(A,B))))) # label(t74_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5016 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> k6_pre_topc(A,k5_subset_1(u1_struct_0(A),B,C)) = k5_subset_1(u1_struct_0(A),k6_pre_topc(A,B),k6_pre_topc(A,C))))))))) # label(t34_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5017 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v2_tops_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & r1_tarski(C,B) -> C = k1_xboole_0)))))))) # label(t86_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5018 $T # label(t42_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5019 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_tops_1(C,A) & v6_tops_1(B,A) -> v6_tops_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t109_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5020 (all A (l1_struct_0(A) -> k1_pre_topc(A) = k3_subset_1(u1_struct_0(A),k2_pre_topc(A)))) # label(t8_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5021 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> v3_pre_topc(k2_pre_topc(A),A))) # label(t53_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5022 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_tops_1(B,A) -> k1_xboole_0 = k1_tops_1(A,k2_tops_1(A,B))))))) # label(t110_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5023 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,B) & v4_pre_topc(B,A) -> r1_tarski(k6_pre_topc(A,C),B)))))))) # label(t31_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5024 $T # label(t99_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5025 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v1_xboole_0(B) -> v2_tops_1(B,A)))))) # label(cc2_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5026 $T # label(t18_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5027 $T # label(t28_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5028 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> v3_pre_topc(k1_tops_1(A,B),A))))) # label(t51_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5029 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_tops_1(B,A) -> v3_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) & v4_membered(B) & v2_membered(B) & v1_membered(B) & v4_pre_topc(B,A) & v3_pre_topc(B,A) & v1_xboole_0(B)))))) # label(cc6_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5030 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v5_tops_1(C,A) -> v4_pre_topc(C,A) & v4_tops_1(C,A)) & (v4_pre_topc(D,B) & v4_tops_1(D,B) -> v5_tops_1(D,B)))))))))) # label(t106_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5031 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r1_tarski(k1_tops_1(A,B),k1_tops_1(A,C))))))))) # label(t48_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5032 $T # label(t9_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5033 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & v3_pre_topc(C,A) -> v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t37_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5034 $T # label(t78_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5035 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k1_tops_1(A,B) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5036 $T # label(t17_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5037 $T # label(t89_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5038 $T # label(t10_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5039 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) & l1_pre_topc(A) -> v2_tops_1(k2_tops_1(A,B),A) & v3_tops_1(k2_tops_1(A,B),A))) # label(fc13_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5040 (all A (l1_pre_topc(A) -> k6_pre_topc(A,k2_pre_topc(A)) = k2_pre_topc(A))) # label(t27_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5041 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> k6_pre_topc(A,B) = k4_subset_1(u1_struct_0(A),B,k2_tops_1(A,B)))))) # label(t65_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5042 $T # label(t24_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5043 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_tops_1(B,A) -> v1_tops_1(k3_subset_1(u1_struct_0(A),B),A)))))) # label(t91_tops_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5044 $T # label(t32_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5045 (all A (l1_rlvect_1(A) -> (v1_rlvect_1(A) -> A = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A))))) # label(abstractness_v1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5046 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_rlvect_1(A),B,C) = k2_rlvect_1(A,B,C))))))) # label(t5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5047 (all A (l1_struct_0(A) -> (all B (r1_rlvect_1(A,B) <-> r2_hidden(B,u1_struct_0(A)))))) # label(d1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5048 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),B)) = B & k9_rlvect_1(A,k7_rlvect_1(A,B,k1_rlvect_1(A))) = B)))) # label(t75_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5049 (all A (v3_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) = k4_rlvect_1(A,B,B) -> k1_rlvect_1(A) = B))))) # label(t34_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5050 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k1_rlvect_1(A))) # label(t60_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5051 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,D,B)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t85_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5052 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B))))) # label(t27_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5053 (all A (v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,D,C)) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t87_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5054 (exists A (l2_rlvect_1(A) & -v3_struct_0(A))) # label(rc3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5055 $T # label(t88_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5056 (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_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & v1_funct_1(C) & m1_subset_1(B,A) -> (all E all F all G all H (g2_rlvect_1(E,F,G,H) = g2_rlvect_1(A,B,C,D) -> E = A & H = D & G = C & B = F)))) # label(free_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5057 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)))))))))) # label(t86_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5058 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k5_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C))))))))) # label(t70_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5059 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,k5_rlvect_1(A,B),C) = k6_rlvect_1(A,k5_rlvect_1(A,C),B))))))) # label(t46_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5060 (all A all B all C (l1_rlvect_1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5061 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_rlvect_1(A,B))))) # label(t3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5062 (exists A (v3_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v1_rlvect_1(A) & -v3_struct_0(A) & l1_rlvect_1(A))) # label(rc5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5063 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k6_rlvect_1(A,B,C))))))) # label(d11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5064 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (-v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v5_rlvect_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_rlvect_1(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)) = k3_rlvect_1(C,D,k5_real_1(A,B)))))))))) # label(t49_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5065 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_funct_1(B,np__1) = C & D = k1_funct_1(B,np__2) & np__2 = k3_finseq_1(B) -> k2_rlvect_1(A,C,D) = k9_rlvect_1(A,B)))))))))) # label(t96_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5066 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,C,B)) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t72_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5067 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> k5_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))) = k1_rlvect_1(A))) # label(t68_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5068 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> B = C))))))) # label(t35_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5069 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) -> k7_rlvect_1(A,B,C) = k10_finseq_1(B,C))) # label(redefinition_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5070 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k6_rlvect_1(A,k5_rlvect_1(A,C),B))))))) # label(t44_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5071 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,C,A) = k3_rlvect_1(B,k5_rlvect_1(B,C),k1_real_1(A)))))))) # label(t40_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5072 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) & v6_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (k3_rlvect_1(C,D,A) = k3_rlvect_1(C,D,B) -> A = B | D = k1_rlvect_1(C)))))))))) # label(t51_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5073 (all A (l1_rlvect_1(A) -> l2_struct_0(A))) # label(dt_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5074 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & k2_rlvect_1(A,B,D) = C)))))))) # label(t20_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5075 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (np__0 = A | C = k1_rlvect_1(B) -> k1_rlvect_1(B) = k3_rlvect_1(B,C,A)))))))) # label(t23_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5076 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5077 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,C) -> B = k5_rlvect_1(A,C)))))))) # label(t19_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5078 $T # label(t9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5079 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)) = k9_rlvect_1(A,k8_rlvect_1(A,D,B,C)))))))))) # label(t89_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5080 (all A all B all C all D (-v1_xboole_0(A) & m1_subset_1(B,A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> v2_rlvect_1(g2_rlvect_1(A,B,C,D)) & -v3_struct_0(g2_rlvect_1(A,B,C,D)))) # label(fc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5081 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t63_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5082 $T # label(t12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5083 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B = k5_rlvect_1(A,B) -> B = k1_rlvect_1(A)))))) # label(t33_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5084 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v5_rlvect_1(B) & v3_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k3_rlvect_1(B,D,A) = k3_rlvect_1(B,C,A) -> C = D | np__0 = A))))))))) # label(t50_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5085 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))) = k5_rlvect_1(A,B))))) # label(t69_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.69/23.93 5086 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))))))))))) # label(t81_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5087 (all A (l2_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_numbers) -> k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) = k3_rlvect_1(A,B,C))))))) # label(d4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5088 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (v2_funct_1(B) & v2_funct_1(C) & k2_relat_1(B) = k2_relat_1(C) -> k9_rlvect_1(A,C) = k9_rlvect_1(A,B)))))))) # label(t59_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5089 $T # label(t14_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5090 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_rlvect_1(B,k3_rlvect_1(B,C,A),k3_rlvect_1(B,D,A)) = k3_rlvect_1(B,k6_rlvect_1(B,C,D),A))))))))) # label(t48_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5091 $T # label(t6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5092 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k6_rlvect_1(A,B,C) = k6_rlvect_1(A,B,D) -> C = D))))))))) # label(t37_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5093 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (D = k3_finseq_1(B) & r2_hidden(C,k2_finseq_1(D)) -> m1_subset_1(k1_funct_1(B,C),u1_struct_0(A))))))))))) # label(t54_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5094 (all A (m1_subset_1(A,k1_numbers) -> (all B (v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,C,k1_real_1(A)) = k3_rlvect_1(B,k5_rlvect_1(B,C),A))))))) # label(t38_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5095 $T # label(t4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5096 $T # label(t11_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5097 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,k1_rlvect_1(A)) = B)))) # label(t26_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5098 $T # label(t53_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5099 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,k5_rlvect_1(A,B)) = B)))) # label(t30_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5100 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v8_rlvect_1(B,A) <-> B != k1_rlvect_1(A)))))) # label(d13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5101 (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_rlvect_1(A) & v3_rlvect_1(A) -> k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C))) # label(redefinition_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5102 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k6_rlvect_1(A,B,C)) = k2_rlvect_1(A,C,k5_rlvect_1(A,B)))))))) # label(t47_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5103 (all A (l2_rlvect_1(A) -> (v2_rlvect_1(A) -> A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))))) # label(abstractness_v2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5104 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k3_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,C,D,E)),B) = k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)),k3_rlvect_1(A,E,B)))))))))))) # label(t67_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5105 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A))) & B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,k1_rlvect_1(A))) & B = k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),B)))))) # label(t91_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5106 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,k6_rlvect_1(A,B,C),D))))))))) # label(t43_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5107 (all A (l2_struct_0(A) -> u2_struct_0(A) = k1_rlvect_1(A))) # label(d2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5108 (all A (l2_struct_0(A) -> m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)))) # label(dt_k1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5109 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__3) = k9_rlvect_1(A,k8_rlvect_1(A,B,B,B)))))) # label(t93_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5110 (all A (m1_subset_1(A,k1_numbers) -> (all B (v3_rlvect_1(B) & v4_rlvect_1(B) & l2_rlvect_1(B) & v7_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> -(C != k1_rlvect_1(B) & np__0 != A & k1_rlvect_1(B) = k3_rlvect_1(B,C,A)))))))) # label(t24_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5111 (exists A (l1_rlvect_1(A) & -v3_struct_0(A) & v1_rlvect_1(A))) # label(rc4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5112 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,C,B)) = k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C))))))))) # label(t78_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5113 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) = k3_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B))))))))) # label(t66_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5114 $T # label(t17_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5115 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) = k2_rlvect_1(A,B,C))))))) # label(d3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5116 (all A all B all C (l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m2_finseq_1(k7_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5117 (all A all B all C (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B))) # label(commutativity_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5118 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,B,C) = k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,C))))))))) # label(t77_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5119 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,k2_rlvect_1(A,B,C),D))))))))) # label(t42_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5120 (all A (l1_rlvect_1(A) -> m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(u1_rlvect_1(A)))) # label(dt_u1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5121 (all A all B all C (l2_rlvect_1(A) & m1_subset_1(C,k1_numbers) & m1_subset_1(B,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k3_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5122 (exists A (l1_rlvect_1(A) & v1_rlvect_1(A))) # label(rc1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.93 5123 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (np__1 = k3_finseq_1(B) -> k1_funct_1(B,np__1) = k9_rlvect_1(A,B)))))) # label(t95_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5124 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B)))) # label(t61_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5125 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B & B = k2_rlvect_1(A,k1_rlvect_1(A),B))))) # label(t10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5126 $T # label(t1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5127 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> k9_rlvect_1(A,k7_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A))) # label(t74_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5128 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k9_rlvect_1(A,k8_rlvect_1(A,B,C,D)) = k2_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,C)),D))))))))) # label(t82_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5129 (exists A l2_rlvect_1(A)) # label(existence_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5130 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),B)) = k1_rlvect_1(A) & k9_rlvect_1(A,k7_rlvect_1(A,B,k5_rlvect_1(A,B))) = k1_rlvect_1(A))))) # label(t76_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5131 (all A (l2_rlvect_1(A) -> v1_funct_1(u2_rlvect_1(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5132 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,C)) = k2_rlvect_1(A,B,C))))))) # label(t62_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5133 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k9_rlvect_1(A,k8_rlvect_1(A,B,C,k1_rlvect_1(A))) & k9_rlvect_1(A,k8_rlvect_1(A,B,k1_rlvect_1(A),C)) = k2_rlvect_1(A,B,C) & k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),B,C)) = k2_rlvect_1(A,B,C))))))) # label(t92_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5134 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k6_rlvect_1(A,C,D) = B & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t36_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5135 (exists A (v2_rlvect_1(A) & l2_rlvect_1(A))) # label(rc2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5136 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) -> m1_subset_1(k9_rlvect_1(A,B),u1_struct_0(A)))) # label(dt_k9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5137 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> ((all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(D,k4_finseq_1(B)) & k1_funct_1(C,D) = E -> k5_rlvect_1(A,E) = k1_funct_1(B,D)))))) & k3_finseq_1(B) = k3_finseq_1(C) -> k5_rlvect_1(A,k9_rlvect_1(A,C)) = k9_rlvect_1(A,B)))))))) # label(t57_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5138 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> k1_rlvect_1(A) = k5_rlvect_1(A,k1_rlvect_1(A)))) # label(t25_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5139 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (np__3 = k3_finseq_1(B) & D = k1_funct_1(B,np__2) & E = k1_funct_1(B,np__3) & C = k1_funct_1(B,np__1) -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k2_rlvect_1(A,C,D),E)))))))))))) # label(t97_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5140 (exists A l1_rlvect_1(A)) # label(existence_l1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5141 $T # label(t8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5142 (all A all B all C all D (m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_struct_0(A) & -v3_struct_0(A) -> m2_finseq_1(k8_rlvect_1(A,B,C,D),u1_struct_0(A)))) # label(dt_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5143 (all A (m1_subset_1(A,k1_numbers) -> (all B (-v3_struct_0(B) & v3_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m2_finseq_1(C,u1_struct_0(B)) -> (all D (m2_finseq_1(D,u1_struct_0(B)) -> (k3_finseq_1(D) = k3_finseq_1(C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> (r2_hidden(E,k4_finseq_1(C)) & k1_funct_1(D,E) = F -> k1_funct_1(C,E) = k3_rlvect_1(B,F,A)))))) -> k9_rlvect_1(B,C) = k3_rlvect_1(B,k9_rlvect_1(B,D),A)))))))))) # label(t56_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5144 (all A (l2_rlvect_1(A) -> l1_rlvect_1(A))) # label(dt_l2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5145 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,B,B)) = k3_rlvect_1(A,B,np__2))))) # label(t79_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5146 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (v6_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,C)))))))) # label(d8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5147 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)),k9_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C))) = k9_rlvect_1(A,k7_rlvect_1(A,B,C)))))))) # label(t73_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5148 $T # label(t15_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5149 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,C) = k5_rlvect_1(A,B) -> C = B))))))) # label(t31_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5150 (all A all B all C (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all D all E all F (g1_rlvect_1(D,E,F) = g1_rlvect_1(A,B,C) -> A = D & E = B & C = F)))) # label(free_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5151 (all A all B all C all D (v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_subset_1(B,A) -> v2_rlvect_1(g2_rlvect_1(A,B,C,D)) & l2_rlvect_1(g2_rlvect_1(A,B,C,D)))) # label(dt_g2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5152 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k2_rlvect_1(A,C,B) | k2_rlvect_1(A,B,C) = B -> k1_rlvect_1(A) = C))))))) # label(t22_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5153 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,k9_rlvect_1(A,B),k9_rlvect_1(A,C)) = k9_rlvect_1(A,k8_finseq_1(u1_struct_0(A),B,C)))))))) # label(t58_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5154 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,B,C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B)))))))) # label(t45_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5155 (all A (-v3_struct_0(A) & l2_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_rlvect_1(A,B,np__1))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)))))))) <-> v7_rlvect_1(A)))) # label(d9_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5156 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m2_finseq_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (D = k1_funct_1(B,k3_finseq_1(B)) & C = k7_relat_1(B,k4_finseq_1(C)) & k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),np__1) -> k9_rlvect_1(A,B) = k2_rlvect_1(A,k9_rlvect_1(A,C),D)))))))))) # label(t55_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5157 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,B,B) = k1_rlvect_1(A))))) # label(t28_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5158 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_numbers) -> k3_rlvect_1(A,k9_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k1_rlvect_1(A))))) # label(t64_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5159 $T # label(t13_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 22.78/23.94 5160 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,C,D)),B) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t84_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5161 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> ((exists D (v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & k8_funct_2(k5_numbers,u1_struct_0(A),D,k3_finseq_1(B)) = C & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = k1_funct_1(B,k1_nat_1(E,np__1)) -> k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(E,np__1)) = k2_rlvect_1(A,k8_funct_2(k5_numbers,u1_struct_0(A),D,E),F) | r1_xreal_0(k3_finseq_1(B),E)))))) & k1_rlvect_1(A) = k8_funct_2(k5_numbers,u1_struct_0(A),D,np__0) & m2_relset_1(D,k5_numbers,u1_struct_0(A)))) <-> C = k9_rlvect_1(A,B)))))))) # label(d12_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5162 $T # label(t65_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5163 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> k8_rlvect_1(A,B,C,D) = k11_finseq_1(B,C,D))) # label(redefinition_k8_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5164 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_rlvect_1(A,B) = k3_rlvect_1(A,B,k1_real_1(np__1)))))) # label(t29_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5165 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l2_rlvect_1(A) & v7_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_rlvect_1(A,k7_rlvect_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,B))) = k3_rlvect_1(A,B,k1_real_1(np__2)))))) # label(t80_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5166 (all A (m1_subset_1(A,k1_numbers) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) & v4_rlvect_1(B) & v3_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_rlvect_1(B,k5_rlvect_1(B,C),A) = k5_rlvect_1(B,k3_rlvect_1(B,C,A)))))))) # label(t39_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5167 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k4_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5168 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))) <-> v4_rlvect_1(A)))) # label(d6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5169 (all A all B all C (l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(A) -> m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5170 $T # label(t52_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5171 (all A (-v3_struct_0(A) & l2_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & k1_rlvect_1(A) = k2_rlvect_1(A,B,C))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)))))))) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k3_rlvect_1(A,B,np__1) = B)) & (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B)) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B))))) -> l2_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5172 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k2_rlvect_1(A,B,C) = k1_rlvect_1(A))))))))) # label(d10_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5173 $T # label(t2_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5174 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_rlvect_1(A,k9_rlvect_1(A,k7_rlvect_1(A,B,D)),C) = k9_rlvect_1(A,k8_rlvect_1(A,C,B,D)))))))))) # label(t83_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5175 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v5_rlvect_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_rlvect_1(A,B,k1_rlvect_1(A)) = B))))) # label(d7_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5176 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,B),C),D) = k5_rlvect_1(A,k9_rlvect_1(A,k8_rlvect_1(A,B,C,D))))))))))) # label(t71_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5177 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> k9_rlvect_1(A,k8_rlvect_1(A,k1_rlvect_1(A),k1_rlvect_1(A),k1_rlvect_1(A))) = k1_rlvect_1(A))) # label(t90_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5178 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,B)) & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A))))) # label(t16_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5179 (exists A (l2_rlvect_1(A) & v2_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v7_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(rc6_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5180 $T # label(t18_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5181 (all A all B all C (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) -> v1_rlvect_1(g1_rlvect_1(A,B,C)) & l1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(dt_g1_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5182 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,B,k2_rlvect_1(A,C,D)) = k6_rlvect_1(A,k6_rlvect_1(A,B,D),C))))))))) # label(t41_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5183 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) | k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E) -> E = D))))))))))) # label(t21_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5184 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m2_finseq_1(B,u1_struct_0(A)) -> (k3_finseq_1(B) = np__0 -> k1_rlvect_1(A) = k9_rlvect_1(A,B)))))) # label(t94_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5185 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B))))) <-> v3_rlvect_1(A)))) # label(d5_rlvect_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5186 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C)) <-> k1_group_1(A,C,B) = k1_group_1(A,B,C)))))))) # label(t27_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5187 $T # label(t87_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5188 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,C,B) & k1_group_1(A,B,C) = C)) <-> B = k2_group_1(A))))))) # label(d5_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5189 $T # label(t40_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5190 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (v6_group_1(A) -> r1_xreal_0(np__1,k9_group_1(A))))) # label(t90_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5191 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = k1_group_1(A,B,C))))) <-> v7_group_1(A)))) # label(d16_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5192 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> k4_group_1(A) = k6_finseqop(u1_struct_0(A),u1_group_1(A)))) # label(t37_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5193 (all A (-v3_struct_0(A) & l1_group_1(A) -> (v4_group_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D))))))))))) # label(d4_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5194 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k1_group_1(B,C,k6_group_1(B,A,D)) = k1_group_1(B,k6_group_1(B,A,D),C)))))))))) # label(t52_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5195 (all A (-v3_struct_0(A) & l1_group_1(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,k1_nat_1(D,np__1)) = k1_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,D),C))) & k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),B,C,np__0) = k2_group_1(A))) <-> B = k5_group_1(A)))))) # label(d8_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5196 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> k2_group_1(B) = k6_group_1(B,A,k2_group_1(B)))))) # label(t42_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5197 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,B,C) = D <-> k1_group_1(A,D,k3_group_1(A,C)) = B))))))))) # label(t22_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5198 $T # label(t30_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5199 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (k6_group_1(B,A,C) = k2_group_1(B) -> r1_nat_1(k7_group_1(B,C),A)))))))) # label(t86_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5200 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v1_card_1(k8_group_1(A)))) # label(dt_k8_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5201 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_group_1(A) & v7_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5202 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> v1_funct_1(k4_group_1(A)) & v1_funct_2(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k4_group_1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k4_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5203 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(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) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k3_group_1(A,C))) <-> k4_group_1(A) = B))))) # label(d7_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5204 $T # label(t81_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5205 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & B = k1_group_1(A,D,C) & B = k1_group_1(A,C,D))) & k1_group_1(A,B,C) = C & C = k1_group_1(A,C,B))) & m1_subset_1(B,u1_struct_0(A)))) <-> v3_group_1(A)))) # label(d3_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5206 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k3_group_1(A,B) = B <-> k6_group_1(A,np__2,B) = k2_group_1(A)))))) # label(t47_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5207 (all A (v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> v2_binop_1(u1_group_1(A),u1_struct_0(A)))) # label(t31_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5208 $T # label(t89_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5209 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & l1_group_1(C) & v4_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D)) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E))))))))))))) # label(t75_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5210 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (np__0 = A -> k6_group_1(B,A,C) = k2_group_1(B)))))))) # label(t59_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5211 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & l1_group_1(C) & v4_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,B,k6_group_1(C,A,D)) = k6_group_1(C,k3_xcmplx_0(A,B),D))))))))) # label(t68_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5212 $T # label(t2_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5213 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,B))))))) # label(d10_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5214 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,C,B) | k1_group_1(A,B,C) = k2_group_1(A) -> C = k3_group_1(A,B) & B = k3_group_1(A,C)))))))) # label(t20_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5215 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (v5_group_1(B,A) -> (C = k7_group_1(A,B) <-> C = np__0)) & (-v5_group_1(B,A) -> (C = k7_group_1(A,B) <-> np__0 != C & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k2_group_1(A) = k6_group_1(A,D,B) -> r1_xreal_0(C,D) | np__0 = D))) & k2_group_1(A) = k6_group_1(A,C,B))))))))) # label(d12_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5216 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k6_group_1(A,C,B) = k2_group_1(A) -> C = np__0))) <-> v5_group_1(B,A)))))) # label(d11_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5217 $T # label(t78_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5218 (all A all B (v4_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k3_group_1(A,B),u1_struct_0(A)))) # label(dt_k3_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5219 $T # label(t38_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5220 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (l1_group_1(C) & v4_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k1_nat_1(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t48_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5221 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(B,A),D) = k1_group_1(C,k6_group_1(C,B,D),k6_group_1(C,A,D)))))))))) # label(t65_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5222 $T # label(t39_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5223 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> m2_subset_1(k9_group_1(A),k1_numbers,k5_numbers))) # label(dt_k9_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5224 (exists A (l1_group_1(A) & v2_group_1(A) & v3_group_1(A) & v4_group_1(A) & v1_group_1(A) & -v3_struct_0(A))) # label(rc3_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5225 (all A all B all C (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_struct_0(g1_rlvect_1(A,B,C)) & v1_rlvect_1(g1_rlvect_1(A,B,C)))) # label(fc2_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5226 (all A all B all C (m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5227 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (v1_int_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (-r1_xreal_0(np__0,B) -> k3_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B))) = k6_group_1(A,B,C)) & (r1_xreal_0(np__0,B) -> k6_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),C,k1_int_2(B))))))))) # label(d9_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5228 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k6_group_1(B,A,k3_group_1(B,C)) = k3_group_1(B,k6_group_1(B,A,C)))))))) # label(t51_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5229 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,B) = k6_group_1(A,np__2,B))))) # label(t45_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5230 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & v1_int_1(B) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> m1_subset_1(k6_group_1(A,B,C),u1_struct_0(A)))) # label(dt_k6_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5231 (all A (l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),B,C) = k1_group_1(A,B,C))))))) # label(d1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5232 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)) = k6_group_1(C,k2_xcmplx_0(A,B),D))))))))) # label(t64_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5233 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k6_group_1(A,np__0,B))))) # label(t43_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5234 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v7_group_1(A) & v4_group_1(A) -> v4_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v5_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v6_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))) & v3_rlvect_1(g1_rlvect_1(u1_struct_0(A),u1_group_1(A),k2_group_1(A))))) # label(t97_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5235 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (k1_group_1(A,D,B) = C & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t24_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5236 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v2_group_1(A) <-> (exists B (m1_subset_1(B,u1_struct_0(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) = C & k1_group_1(A,C,B) = C))))))) # label(d2_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5237 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_group_1(B,k6_group_1(B,A,C),C) = k6_group_1(B,k1_nat_1(A,np__1),C) & k6_group_1(B,k1_nat_1(A,np__1),C) = k1_group_1(B,C,k6_group_1(B,A,C)))))))) # label(t49_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5238 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> r1_finseqop(u1_struct_0(A),k4_group_1(A),u1_group_1(A)))) # label(t35_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5239 $T # label(t76_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5240 (all A (-v3_struct_0(A) & l1_group_1(A) & v2_group_1(A) -> r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)))) # label(t32_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5241 (all A (l1_group_1(A) -> l1_struct_0(A))) # label(dt_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5242 $T # label(t13_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5243 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> -v5_group_1(k2_group_1(A),A))) # label(t79_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5244 (all A all B all C (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v7_group_1(A) -> k1_group_1(A,B,C) = k10_group_1(A,B,C))) # label(redefinition_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5245 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k4_xcmplx_0(A),C))))))) # label(t70_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5246 (all A (-v3_struct_0(A) & l1_group_1(A) -> m2_relset_1(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_2(k5_group_1(A),k2_zfmisc_1(u1_struct_0(A),k5_numbers),u1_struct_0(A)) & v1_funct_1(k5_group_1(A)))) # label(dt_k5_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5247 (exists A l1_group_1(A)) # label(existence_l1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5248 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & l1_group_1(B) & v7_group_1(B) & v4_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_group_1(B,A,k10_group_1(B,C,D)) = k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)))))))))) # label(t96_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5249 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_xcmplx_0(A,B),D) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,D)))))))))) # label(t63_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5250 $T # label(t1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5251 (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 (g1_group_1(C,D) = g1_group_1(A,B) -> D = B & A = C)))) # label(free_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5252 (all A all B all C (l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v7_group_1(A) & -v3_struct_0(A) -> k10_group_1(A,B,C) = k10_group_1(A,C,B))) # label(commutativity_k10_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5253 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_group_1(A) = k3_group_1(A,B) -> k2_group_1(A) = B))))) # label(t18_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5254 $T # label(t83_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5255 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v4_group_1(C) & l1_group_1(C) & v3_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D)) = k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E))))))))))))) # label(t53_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5256 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k3_group_1(A,B) = k3_group_1(A,C) -> C = B))))))) # label(t17_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5257 $T # label(t11_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5258 $T # label(t58_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5259 (exists A (l1_group_1(A) & -v3_struct_0(A) & v1_group_1(A) & v7_group_1(A) & v4_group_1(A) & v3_group_1(A) & v2_group_1(A))) # label(rc4_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5260 $T # label(t4_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5261 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (np__1 = k7_group_1(A,B) -> B = k2_group_1(A)))))) # label(t85_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5262 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,C,B) = C & C = k1_group_1(A,B,C))) -> B = k2_group_1(A)))))) # label(t10_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5263 (all A (l1_group_1(A) -> (v1_group_1(A) -> A = g1_group_1(u1_struct_0(A),u1_group_1(A))))) # label(abstractness_v1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5264 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,B,C) = D <-> k1_group_1(A,k3_group_1(A,B),D) = C))))))))) # label(t21_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5265 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (v6_group_1(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (k9_group_1(A) = B <-> (exists C (v1_finset_1(C) & u1_struct_0(A) = C & B = k4_card_1(C))))))))) # label(d15_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5266 $T # label(t88_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5267 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & l1_group_1(B) & v7_group_1(B) & v4_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k10_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D)) = k6_group_1(B,A,k10_group_1(B,C,D)))))))))) # label(t95_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5268 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_group_1(A,k7_binop_2(np__1),B) = k3_group_1(A,B))))) # label(t62_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5269 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k2_group_1(A) = k1_group_1(A,C,B) & k1_group_1(A,B,C) = k2_group_1(A) <-> C = k3_group_1(A,B)))))))) # label(d6_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5270 (all A (v4_group_1(A) & l1_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,B),B) = k6_group_1(A,np__3,B))))) # label(t46_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5271 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v3_group_1(C) & l1_group_1(C) & v4_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k3_xcmplx_0(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t67_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5272 (all A (-v3_struct_0(A) & v2_group_1(A) & l1_group_1(A) -> k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k2_group_1(A))) # label(t33_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5273 (all A all B (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & -v1_xboole_0(A) -> v1_group_1(g1_group_1(A,B)) & -v3_struct_0(g1_group_1(A,B)))) # label(fc1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5274 $T # label(t57_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5275 (all A (l1_group_1(A) & v2_group_1(A) & -v3_struct_0(A) -> v1_setwiseo(u1_group_1(A),u1_struct_0(A)))) # label(t34_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5276 (all A (v1_int_1(A) -> (all B (v4_group_1(B) & l1_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,D,C) = k1_group_1(B,C,D) -> k1_group_1(B,k6_group_1(B,A,D),C) = k1_group_1(B,C,k6_group_1(B,A,D))))))))))) # label(t77_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5277 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(A,np__0) -> k6_group_1(B,A,C) = k3_group_1(B,k6_group_1(B,k1_int_2(A),C))))))))) # label(t60_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5278 (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) -> l1_group_1(g1_group_1(A,B)) & v1_group_1(g1_group_1(A,B)))) # label(dt_g1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5279 (all A (v1_int_1(A) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (all E (m1_subset_1(E,u1_struct_0(C)) -> (k1_group_1(C,E,D) = k1_group_1(C,D,E) -> k1_group_1(C,k6_group_1(C,A,D),k6_group_1(C,B,E)) = k1_group_1(C,k6_group_1(C,B,E),k6_group_1(C,A,D))))))))))))) # label(t74_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5280 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v1_int_1(B) -> (all C (-v3_struct_0(C) & v4_group_1(C) & l1_group_1(C) & v3_group_1(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k3_xcmplx_0(B,A),D) = k6_group_1(C,A,k6_group_1(C,B,D)))))))))) # label(t69_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5281 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,k7_binop_2(A),C))))))) # label(t71_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5282 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> k1_card_1(u1_struct_0(A)) = k8_group_1(A))) # label(d13_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5283 $T # label(t9_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5284 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r1_xreal_0(np__0,A) -> k6_group_1(B,k1_int_2(A),C) = k6_group_1(B,A,C)))))))) # label(t55_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5285 (all A (l1_group_1(A) & v4_group_1(A) & v3_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k3_group_1(A,k3_group_1(A,B)))))) # label(t19_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5286 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (all C (v3_group_1(C) & l1_group_1(C) & v4_group_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_group_1(C,k2_nat_1(A,B),D) = k6_group_1(C,B,k6_group_1(C,A,D)))))))))) # label(t50_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5287 (all A (v1_int_1(A) -> (all B (l1_group_1(B) & v4_group_1(B) & v3_group_1(B) & -v3_struct_0(B) -> k6_group_1(B,A,k2_group_1(B)) = k2_group_1(B))))) # label(t61_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5288 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k1_group_1(A,k3_group_1(A,C),B) = k1_group_1(A,B,k3_group_1(A,C))))))))) # label(t28_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5289 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_group_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k3_group_1(A,C),k3_group_1(A,B)))))))) # label(t25_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5290 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k1_group_1(A,B,C) <-> k3_group_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k3_group_1(A,B),k3_group_1(A,C))))))))) # label(t26_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5291 (all A (m2_subset_1(A,k1_numbers,k5_numbers) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k6_group_1(B,A,k1_group_1(B,C,D)) = k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D))))))))))) # label(t54_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5292 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k3_group_1(B,k6_group_1(B,A,C)) = k6_group_1(B,A,k3_group_1(B,C)))))))) # label(t72_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5293 $T # label(t91_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.80 5294 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> k7_group_1(A,k2_group_1(A)) = np__1)) # label(t84_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5295 $T # label(t8_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5296 (exists A (v1_group_1(A) & l1_group_1(A))) # label(rc1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5297 (exists A (-v3_struct_0(A) & v1_group_1(A) & l1_group_1(A))) # label(rc2_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5298 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D)))))))) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(all C (m1_subset_1(C,u1_struct_0(A)) -> C = k1_group_1(A,B,C) & (exists D (m1_subset_1(D,u1_struct_0(A)) & k1_group_1(A,D,C) = B & k1_group_1(A,C,D) = B)) & k1_group_1(A,C,B) = C)))) | -v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))) # label(t5_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5299 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k1_group_1(A,D,B) & m1_subset_1(D,u1_struct_0(A)))) & (exists D (m1_subset_1(D,u1_struct_0(A)) & C = k1_group_1(A,B,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)) -> k1_group_1(A,B,k1_group_1(A,C,D)) = k1_group_1(A,k1_group_1(A,B,C),D))))))) -> v4_group_1(A) & v3_group_1(A)))) # label(t6_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5300 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> v1_finseqop(u1_group_1(A),u1_struct_0(A)))) # label(t36_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5301 (all A (l1_group_1(A) -> v1_funct_1(u1_group_1(A)) & m2_relset_1(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(u1_group_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)))) # label(dt_u1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5302 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v3_group_1(B) & l1_group_1(B) & v4_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (-r1_xreal_0(np__0,A) -> k3_group_1(B,k6_group_1(B,k1_int_2(A),C)) = k6_group_1(B,A,C)))))))) # label(t56_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5303 $T # label(t29_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5304 $T # label(t3_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5305 (all A (v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k6_group_1(A,np__1,B))))) # label(t44_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5306 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (C = k1_group_1(A,B,D) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t23_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5307 $T # label(t41_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5308 (all A (l1_group_1(A) -> (v3_group_1(A) & -v3_struct_0(A) -> v2_group_1(A) & -v3_struct_0(A)))) # label(cc1_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5309 $T # label(t93_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5310 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k2_group_1(A) = k6_group_1(A,k7_group_1(A,B),B))))) # label(t82_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5311 (all A (v3_group_1(A) & l1_group_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (B = k1_group_1(A,B,C) | k1_group_1(A,C,B) = B -> C = k2_group_1(A)))))))) # label(t15_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5312 (all A (-v3_struct_0(A) & v4_group_1(A) & l1_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_group_1(A,C,B) = k2_group_1(A) & k1_group_1(A,B,C) = k2_group_1(A) -> C = k3_group_1(A,B)))))))) # label(t12_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5313 (all A (v1_int_1(A) -> (all B (-v3_struct_0(B) & v4_group_1(B) & l1_group_1(B) & v3_group_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (k1_group_1(B,C,D) = k1_group_1(B,D,C) -> k6_group_1(B,A,k1_group_1(B,C,D)) = k1_group_1(B,k6_group_1(B,A,C),k6_group_1(B,A,D))))))))))) # label(t73_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5314 $T # label(t80_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5315 (all A (l1_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k2_group_1(A),u1_struct_0(A)))) # label(dt_k2_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5316 (all A all B (-v3_struct_0(A) & l1_group_1(A) & m1_subset_1(B,u1_struct_0(A)) & v4_group_1(A) & v3_group_1(A) -> m2_subset_1(k7_group_1(A,B),k1_numbers,k5_numbers))) # label(dt_k7_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5317 (all A (l1_struct_0(A) -> (v1_finset_1(u1_struct_0(A)) <-> v6_group_1(A)))) # label(d14_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5318 (all A (-v3_struct_0(A) & v3_group_1(A) & l1_group_1(A) & v4_group_1(A) -> k2_group_1(A) = k3_group_1(A,k2_group_1(A)))) # label(t16_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5319 (all A (-v3_struct_0(A) & v3_group_1(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k10_group_1(A,k3_group_1(A,B),k3_group_1(A,C)) = k3_group_1(A,k10_group_1(A,B,C)))))))) # label(t94_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5320 (all A (v1_int_1(A) -> (all B (v3_group_1(B) & v4_group_1(B) & l1_group_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_group_1(B,C,k6_group_1(B,A,C)) = k6_group_1(B,k2_xcmplx_0(A,np__1),C) & k6_group_1(B,k2_xcmplx_0(A,np__1),C) = k1_group_1(B,k6_group_1(B,A,C),C))))))) # label(t66_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5321 (all A (-v3_struct_0(A) & l1_group_1(A) & v4_group_1(A) & v3_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_group_1(A,D,B) = k1_group_1(A,C,B) | k1_group_1(A,B,D) = k1_group_1(A,B,C) -> D = C))))))))) # label(t14_group_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5322 (all A (l3_vectsp_1(A) -> l1_rlvect_1(A) & l2_vectsp_1(A))) # label(dt_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5323 $T # label(t61_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5324 (exists A (l3_vectsp_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v7_group_1(A) & v6_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v3_vectsp_1(A) & v3_rlvect_1(A) & -v3_struct_0(A))) # label(rc10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5325 (all A all B all C (v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> v1_vectsp_1(g1_vectsp_1(A,B,C)) & l1_vectsp_1(g1_vectsp_1(A,B,C)))) # label(dt_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5326 $T # label(t11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5327 (all A (l1_vectsp_1(A) -> u1_vectsp_1(A) = k2_vectsp_1(A))) # label(d9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5328 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> C = B))))))) # label(t84_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5329 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)))))))) <-> v5_vectsp_1(A)))) # label(d12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5330 (all A (l1_vectsp_1(A) -> (v2_group_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v8_vectsp_1(A) & v6_vectsp_1(A)))) # label(cc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5331 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,k5_rlvect_1(A,B),k5_rlvect_1(A,C)) = k1_group_1(A,B,C))))))) # label(t42_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5332 (all A (l3_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_rlvect_1(A) = k1_group_1(A,B,k1_rlvect_1(A)))))) # label(t36_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5333 (all A (v3_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v12_vectsp_1(B,A) & l4_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)) = k6_vectsp_1(A,B,k5_rlvect_1(A,C),D) & k6_rlvect_1(B,E,k6_vectsp_1(A,B,C,D)) = k2_rlvect_1(B,E,k6_vectsp_1(A,B,k5_rlvect_1(A,C),D)))))))))))) # label(t68_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5334 (all A (l1_struct_0(A) -> (exists B (-v3_struct_0(B) & v11_vectsp_1(B,A) & l4_vectsp_1(B,A))))) # label(rc12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5335 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (all B (l4_vectsp_1(B,A) & -v3_struct_0(B) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> (all F (m1_subset_1(F,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k2_rlvect_1(B,E,F)) = k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,C,F)) & k2_rlvect_1(B,k6_vectsp_1(A,B,C,E),k6_vectsp_1(A,B,D,E)) = k6_vectsp_1(A,B,k2_rlvect_1(A,C,D),E) & k6_vectsp_1(A,B,k2_group_1(A),E) = E & k6_vectsp_1(A,B,k1_group_1(A,C,D),E) = k6_vectsp_1(A,B,C,k6_vectsp_1(A,B,D,E)))))))))) <-> v12_vectsp_1(B,A)))))) # label(d26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5336 (all A (l1_struct_0(A) -> (exists B l4_vectsp_1(B,A)))) # label(existence_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5337 $T # label(t19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5338 (all A (m1_subset_1(A,u1_struct_0(k1_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k1_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k1_vectsp_1)) -> k4_rlvect_1(k1_vectsp_1,A,k4_rlvect_1(k1_vectsp_1,B,C)) = k4_rlvect_1(k1_vectsp_1,k4_rlvect_1(k1_vectsp_1,A,B),C) & k4_rlvect_1(k1_vectsp_1,A,k5_rlvect_1(k1_vectsp_1,A)) = k1_rlvect_1(k1_vectsp_1) & k4_rlvect_1(k1_vectsp_1,A,k1_rlvect_1(k1_vectsp_1)) = A & k4_rlvect_1(k1_vectsp_1,A,B) = k4_rlvect_1(k1_vectsp_1,B,A))))))) # label(t6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5339 (all A (-v3_struct_0(A) & v4_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) & v5_rlvect_1(A) & v3_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (D = k1_rlvect_1(C) | B = k1_rlvect_1(A) <-> k6_vectsp_1(A,C,B,D) = k1_rlvect_1(C)))))))))) # label(t60_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5340 (all A (-v3_struct_0(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v5_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k1_group_1(A,B,D),k1_group_1(A,C,D)) = k1_group_1(A,k6_rlvect_1(A,B,C),D))))))))) # label(t45_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5341 $T # label(t13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5342 $T # label(t49_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5343 (exists A (v3_vectsp_1(A) & l3_vectsp_1(A))) # label(rc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5344 $T # label(t12_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5345 (all A (v6_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) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v6_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> (B != k1_rlvect_1(A) -> k6_vectsp_1(A,C,k4_vectsp_1(A,B),k6_vectsp_1(A,C,B,D)) = D))))))))) # label(t67_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5346 (all A (v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> -v3_struct_0(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & l1_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v7_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v4_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))) & v3_group_1(g1_group_1(u1_struct_0(A),u1_rlvect_1(A))))) # label(t94_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5347 (all A (l2_vectsp_1(A) -> l2_struct_0(A) & l1_vectsp_1(A))) # label(dt_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5348 $T # label(d2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5349 (exists A (l1_vectsp_1(A) & v2_group_1(A) & v7_group_1(A) & v8_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A))) # label(rc9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5350 (all A (l1_vectsp_1(A) -> (v1_vectsp_1(A) -> g1_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A)) = A))) # label(abstractness_v1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5351 (all A (l1_vectsp_1(A) -> (v7_group_1(A) & v8_vectsp_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v6_vectsp_1(A)))) # label(cc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5352 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,C),k5_rlvect_1(A,B))) = k2_rlvect_1(A,B,C))))))) # label(t89_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5353 $T # label(t57_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5354 $T # label(t5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5355 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,k10_group_1(A,B,D),C) -> D = k10_group_1(A,C,k4_vectsp_1(A,B)) | B = k1_rlvect_1(A)) & (k1_rlvect_1(A) = k6_rlvect_1(A,C,k10_group_1(A,D,B)) -> B = k1_rlvect_1(A) | D = k10_group_1(A,C,k4_vectsp_1(A,B))))))))))) # label(t88_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5356 (all A (-v3_struct_0(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v7_vectsp_1(A) & v6_vectsp_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v4_rlvect_1(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k6_rlvect_1(B,D,E)) = k6_rlvect_1(B,k6_vectsp_1(A,B,C,D),k6_vectsp_1(A,B,C,E)))))))))))) # label(t70_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5357 (all A (l1_rlvect_1(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)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> k7_vectsp_1(A) = B))))) # label(d25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5358 $T # label(t29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5359 $T # label(d14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5360 $T # label(t47_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5361 (exists A (-v3_struct_0(A) & v1_vectsp_1(A) & l1_vectsp_1(A))) # label(rc3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5362 $T # label(t79_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5363 $T # label(t53_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5364 $T # label(t72_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5365 $T # label(t58_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5366 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> (v7_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) & k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D))))))))))) # label(d18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5367 (all A (v5_rlvect_1(A) & v4_group_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (v13_vectsp_1(A) <-> k1_rlvect_1(A) != k2_rlvect_1(A,k2_group_1(A),k2_group_1(A))))) # label(d29_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5368 $T # label(t77_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5369 $T # label(t25_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5370 $T # label(t54_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5371 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_rlvect_1(A,k1_rlvect_1(A),B) = k5_rlvect_1(A,B) & B = k6_rlvect_1(A,B,k1_rlvect_1(A)))))) # label(t65_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5372 $T # label(t17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5373 (exists A l2_vectsp_1(A)) # label(existence_l2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5374 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & -v10_vectsp_1(A) & v9_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k1_rlvect_1(A) != B -> k4_vectsp_1(A,k4_vectsp_1(A,B)) = B))))) # label(t73_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5375 (all A (v3_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k6_rlvect_1(A,B,D),C) = k6_rlvect_1(A,k6_rlvect_1(A,B,C),D))))))))) # label(t93_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5376 (all A all B all C all D all E (m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> l3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) & v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)))) # label(dt_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5377 $T # label(t51_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5378 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v6_vectsp_1(A) & v5_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & l4_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,k5_rlvect_1(B,D)) = k5_rlvect_1(B,k6_vectsp_1(A,B,C,D)))))))))) # label(t69_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5379 (all A (m1_subset_1(A,u1_struct_0(k3_vectsp_1)) -> (all B (m1_subset_1(B,u1_struct_0(k3_vectsp_1)) -> (all C (m1_subset_1(C,u1_struct_0(k3_vectsp_1)) -> k4_rlvect_1(k3_vectsp_1,A,k5_rlvect_1(k3_vectsp_1,A)) = k1_rlvect_1(k3_vectsp_1) & k10_group_1(k3_vectsp_1,B,A) = k10_group_1(k3_vectsp_1,A,B) & k10_group_1(k3_vectsp_1,k2_group_1(k3_vectsp_1),A) = A & k10_group_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,B,C),A) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,B,A),k10_group_1(k3_vectsp_1,C,A)) & k10_group_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) = k4_rlvect_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),k10_group_1(k3_vectsp_1,A,C)) & -(k1_rlvect_1(k3_vectsp_1) != A & (all D (m1_subset_1(D,u1_struct_0(k3_vectsp_1)) -> k10_group_1(k3_vectsp_1,A,D) != k2_group_1(k3_vectsp_1)))) & k10_group_1(k3_vectsp_1,k10_group_1(k3_vectsp_1,A,B),C) = k10_group_1(k3_vectsp_1,A,k10_group_1(k3_vectsp_1,B,C)) & A = k4_rlvect_1(k3_vectsp_1,A,k1_rlvect_1(k3_vectsp_1)) & k4_rlvect_1(k3_vectsp_1,k4_rlvect_1(k3_vectsp_1,A,B),C) = k4_rlvect_1(k3_vectsp_1,A,k4_rlvect_1(k3_vectsp_1,B,C)) & k4_rlvect_1(k3_vectsp_1,B,A) = k4_rlvect_1(k3_vectsp_1,A,B))))))) # label(t21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5380 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> k1_rlvect_1(A) = k6_rlvect_1(A,C,B)))))))) # label(t87_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5381 $T # label(t31_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5382 (all A (-v3_struct_0(A) & l2_vectsp_1(A) -> (k2_group_1(A) = k1_rlvect_1(A) <-> v10_vectsp_1(A)))) # label(d21_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5383 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k10_group_1(A,B,C) = k1_rlvect_1(A) <-> k1_rlvect_1(A) = B | k1_rlvect_1(A) = C))))))) # label(t44_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5384 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = k1_rlvect_1(A) -> k1_rlvect_1(A) = B))))) # label(t86_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5385 $T # label(d4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5386 (all A (l1_vectsp_1(A) -> m1_subset_1(k2_vectsp_1(A),u1_struct_0(A)))) # label(dt_k2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5387 $T # label(t9_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5388 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & v4_vectsp_1(A) & l3_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,k5_rlvect_1(A,C)) = k5_rlvect_1(A,k1_group_1(A,B,C)))))))) # label(t40_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5389 $T # label(t50_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5390 (all A (l1_vectsp_1(A) -> m1_subset_1(u1_vectsp_1(A),u1_struct_0(A)))) # label(dt_u1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5391 $T # label(t91_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5392 $T # label(d16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5393 $T # label(t82_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5394 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l3_vectsp_1(A) & v5_vectsp_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k1_group_1(A,B,C)) = k1_group_1(A,k5_rlvect_1(A,B),C))))))) # label(t41_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5395 $T # label(t16_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5396 $T # label(t24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5397 $T # label(t3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5398 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k1_group_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k1_group_1(A,C,B),k1_group_1(A,D,B)) & k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) & -(B != k1_rlvect_1(A) & (all E (m1_subset_1(E,u1_struct_0(A)) -> k2_group_1(A) != k1_group_1(A,B,E)))))))))) <-> -v3_struct_0(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A)))) # label(t22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5399 $T # label(t26_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5400 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,D,k5_rlvect_1(A,C))) = k6_rlvect_1(A,C,D) & k2_rlvect_1(A,D,k5_rlvect_1(A,C)) = k5_rlvect_1(A,k6_rlvect_1(A,C,D)) & k2_rlvect_1(A,D,C) = k5_rlvect_1(A,k6_rlvect_1(A,k5_rlvect_1(A,C),D)) & k6_rlvect_1(A,B,k2_rlvect_1(A,D,C)) = k6_rlvect_1(A,k6_rlvect_1(A,B,C),D) & k6_rlvect_1(A,k5_rlvect_1(A,D),C) = k5_rlvect_1(A,k2_rlvect_1(A,C,D)))))))))) # label(t64_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5401 $T # label(t18_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5402 (all A all B (l1_struct_0(A) & l4_vectsp_1(B,A) -> v1_funct_1(u2_vectsp_1(A,B)) & m2_relset_1(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)) & v1_funct_2(u2_vectsp_1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B)))) # label(dt_u2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5403 (all A (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k5_rlvect_1(A,B) = C <-> k1_rlvect_1(A) = k2_rlvect_1(A,B,C)))))))) # label(t63_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5404 $T # label(t2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5405 $T # label(t80_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5406 (all A (-v3_struct_0(A) & l3_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k2_rlvect_1(A,C,D)))))))) <-> v4_vectsp_1(A)))) # label(d11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5407 $T # label(d7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5408 $T # label(t37_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5409 (all A (l3_vectsp_1(A) -> (v3_vectsp_1(A) -> A = g3_vectsp_1(u1_struct_0(A),u1_rlvect_1(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A))))) # label(abstractness_v3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5410 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k6_rlvect_1(A,C,B) = k5_rlvect_1(A,k6_rlvect_1(A,B,C)))))))) # label(t81_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5411 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_1(E) & m1_subset_1(D,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) -> l4_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A))) # label(dt_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5412 $T # label(t85_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5413 $T # label(t46_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5414 $T # label(t34_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5415 (all A all B all C (m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all D all E all F (g1_vectsp_1(D,E,F) = g1_vectsp_1(A,B,C) -> B = E & C = F & D = A)))) # label(free_g1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5416 (all A (v6_rlvect_1(A) & l3_vectsp_1(A) & v5_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,k1_rlvect_1(A),B) = k1_rlvect_1(A))))) # label(t39_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5417 $T # label(d3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5418 $T # label(t8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5419 $T # label(d1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5420 $T # label(d10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5421 (all A (v5_rlvect_1(A) & v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v4_rlvect_1(C) & v6_rlvect_1(C) & l4_vectsp_1(C,A) & v12_vectsp_1(C,A) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_subset_1(D,u1_struct_0(C)) -> k6_vectsp_1(A,C,k1_rlvect_1(A),D) = k1_rlvect_1(C) & k6_vectsp_1(A,C,B,k1_rlvect_1(C)) = k1_rlvect_1(C) & k6_vectsp_1(A,C,k5_rlvect_1(A,k2_group_1(A)),D) = k5_rlvect_1(C,D))))))))) # label(t59_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5422 (exists A (l1_vectsp_1(A) & v1_vectsp_1(A))) # label(rc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5423 (all A (-v3_struct_0(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v7_group_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_vectsp_1(A,B,C) = k10_group_1(A,B,k4_vectsp_1(A,C)))))))) # label(d23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5424 $T # label(t27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5425 (exists A l1_vectsp_1(A)) # label(existence_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5426 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_rlvect_1(A,k2_rlvect_1(A,k5_rlvect_1(A,B),C)) = k2_rlvect_1(A,k5_rlvect_1(A,C),B))))))) # label(t92_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5427 $T # label(d5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5428 (all A (l3_vectsp_1(A) -> (-v3_struct_0(A) & v4_vectsp_1(A) & v5_vectsp_1(A) -> v7_vectsp_1(A) & -v3_struct_0(A)))) # label(cc2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5429 (exists A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v3_rlvect_1(A) & v1_rlvect_1(A) & l1_rlvect_1(A))) # label(rc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5430 $T # label(t71_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5431 $T # label(d27_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5432 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> (v6_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_group_1(A,B,k2_group_1(A)) = B))))) # label(d13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5433 (all A all B all C all D (m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_subset_1(C,A) & m1_subset_1(D,A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all E all F all G all H (g2_vectsp_1(A,B,C,D) = g2_vectsp_1(E,F,G,H) -> A = E & C = G & H = D & F = B)))) # label(free_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5434 $T # label(d8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5435 (all A (l1_struct_0(A) -> (exists B (l4_vectsp_1(B,A) & v11_vectsp_1(B,A))))) # label(rc11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5436 (all A (l1_struct_0(A) -> (all B (l4_vectsp_1(B,A) -> l1_rlvect_1(B))))) # label(dt_l4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5437 (all A (v6_rlvect_1(A) & v4_group_1(A) & v7_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A) -> (exists B (v3_rlvect_1(B) & v4_rlvect_1(B) & v11_vectsp_1(B,A) & v12_vectsp_1(B,A) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & l4_vectsp_1(B,A))))) # label(rc13_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5438 $T # label(t62_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5439 $T # label(t14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5440 (all A all B all C all D (v1_funct_1(B) & m1_subset_1(D,A) & m1_subset_1(C,A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) -> v2_vectsp_1(g2_vectsp_1(A,B,C,D)) & l2_vectsp_1(g2_vectsp_1(A,B,C,D)))) # label(dt_g2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5441 (all A (v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,C,D) = k6_rlvect_1(A,k2_rlvect_1(A,C,B),k2_rlvect_1(A,D,B)))))))))) # label(t90_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5442 (exists A (v2_vectsp_1(A) & l2_vectsp_1(A))) # label(rc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5443 $T # label(t10_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5444 $T # label(t83_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5445 $T # label(t28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5446 $T # label(t4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5447 $T # label(t32_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5448 (all A (-v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_group_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & l3_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> k1_rlvect_1(A) != k4_vectsp_1(A,B) & k1_rlvect_1(A) != k5_rlvect_1(A,k4_vectsp_1(A,B))))))) # label(t74_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5449 (exists A (v3_vectsp_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5450 (all A all B all C (v7_group_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v9_vectsp_1(A) & v8_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k5_vectsp_1(A,B,C),u1_struct_0(A)))) # label(dt_k5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5451 $T # label(t48_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5452 $T # label(t38_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5453 (all A (v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & v9_vectsp_1(A) & l3_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (B != k1_rlvect_1(A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C = k4_vectsp_1(A,B) <-> k2_group_1(A) = k10_group_1(A,B,C))))))))) # label(d22_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5454 $T # label(t52_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5455 $T # label(t35_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.81 5456 (all A all B all C all D all E (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_1(E) & m1_subset_1(D,B) & l1_struct_0(A) -> (all F all G all H all I all J (g4_vectsp_1(F,G,H,I,J) = g4_vectsp_1(A,B,C,D,E) -> E = J & D = I & C = H & G = B & A = F)))) # label(free_g4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5457 (exists A (l2_vectsp_1(A) & v2_vectsp_1(A) & -v3_struct_0(A))) # label(rc5_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5458 (all A all B (l1_struct_0(A) & l4_vectsp_1(B,A) -> (v11_vectsp_1(B,A) -> B = g4_vectsp_1(A,u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B),u2_vectsp_1(A,B))))) # label(abstractness_v11_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5459 $T # label(t15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5460 (all A (l2_vectsp_1(A) & -v3_struct_0(A) -> (v9_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> -((all C (m1_subset_1(C,u1_struct_0(A)) -> k1_group_1(A,B,C) != k2_group_1(A))) & k1_rlvect_1(A) != B)))))) # label(d20_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5461 (all A (l2_vectsp_1(A) -> (v2_vectsp_1(A) -> g2_vectsp_1(u1_struct_0(A),u1_group_1(A),u1_vectsp_1(A),u2_struct_0(A)) = A))) # label(abstractness_v2_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5462 (all A (l1_struct_0(A) & -v3_struct_0(A) -> (all B (l4_vectsp_1(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> k6_vectsp_1(A,B,C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D))))))))) # label(d24_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5463 (all A all B all C all D all E (v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & m1_subset_1(E,A) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> (all F all G all H all I all J (g3_vectsp_1(F,G,H,I,J) = g3_vectsp_1(A,B,C,D,E) -> A = F & G = B & I = D & J = E & H = C)))) # label(free_g3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5464 (all A (v7_group_1(A) & v7_vectsp_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & v9_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k10_group_1(A,B,C) = k10_group_1(A,B,D) -> k1_rlvect_1(A) = B | D = C))))))))) # label(t33_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5465 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (k1_rlvect_1(A) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) -> B = C) & (B = C -> k2_rlvect_1(A,B,k5_rlvect_1(A,C)) = k1_rlvect_1(A)) & (k1_rlvect_1(A) = k6_rlvect_1(A,B,C) -> C = B) & (C = B -> k6_rlvect_1(A,B,C) = k1_rlvect_1(A)))))))) # label(t66_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5466 $T # label(d17_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5467 (all A (l1_vectsp_1(A) -> (v6_vectsp_1(A) & v8_vectsp_1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v2_group_1(A)))) # label(cc4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5468 $T # label(t56_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5469 $T # label(t75_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5470 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> v1_funct_1(k7_vectsp_1(A)) & v1_funct_2(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_vectsp_1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5471 (all A (l1_vectsp_1(A) -> l1_group_1(A))) # label(dt_l1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5472 (all A (-v3_struct_0(A) & l1_vectsp_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> B = k1_group_1(A,k2_group_1(A),B))) <-> v8_vectsp_1(A)))) # label(d19_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5473 (all A all B (v7_group_1(A) & v8_vectsp_1(A) & l3_vectsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & v9_vectsp_1(A) & v7_vectsp_1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k4_vectsp_1(A,B),u1_struct_0(A)))) # label(dt_k4_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5474 $T # label(t23_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5475 (exists A (v3_rlvect_1(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & v2_group_1(A) & v4_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & v7_vectsp_1(A) & v9_vectsp_1(A) & -v10_vectsp_1(A) & v13_vectsp_1(A) & v8_vectsp_1(A) & v5_vectsp_1(A) & v7_group_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) & l3_vectsp_1(A))) # label(rc15_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5476 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k2_rlvect_1(A,C,B) = k2_rlvect_1(A,B,C) & (exists E (k1_rlvect_1(A) = k2_rlvect_1(A,B,E) & m1_subset_1(E,u1_struct_0(A)))) & k2_rlvect_1(A,B,k1_rlvect_1(A)) = B & k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)))))))) <-> v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) & v3_rlvect_1(A) & -v3_struct_0(A)))) # label(t7_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5477 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (v13_vectsp_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (k2_rlvect_1(A,B,B) = k1_rlvect_1(A) -> B = k1_rlvect_1(A))))))) # label(d28_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5478 (all A all B all C all D (-v3_struct_0(A) & l1_struct_0(A) & l4_vectsp_1(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & -v3_struct_0(B) -> m1_subset_1(k6_vectsp_1(A,B,C,D),u1_struct_0(B)))) # label(dt_k6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5479 (exists A (l1_rlvect_1(A) & v13_vectsp_1(A) & -v3_struct_0(A))) # label(rc14_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5480 $T # label(t1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5481 (exists A (-v3_struct_0(A) & v4_group_1(A) & v7_group_1(A) & l1_group_1(A))) # label(rc8_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5482 (exists A l3_vectsp_1(A)) # label(existence_l3_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5483 $T # label(t76_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5484 (all A (l3_vectsp_1(A) -> (-v3_struct_0(A) & v7_vectsp_1(A) -> v5_vectsp_1(A) & v4_vectsp_1(A) & -v3_struct_0(A)))) # label(cc1_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5485 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & l3_vectsp_1(A) & v4_vectsp_1(A) & v6_rlvect_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k6_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,D)) = k1_group_1(A,B,k6_rlvect_1(A,C,D)))))))))) # label(t43_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5486 (all A all B all C all D all E (l1_struct_0(A) & v1_funct_2(C,k2_zfmisc_1(B,B),B) & v1_funct_1(E) & m1_relset_1(E,k2_zfmisc_1(u1_struct_0(A),B),B) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),B),B) & m1_subset_1(D,B) & m1_relset_1(C,k2_zfmisc_1(B,B),B) & v1_funct_1(C) & -v1_xboole_0(B) -> v11_vectsp_1(g4_vectsp_1(A,B,C,D,E),A) & -v3_struct_0(g4_vectsp_1(A,B,C,D,E)))) # label(fc6_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5487 $T # label(t30_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5488 $T # label(t55_vectsp_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5489 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v3_compts_1(A) & v2_compts_1(A) -> v4_compts_1(A)))) # label(t21_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5490 (all A (l1_pre_topc(A) -> (v2_compts_1(A) <-> v6_compts_1(k2_pre_topc(A),A)))) # label(t10_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5491 $T # label(t6_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5492 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (v3_compts_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) & (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))) -> -(v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_tarski(B,E) & r1_xboole_0(D,E) & r2_hidden(C,D))))))))) | k1_xboole_0 = B)))))) # label(t15_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5493 $T # label(t1_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5494 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) & v3_compts_1(A) -> v4_pre_topc(B,A)))))) # label(t16_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5495 (all A (l1_pre_topc(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) & r1_xboole_0(D,E) & r2_hidden(B,D) & v3_pre_topc(E,A) & v3_pre_topc(D,A)))))) & C != B))))) <-> v3_compts_1(A)))) # label(d4_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5496 (all A (l1_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(C,k5_setfam_1(u1_struct_0(A),B)) <-> r1_compts_1(A,B,C)))))))) # label(d1_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5497 (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))) -> -(B != k1_xboole_0 & v4_pre_topc(B,A) & v4_pre_topc(C,A) & r1_xboole_0(B,C) & (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))) -> -(v3_pre_topc(E,A) & r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(D,E) & v3_pre_topc(D,A)))))) & C != k1_xboole_0))))) <-> v5_compts_1(A)))) # label(d6_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5498 $T # label(t4_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5499 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(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_compts_1(A) & v3_compts_1(B) & k2_pre_topc(A) = k1_relat_1(C) & k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & v5_pre_topc(C,A,B) -> v3_tops_2(C,A,B)))))))) # label(t26_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5500 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_compts_1(A) & v3_compts_1(B) & k2_pre_topc(B) = k2_relat_1(C) & v5_pre_topc(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(D,A) -> v4_pre_topc(k4_pre_topc(A,B,C,D),B))))))))))) # label(t25_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5501 $T # label(t8_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5502 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v2_compts_1(A) -> v6_compts_1(B,A)))))) # label(t17_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5503 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,C) & v1_finset_1(C) & r1_tarski(C,B)))) & v1_tops_2(B,A)))) <-> v2_compts_1(A)))) # label(d3_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5504 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_compts_1(A,C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_tarski(D,C) & r1_compts_1(A,D,B) & v1_finset_1(D)))) & v1_tops_2(C,A))))))))) # label(d7_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5505 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (k1_xboole_0 = B -> (v6_compts_1(B,A) <-> v2_compts_1(k3_pre_topc(A,B)))) & (v2_pre_topc(A) -> k1_xboole_0 = B | (v2_compts_1(k3_pre_topc(A,B)) <-> v6_compts_1(B,A))))))) # label(t12_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5506 (all A ((all B -(r1_tarski(B,A) & k1_xboole_0 = k1_setfam_1(B) & v1_finset_1(B) & k1_xboole_0 != B)) & A != k1_xboole_0 <-> v1_compts_1(A))) # label(d2_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5507 $T # label(t7_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5508 $T # label(t5_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5509 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> (v2_compts_1(A) & v5_pre_topc(C,A,B) & k2_pre_topc(B) = k2_relat_1(C) -> v2_compts_1(B)))))))) # label(t23_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5510 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(B != k1_xboole_0 & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(k1_xboole_0 != C & r1_tarski(C,B) & v1_finset_1(C) & k6_setfam_1(u1_struct_0(A),C) = k1_xboole_0))) & k1_xboole_0 = k6_setfam_1(u1_struct_0(A),B) & v2_tops_2(B,A)))) <-> v2_compts_1(A)))) # label(t14_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5511 (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))) -> (v6_compts_1(B,A) & v6_compts_1(C,A) -> v6_compts_1(k4_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t19_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5512 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (l1_pre_topc(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(C)) -> (v5_pre_topc(D,A,C) & k2_relat_1(D) = k2_pre_topc(C) & v6_compts_1(B,A) -> v6_compts_1(k4_pre_topc(A,C,D,B),C)))))))))) # label(t24_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5513 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) & v4_pre_topc(C,A) & r1_tarski(C,B) -> v6_compts_1(C,A)))))))) # label(t18_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5514 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v2_compts_1(A) <-> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(k1_xboole_0 = k6_setfam_1(u1_struct_0(A),B) & v2_tops_2(B,A) & v1_compts_1(B))))))) # label(t13_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5515 $T # label(t2_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5516 (all A (l1_pre_topc(A) -> v6_compts_1(k1_pre_topc(A),A))) # label(t9_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5517 (all A (l1_pre_topc(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))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,D) & r1_xboole_0(D,E) & r1_tarski(C,E) & v3_pre_topc(E,A) & v3_pre_topc(D,A)))))) & r2_hidden(B,k3_subset_1(u1_struct_0(A),C)) & v4_pre_topc(C,A) & k1_xboole_0 != C))))) <-> v4_compts_1(A)))) # label(d5_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5518 (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))) -> (r1_tarski(C,k2_pre_topc(B)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (D = C -> v6_compts_1(D,B)))) <-> v6_compts_1(C,A))))))))) # label(t11_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5519 $T # label(t3_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5520 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (v2_compts_1(A) & v3_compts_1(A) -> v5_compts_1(A)))) # label(t22_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5521 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v6_compts_1(B,A) & v6_compts_1(C,A) & v3_compts_1(A) -> v6_compts_1(k5_subset_1(u1_struct_0(A),B,C),A)))))))) # label(t20_compts_1) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5522 (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))) -> k2_orders_2(A,B) = a_2_1_orders_2(A,B))))) # label(d13_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5523 (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_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]. 183.60/184.82 5524 $T # label(t12_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5525 (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_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]. 183.60/184.82 5526 (all A all B all C (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_orders_2(A) & v3_orders_2(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]. 183.60/184.82 5527 $T # label(t105_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5528 $T # label(t53_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5529 $T # label(t126_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5530 (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))) & v5_orders_2(B,A) -> (exists C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,B) -> r3_orders_2(A,C,D)))) & m1_subset_1(C,u1_struct_0(A)))))) & (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,u1_struct_0(A)) & r2_orders_2(A,C,B)))))))) # label(t163_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5531 $T # label(t8_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5532 (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,k1_zfmisc_1(u1_struct_0(A))) -> -(-(k1_xboole_0 = B & C = k1_xboole_0) & m1_orders_2(C,A,B) & m1_orders_2(B,A,C)))))))) # label(t69_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5533 (exists 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(rc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5534 $T # label(t33_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5535 (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,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]. 183.60/184.82 5536 (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))) -> (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]. 183.60/184.82 5537 (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))) -> m2_orders_2(k3_tarski(k4_orders_2(A,B)),A,B))))) # label(t89_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5538 $T # label(t20_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5539 (all A (-v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) -> k1_xboole_0 = k1_orders_2(A,k2_pre_topc(A)))) # label(t44_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5540 $T # label(t93_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5541 $T # label(d1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5542 (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)) -> (all C (m1_orders_1(C,k1_orders_1(u1_struct_0(A))) -> (all D (m2_orders_2(D,A,C) -> (B = k1_funct_1(C,u1_struct_0(A)) -> k1_xboole_0 = k3_orders_2(A,D,B)))))))))) # label(t81_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5543 (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,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]. 183.60/184.82 5544 (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_orders_2(A,B,C) & r2_orders_2(A,C,B)))))))) # label(t28_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5545 $T # label(t63_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5546 (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)) -> -r2_hidden(B,k1_orders_2(A,k1_struct_0(A,B))))))) # label(t48_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5547 $T # label(t100_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5548 (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,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]. 183.60/184.82 5549 $T # label(t143_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5550 (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) & (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & r2_hidden(B,D) & v5_orders_2(D,A)))) & -((all D (v5_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,D) & r2_hidden(C,D)))) & (r1_orders_2(A,C,B) | r1_orders_2(A,B,C))))))))) # label(t38_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5551 $T # label(t41_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5552 (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,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))) -> (m1_orders_2(C,A,D) & r2_hidden(B,C) -> k3_orders_2(A,C,B) = k3_orders_2(A,D,B)))))))))) # label(t71_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5553 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_orders_2(A) & v3_orders_2(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]. 183.60/184.82 5554 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r7_relat_2(u1_orders_2(A),B) <-> v5_orders_2(B,A)))))) # label(d11_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5555 (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) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A)))))) # label(t40_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5556 $T # label(t133_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5557 $T # label(t102_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5558 $T # label(t76_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5559 (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]. 183.60/184.82 5560 $T # label(t75_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5561 $T # label(t132_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5562 (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_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) -> (C != D -> (m1_orders_2(C,A,D) <-> -m1_orders_2(D,A,C))))))))))) # label(t83_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5563 $T # label(t90_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5564 $T # label(t7_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5565 (all A (l1_orders_2(A) -> (v2_orders_2(A) <-> r1_relat_2(u1_orders_2(A),u1_struct_0(A))))) # label(d4_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5566 $T # label(t95_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5567 (all A all B (-v3_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & m1_orders_1(B,k1_orders_1(u1_struct_0(A))) & l1_orders_2(A) & v2_orders_2(A) -> (exists C m2_orders_2(C,A,B)))) # label(existence_m2_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5568 $T # label(t142_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5569 (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]. 183.60/184.82 5570 $T # label(t131_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5571 $T # label(t23_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5572 (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_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]. 183.60/184.82 5573 (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))) -> (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))) & (B = k1_xboole_0 -> (m1_orders_2(C,A,B) <-> k1_xboole_0 = C)))))))) # label(d15_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5574 $T # label(t2_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5575 $T # label(t127_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5576 (exists A l1_orders_2(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5577 $T # label(t145_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5578 $T # label(t103_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5579 $T # label(t59_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5580 $T # label(t6_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5581 $T # label(t128_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5582 $T # label(t156_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5583 (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]. 183.60/184.82 5584 $T # label(t149_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5585 (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]. 183.60/184.82 5586 $T # label(t98_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5587 (all A (v2_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)) -> ((-r1_orders_2(A,C,B) <-> r2_orders_2(A,B,C)) <-> (exists D (v5_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r2_hidden(C,D)))))))))) # label(t39_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5588 $T # label(d2_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5589 $T # label(t122_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5590 $T # label(t106_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5591 (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)) -> (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]. 183.60/184.82 5592 $T # label(t19_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5593 $T # label(t11_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5594 (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]. 183.60/184.82 5595 $T # label(t134_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5596 $T # label(t58_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5597 $T # label(t115_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5598 (all A all B (v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_relat_2(B) -> v1_orders_2(g1_orders_2(A,B)) & v2_orders_2(g1_orders_2(A,B)) & v3_orders_2(g1_orders_2(A,B)) & v4_orders_2(g1_orders_2(A,B)))) # label(fc3_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5599 (all A all B (m1_relset_1(B,A,A) & -v1_xboole_0(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]. 183.60/184.82 5600 (all A (v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & -v3_struct_0(A) -> u1_struct_0(A) = k2_orders_2(A,k1_pre_topc(A)))) # label(t45_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5601 $T # label(t101_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5602 $T # label(t139_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5603 (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))) & v4_orders_2(A) & -v3_struct_0(A) -> (exists C m1_orders_2(C,A,B)))) # label(existence_m1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5604 $T # label(t144_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5605 $T # label(t124_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5606 (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))) -> (all C (m1_orders_2(C,A,B) -> r1_tarski(C,B))))))) # label(t67_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5607 $T # label(d3_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.82 5608 (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) -> -v1_xboole_0(k4_orders_2(A,B)))) # label(fc5_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5609 (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_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]. 183.60/184.83 5610 (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)) -> -r2_hidden(B,k2_orders_2(A,k1_struct_0(A,B))))))) # label(t50_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5611 $T # label(t152_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5612 $T # label(dt_k4_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5613 (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_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]. 183.60/184.83 5614 (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,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) -> (k1_funct_1(D,u1_struct_0(A)) = C & r2_hidden(B,E) -> r3_orders_2(A,C,B)))))))))))) # label(t80_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5615 (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_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]. 183.60/184.83 5616 $T # label(t148_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5617 $T # label(t1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5618 $T # label(t141_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5619 $T # label(t104_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5620 $T # label(t111_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5621 (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,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) & B != C & (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_hidden(D,C) & r2_orders_2(A,D,E) -> r2_hidden(D,B))))))))))))) # label(t73_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5622 (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 & B = D)))) # label(free_g1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5623 (all A (v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) -> (all B (v5_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> r3_orders_1(u1_orders_2(A),B))))) # label(t136_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5624 $T # label(t114_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5625 (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) & C != B <-> r2_orders_2(A,B,C)))))))) # label(d10_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5626 $T # label(t10_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5627 $T # label(t18_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5628 $T # label(t125_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5629 $T # label(t55_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5630 $T # label(t119_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5631 (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))) & v4_orders_2(A) & -v3_struct_0(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]. 183.60/184.83 5632 $T # label(t150_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5633 (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)) -> (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]. 183.60/184.83 5634 $T # label(t91_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5635 $T # label(t151_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5636 $T # label(t94_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5637 $T # label(t120_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5638 (all A (l1_orders_2(A) -> (r8_relat_2(u1_orders_2(A),u1_struct_0(A)) <-> v3_orders_2(A)))) # label(d5_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5639 (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_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]. 183.60/184.83 5640 $T # label(t34_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5641 $T # label(t3_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5642 (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]. 183.60/184.83 5643 $T # label(t77_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5644 (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]. 183.60/184.83 5645 (all 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_subset_1(D,u1_struct_0(A)) -> (r2_orders_2(A,B,C) & r1_orders_2(A,C,D) | r1_orders_2(A,B,C) & r2_orders_2(A,C,D) -> r2_orders_2(A,B,D)))))))))) # label(t32_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5646 (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)) -> k1_xboole_0 = k3_orders_2(A,k1_pre_topc(A),B))))) # label(t60_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5647 $T # label(t21_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5648 $T # label(t85_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5649 (all A (v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_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]. 183.60/184.83 5650 (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,B,C) & r2_orders_2(A,C,B)))))))) # label(t30_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5651 $T # label(t86_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5652 (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)) -> (r7_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> -r2_orders_2(A,C,B)))))))) # label(t158_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5653 $T # label(t110_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5654 $T # label(t4_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5655 $T # label(t146_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5656 $T # label(t117_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5657 $T # label(t140_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5658 $T # label(t157_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5659 $T # label(t15_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5660 (all A all B all C (-v3_struct_0(B) & 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) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & (all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,E,D)))) & A = D)) <-> r2_hidden(A,a_2_0_orders_2(B,C))))) # label(fraenkel_a_2_0_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5661 (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_orders_2(A) & -v3_struct_0(A) -> (r1_orders_2(A,B,C) <-> r3_orders_2(A,B,C)))) # label(redefinition_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5662 $T # label(t97_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5663 (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))) -> -r2_hidden(B,k3_orders_2(A,C,B)))))))) # label(t62_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5664 (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]. 183.60/184.83 5665 $T # label(t14_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5666 $T # label(t155_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5667 (exists A (v1_orders_2(A) & l1_orders_2(A))) # label(rc1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5668 $T # label(t137_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5669 (all A (v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v3_orders_2(A) & -v3_struct_0(A) -> k1_orders_2(A,k1_pre_topc(A)) = u1_struct_0(A))) # label(t43_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5670 $T # label(t9_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5671 $T # label(t112_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5672 $T # label(t154_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5673 $T # label(t66_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5674 (all A (l1_orders_2(A) -> l1_struct_0(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5675 $T # label(t123_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5676 $T # label(t16_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5677 (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_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(C,A) -> (m2_orders_2(C,A,B) <-> k1_xboole_0 != C & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> k1_funct_1(B,k1_orders_2(A,k3_orders_2(A,C,D))) = D))) & r2_wellord1(u1_orders_2(A),C)))))))) # label(d16_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5678 (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,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_orders_2(A,B,C) & m1_orders_2(E,A,D) & r2_hidden(C,E) & r2_hidden(B,D) -> r2_hidden(B,E)))))))))))) # label(t70_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5679 (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]. 183.60/184.83 5680 $T # label(t129_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5681 (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]. 183.60/184.83 5682 (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))) -> -(B = k1_xboole_0 & -m1_orders_2(B,A,B)) & -(k1_xboole_0 != B & m1_orders_2(B,A,B)))))) # label(t68_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5683 (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))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(-m1_orders_2(B,A,C) & B != 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)))))) & r2_wellord1(u1_orders_2(A),C) & r1_tarski(B,C)))))))) # label(t72_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5684 $T # label(t42_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5685 $T # label(t5_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5686 (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_orders_1(B,k1_orders_1(u1_struct_0(A))) -> (all C (C = k4_orders_2(A,B) <-> (all D (r2_hidden(D,C) <-> m2_orders_2(D,A,B))))))))) # label(d17_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5687 (all A all B all C (v2_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & -v3_struct_0(A) -> r3_orders_2(A,B,B))) # label(reflexivity_r3_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5688 (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_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k3_orders_2(A,B,C) = k5_subset_1(u1_struct_0(A),k2_orders_2(A,k1_struct_0(A,C)),B))))))) # label(d14_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5689 (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,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]. 183.60/184.83 5690 $T # label(t17_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5691 (all A (l1_orders_2(A) -> (v4_orders_2(A) <-> r4_relat_2(u1_orders_2(A),u1_struct_0(A))))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5692 (all A all B all C (l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> -r2_orders_2(A,B,B))) # label(irreflexivity_r2_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5693 $T # label(t92_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5694 $T # label(t96_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5695 (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))) -> B = k3_relat_1(k2_wellord1(u1_orders_2(A),B)))))) # label(t107_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5696 $T # label(t99_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5697 $T # label(t113_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5698 $T # label(t27_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5699 (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))) & v4_orders_2(B) & v3_orders_2(B) & v2_orders_2(B) -> ((exists D ((all E (m1_subset_1(E,u1_struct_0(B)) -> (r2_hidden(E,C) -> r2_orders_2(B,D,E)))) & D = A & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_1_orders_2(B,C))))) # label(fraenkel_a_2_1_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.60/184.83 5700 (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))) -> a_2_0_orders_2(A,B) = k1_orders_2(A,B))))) # label(d12_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5701 $T # label(t116_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5702 (all A (v2_orders_2(A) & l1_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]. 183.69/184.83 5703 (all A all B (-v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_orders_2(A) & v3_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]. 183.69/184.83 5704 $T # label(t121_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5705 (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(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]. 183.69/184.83 5706 $T # label(t74_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5707 (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)) -> (r9_orders_1(u1_orders_2(A),B) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (C != B -> r2_orders_2(A,B,C))))))))) # label(t161_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5708 (all A (v2_orders_2(A) & l1_orders_2(A) & v4_orders_2(A) & v3_orders_2(A) -> v1_relat_2(u1_orders_2(A)) & v8_relat_2(u1_orders_2(A)) & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) & v4_relat_2(u1_orders_2(A)) & v1_relat_1(u1_orders_2(A)))) # label(fc2_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5709 $T # label(t147_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5710 (all A (l1_orders_2(A) & v4_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)) -> (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]. 183.69/184.83 5711 $T # label(t118_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5712 $T # label(t153_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5713 (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,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) -> (k3_tarski(k4_orders_2(A,C)) = B -> D = k3_tarski(k4_orders_2(A,C)) | m1_orders_2(D,A,B)))))))))) # label(t88_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5714 $T # label(t54_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5715 (all 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_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,k2_orders_2(B,k1_struct_0(B,C))) & r2_hidden(A,D)))))))) # label(t56_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5716 $T # label(d8_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5717 $T # label(d7_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5718 (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))) -> (v3_orders_1(k2_wellord1(u1_orders_2(A),B)) -> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_orders_2(B,A)))))) # label(t108_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5719 $T # label(t130_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5720 (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_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]. 183.69/184.83 5721 $T # label(t31_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5722 (all A all B (-v3_struct_0(A) & 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) -> (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]. 183.69/184.83 5723 (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))) -> -(r2_hidden(B,k2_orders_2(A,C)) & r2_hidden(B,C)))))))) # label(t49_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5724 $T # label(t13_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5725 $T # label(t22_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5726 $T # label(t138_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5727 (all A (l1_orders_2(A) -> v1_xboole_0(k1_pre_topc(A)) & v2_membered(k1_pre_topc(A)) & v4_membered(k1_pre_topc(A)) & v5_orders_2(k1_pre_topc(A),A) & v5_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]. 183.69/184.83 5728 (all A (-v3_struct_0(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)) -> (r3_orders_2(A,B,C) | r3_orders_2(A,C,B) <-> 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)))))))))) # label(t36_orders_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5729 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (v3_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (np__0 = k1_metric_1(A,A,B,C,D) -> C = D)))))))) # label(d4_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5730 (all A (l1_metric_1(A) -> v1_funct_2(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & v1_funct_1(u1_metric_1(A)))) # label(dt_u1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5731 $T # label(t7_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5732 (all A (v1_xreal_0(A) -> (all B (-v3_struct_0(B) & l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k11_metric_1(B,C,A) = a_3_2_metric_1(A,B,C))))))) # label(t20_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5733 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v4_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> k1_metric_1(A,A,B,C,D) = k1_metric_1(A,A,B,D,C)))))))) # label(d5_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5734 (all A (v6_metric_1(k6_metric_1(A)) & v7_metric_1(k6_metric_1(A)) & v8_metric_1(k6_metric_1(A)) & v9_metric_1(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(fc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5735 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (np__0 = k2_metric_1(A,B,C) -> B = C))))) <-> v7_metric_1(A)))) # label(t2_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5736 (all A (l1_metric_1(A) -> (v8_metric_1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_metric_1(A,B,C) = k2_metric_1(A,C,B)))))))) # label(t3_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5737 (all A (l1_metric_1(A) -> (v8_metric_1(A) <-> v4_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d9_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5738 (all A (v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v6_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_xreal_0(np__0,k4_metric_1(A,B,C)))))))) # label(t5_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5739 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) & l1_metric_1(A) -> m1_subset_1(k9_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k9_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5740 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> a_3_1_metric_1(A,B,C) = k10_metric_1(B,C,A))))))) # label(t19_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5741 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v2_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> np__0 = k1_metric_1(A,A,B,C,C)))))) # label(d3_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5742 (all A all B all C all D (-v3_struct_0(C) & m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) & v1_xreal_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & -r1_xreal_0(B,k2_metric_1(C,D,E)) & A = E)) <-> r2_hidden(A,a_3_0_metric_1(B,C,D))))) # label(fraenkel_a_3_0_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5743 (all A k6_metric_1(A) = g1_metric_1(A,k5_metric_1(A))) # label(d12_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5744 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(D,k9_metric_1(B,C,A)) <-> -v3_struct_0(B) & -r1_xreal_0(A,k2_metric_1(B,C,D))))))))))) # label(t12_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5745 (all A (l1_metric_1(A) -> (v3_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v7_metric_1(A)))) # label(d8_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5746 (all A all B all C all D (v1_xreal_0(B) & m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) & -v3_struct_0(C) -> (r2_hidden(A,a_3_2_metric_1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(C)) & A = E & B = k2_metric_1(C,D,E)))))) # label(fraenkel_a_3_2_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5747 (all A all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (v5_metric_1(B,A) <-> (all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E)))))))))))) # label(d6_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5748 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (r2_hidden(D,k10_metric_1(B,C,A)) <-> r1_xreal_0(k2_metric_1(B,C,D),A) & -v3_struct_0(B)))))))))) # label(t13_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5749 (exists A (v1_metric_1(A) & l1_metric_1(A))) # label(rc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5750 (all A all B (m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> l1_metric_1(g1_metric_1(A,B)) & v1_metric_1(g1_metric_1(A,B)))) # label(dt_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5751 (all A all B all C (m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k2_metric_1(A,B,C),k1_numbers))) # label(dt_k2_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5752 (exists A (v1_metric_1(A) & v6_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) & v7_metric_1(A) & -v3_struct_0(A) & l1_metric_1(A))) # label(rc3_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5753 (all A all B all C all D (m1_subset_1(D,u1_struct_0(C)) & l1_metric_1(C) & -v3_struct_0(C) & v1_xreal_0(B) -> (r2_hidden(A,a_3_1_metric_1(B,C,D)) <-> (exists E (E = A & r1_xreal_0(k2_metric_1(C,D,E),B) & m1_subset_1(E,u1_struct_0(C))))))) # label(fraenkel_a_3_1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5754 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (all C all D (g1_metric_1(C,D) = g1_metric_1(A,B) -> C = A & B = D)))) # label(free_g1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5755 (all A (l1_metric_1(A) -> (v1_metric_1(A) -> g1_metric_1(u1_struct_0(A),u1_metric_1(A)) = A))) # label(abstractness_v1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5756 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_struct_0(A) -> (D = k9_metric_1(A,B,C) <-> v1_xboole_0(D))) & (-v3_struct_0(A) -> (D = k9_metric_1(A,B,C) <-> (exists E (l1_metric_1(E) & (exists F (m1_subset_1(F,u1_struct_0(E)) & A = E & D = a_3_0_metric_1(C,E,F) & B = F)) & -v3_struct_0(E))))))))))))) # label(d15_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5757 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> r1_xreal_0(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B),k3_real_1(k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,C),k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,C,B))))))))) # label(t11_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5758 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (-v3_struct_0(A) -> ((exists E (-v3_struct_0(E) & (exists F (a_3_1_metric_1(C,E,F) = D & B = F & E = A & m1_subset_1(F,u1_struct_0(E)))) & l1_metric_1(E))) <-> k10_metric_1(A,B,C) = D)) & (v3_struct_0(A) -> (D = k10_metric_1(A,B,C) <-> v1_xboole_0(D))))))))))) # label(d16_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5759 (all A (l1_metric_1(A) -> (v5_metric_1(u1_metric_1(A),u1_struct_0(A)) <-> v9_metric_1(A)))) # label(d10_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5760 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) -> m1_subset_1(k10_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k10_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5761 (all A all B all C (v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> k4_metric_1(A,B,C) = k2_metric_1(A,B,C))) # label(redefinition_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5762 (all A (v1_funct_1(k5_metric_1(A)) & m2_relset_1(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(k5_metric_1(A),k2_zfmisc_1(A,A),k1_numbers))) # label(dt_k5_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5763 (all A all B all C all D all E (m1_subset_1(E,B) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) & v1_funct_1(C) -> m1_subset_1(k1_metric_1(A,B,C,D,E),k1_numbers))) # label(dt_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5764 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (D != C -> np__1 = k1_metric_1(A,A,B,C,D)) & np__0 = k1_metric_1(A,A,B,C,C))))) <-> k5_metric_1(A) = B))) # label(d11_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5765 (all A (v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_funct_1(A) -> (k7_metric_1 = A <-> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> k1_metric_1(k1_numbers,k1_numbers,A,B,C) = k18_complex1(k5_real_1(B,C))))))))) # label(d13_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5766 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k4_subset_1(u1_struct_0(B),k11_metric_1(B,C,A),k9_metric_1(B,C,A)) = k10_metric_1(B,C,A))))))) # label(t17_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5767 (all A (l1_metric_1(A) -> l1_struct_0(A))) # label(dt_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5768 (all A (l1_metric_1(A) -> (v6_metric_1(A) <-> v2_metric_1(u1_metric_1(A),u1_struct_0(A))))) # label(d7_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5769 (exists A (-v3_struct_0(A) & v1_metric_1(A) & l1_metric_1(A))) # label(rc2_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5770 (all A all B all C all D all E (v1_funct_1(C) & m1_subset_1(E,B) & m1_subset_1(D,A) & m1_relset_1(C,k2_zfmisc_1(A,B),k1_numbers) -> k1_binop_1(C,D,E) = k1_metric_1(A,B,C,D,E))) # label(redefinition_k1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5771 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k9_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t15_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5772 (all A all B all C (l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & v8_metric_1(A) -> k4_metric_1(A,B,C) = k4_metric_1(A,C,B))) # label(commutativity_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5773 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (-v3_struct_0(B) & A = k2_metric_1(B,C,D) <-> r2_hidden(D,k11_metric_1(B,C,A))))))))))) # label(t14_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5774 (all A (-v1_xboole_0(A) -> -v3_struct_0(k6_metric_1(A)) & v1_metric_1(k6_metric_1(A)))) # label(fc1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5775 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B) = k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,B,A))))) # label(t10_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5776 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_struct_0(A) -> (k11_metric_1(A,B,C) = D <-> v1_xboole_0(D))) & (-v3_struct_0(A) -> (D = k11_metric_1(A,B,C) <-> (exists E (l1_metric_1(E) & (exists F (m1_subset_1(F,u1_struct_0(E)) & a_3_2_metric_1(C,E,F) = D & B = F & E = A)) & -v3_struct_0(E))))))))))))) # label(d17_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5777 (all A (l1_metric_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)) -> (np__0 = k2_metric_1(A,B,C) -> B = C) & (C = B -> np__0 = k2_metric_1(A,B,C)) & r1_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D))) & k2_metric_1(A,C,B) = k2_metric_1(A,B,C))))))) -> v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) & v7_metric_1(A) & v6_metric_1(A)))) # label(t6_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5778 (exists A l1_metric_1(A)) # label(existence_l1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5779 (all A (l1_metric_1(A) -> ((all B (m1_subset_1(B,u1_struct_0(A)) -> np__0 = k2_metric_1(A,B,B))) <-> v6_metric_1(A)))) # label(t1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5780 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_metric_1(u1_struct_0(A),u1_struct_0(A),u1_metric_1(A),B,C) = k2_metric_1(A,B,C))))))) # label(d1_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5781 $T # label(t8_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5782 (all A (m1_subset_1(A,k1_numbers) -> (all B (m1_subset_1(B,k1_numbers) -> (k1_metric_1(k1_numbers,k1_numbers,k7_metric_1,A,B) = np__0 <-> B = A))))) # label(t9_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5783 (all A (v1_metric_1(k6_metric_1(A)) & l1_metric_1(k6_metric_1(A)))) # label(dt_k6_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5784 (all A all B all C (v1_xreal_0(C) & m1_subset_1(B,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k11_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k11_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.83 5785 (all A all B all C (v8_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_metric_1(A) -> m1_subset_1(k4_metric_1(A,B,C),k1_numbers))) # label(dt_k4_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5786 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> r1_tarski(k11_metric_1(B,C,A),k10_metric_1(B,C,A)))))))) # label(t16_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5787 (all A (l1_metric_1(A) -> (v9_metric_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_xreal_0(k2_metric_1(A,B,D),k3_real_1(k2_metric_1(A,B,C),k2_metric_1(A,C,D)))))))))))) # label(t4_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5788 (all A (v1_xreal_0(A) -> (all B (l1_metric_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k9_metric_1(B,C,A) = a_3_0_metric_1(A,B,C))))))) # label(t18_metric_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5789 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,F,k10_cat_1(B,E))) = k8_funct_2(u2_cat_1(A),u2_cat_1(C),k15_cat_2(A,B,C,D,E),F))))))))))))) # label(t50_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5790 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> m2_cat_1(k17_cat_2(A,B),k11_cat_2(A,B),B))) # label(dt_k17_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5791 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (-v1_xboole_0(C) -> (m1_cat_2(C,A,B) <-> (all D (m1_subset_1(D,C) -> m2_cat_1(D,A,B)))))))))) # label(d3_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5792 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> m2_cat_1(k10_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),B))))) # label(t55_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5793 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> k17_cat_2(A,B) = k10_funct_3(u2_cat_1(A),u2_cat_1(B)))))) # label(d11_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5794 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> v10_cat_1(k8_cat_2(A,B),B,A))))) # label(t24_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5795 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k9_funct_3(u2_cat_1(A),u2_cat_1(B)),k11_cat_2(A,B),A))))) # label(t54_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5796 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> k12_cat_2(B,C,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,D),F),k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,E),F)) = k8_funct_2(u1_cat_1(A),u1_cat_1(k11_cat_2(B,C)),k12_cat_1(A,k11_cat_2(B,C),k18_cat_2(A,B,C,D,E)),F))))))))))))) # label(t63_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5797 (all A all B all C all D (v2_cat_1(B) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> k4_tarski(C,D) = k12_cat_2(A,B,C,D))) # label(redefinition_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5798 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k10_pboole(u2_cat_1(A),k10_cat_1(B,C)) = k4_cat_2(A,B,C))))))) # label(d1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5799 (all A all B all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) & l1_cat_1(B) & v2_cat_1(B) -> (r2_hidden(A,a_2_0_cat_2(B,C)) <-> (exists D exists E (m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(E,u1_cat_1(B)) & k6_cat_1(B,D,E) = A & r2_hidden(D,C) & r2_hidden(E,C)))))) # label(fraenkel_a_2_0_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5800 $T # label(t32_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5801 (all A all B all C all D all E all F (m1_fraenkel(D,B,C) & v1_funct_1(E) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_2(E,A,D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> m2_fraenkel(k1_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5802 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F) = k18_cat_2(k11_cat_2(A,C),B,D,k14_cat_1(k11_cat_2(A,C),A,B,k16_cat_2(A,C),E),k14_cat_1(k11_cat_2(A,C),C,D,k17_cat_2(A,C),F)))))))))))))) # label(t64_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5803 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(k11_cat_2(A,B))) -> (exists D ((exists E (C = k12_cat_2(A,B,D,E) & m1_subset_1(E,u1_cat_1(B)))) & m1_subset_1(D,u1_cat_1(A)))))))))) # label(t35_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5804 (all A all B all C all D all E all F (-v1_xboole_0(B) & v1_funct_1(E) & v1_funct_2(E,A,C) & v1_funct_1(F) & v1_funct_2(F,B,D) & m1_relset_1(F,B,D) & m1_relset_1(E,A,C) & -v1_xboole_0(D) & -v1_xboole_0(C) & -v1_xboole_0(A) -> k15_funct_3(E,F) = k9_cat_2(A,B,C,D,E,F))) # label(redefinition_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5805 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (m3_cat_2(B,A) <-> r1_tarski(u1_cat_1(B),u1_cat_1(A)) & (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (E = C & D = F -> r1_tarski(k6_cat_1(B,C,D),k6_cat_1(A,E,F))))))))))) & r1_tarski(u5_cat_1(B),u5_cat_1(A)) & (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (C = D -> k10_cat_1(B,C) = k10_cat_1(A,D))))))))))) # label(d4_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5806 (all A all B all C all D (-v1_xboole_0(B) & v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & -v1_xboole_0(A) -> k3_funct_4(C,D) = k10_cat_2(A,B,C,D))) # label(redefinition_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5807 $T # label(t26_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5808 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> D = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(B),k12_cat_1(k11_cat_2(A,B),B,k17_cat_2(A,B)),k12_cat_2(A,B,C,D)))))))))) # label(t61_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5809 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)) = u2_cat_1(k11_cat_2(A,B)) & k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)) = u5_cat_1(k11_cat_2(A,B)) & k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B)) = u6_cat_1(k11_cat_2(A,B)) & u4_cat_1(k11_cat_2(A,B)) = k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)) & k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)) = u3_cat_1(k11_cat_2(A,B)) & u1_cat_1(k11_cat_2(A,B)) = k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)))))) # label(t33_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5810 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (k3_tarski(a_2_0_cat_2(A,B)) = C -> v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B) & v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C)) & m2_relset_1(k1_realset1(u5_cat_1(A),C),k2_zfmisc_1(C,C),C) & m2_relset_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & v1_funct_2(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B),B,C) & v1_funct_1(k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B)) & v1_funct_1(k1_realset1(u5_cat_1(A),C)) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & v1_funct_2(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C),C,B) & m2_relset_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C),C,B) & v1_funct_1(k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C))))))))) # label(t29_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5811 (all A all B all C (v2_cat_1(A) & m1_subset_1(C,u1_cat_1(B)) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> m2_cat_1(k4_cat_2(A,B,C),A,B))) # label(dt_k4_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5812 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> m1_subset_1(C,u1_cat_1(A)))))))) # label(t12_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5813 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (C = D -> k3_cat_1(B,C) = k3_cat_1(A,D) & k2_cat_1(A,D) = k2_cat_1(B,C)))))))))) # label(t15_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5814 (all A all B all C all D (l1_cat_1(A) & v2_cat_1(B) & m1_subset_1(D,u2_cat_1(B)) & m1_subset_1(C,u2_cat_1(A)) & l1_cat_1(B) & v2_cat_1(A) -> m1_subset_1(k13_cat_2(A,B,C,D),u2_cat_1(k11_cat_2(A,B))))) # label(dt_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5815 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,C,B) & v1_funct_2(D,C,B) -> (all E (v1_funct_2(E,C,B) & m2_relset_1(E,C,B) & v1_funct_1(E) -> (all F (m2_relset_1(F,k2_zfmisc_1(C,C),C) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,B,C) & v1_funct_2(G,B,C) -> (r1_cat_2(g1_cat_1(B,C,D,E,F,G),A) -> k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = D & k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) = E & k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) = G & F = k1_realset1(u5_cat_1(A),C) & k3_tarski(a_2_0_cat_2(A,B)) = C))))))))))))))) # label(t31_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5816 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> l1_cat_1(B) & v2_cat_1(B))))) # label(dt_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5817 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,A,B) -> (all E (m2_cat_1(E,A,C) -> m2_cat_1(k14_funct_3(u2_cat_1(A),u2_cat_1(B),u2_cat_1(C),D,E),A,k11_cat_2(B,C)))))))))))) # label(t62_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5818 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m2_relset_1(D,C,B) & v1_funct_2(D,C,B) & v1_funct_1(D) -> (all E (v1_funct_2(E,C,B) & m2_relset_1(E,C,B) & v1_funct_1(E) -> (all F (v1_funct_1(F) & m2_relset_1(F,k2_zfmisc_1(C,C),C) -> (all G (v1_funct_1(G) & v1_funct_2(G,B,C) & m2_relset_1(G,B,C) -> (k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),C) = D & E = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),C) & F = k1_realset1(u5_cat_1(A),C) & G = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B) & C = k3_tarski(a_2_0_cat_2(A,B)) -> r1_cat_2(g1_cat_1(B,C,D,E,F,G),A)))))))))))))))) # label(t30_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5819 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C ((all D (m2_cat_1(D,A,B) <-> r2_hidden(D,C))) <-> C = k5_cat_2(A,B))))))) # label(d2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5820 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k13_cat_1(B,A,k8_cat_2(A,B),C) = C)))))) # label(t23_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5821 (all A (l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (r1_cat_2(A,B) <-> m3_cat_2(A,B) & (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (F = D & C = E -> k6_cat_1(A,C,D) = k6_cat_1(B,E,F))))))))))))))) # label(d6_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5822 (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,k2_zfmisc_1(A,B),C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) -> v1_funct_2(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) & m2_relset_1(k2_cat_2(A,B,C,D),A,k1_fraenkel(B,C)) & v1_funct_1(k2_cat_2(A,B,C,D)))) # label(dt_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5823 (all A all B all C all D all E all F (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & v2_cat_1(D) & l1_cat_1(D) & m2_cat_1(F,B,D) & m2_cat_1(E,A,C) & l1_cat_1(C) & v2_cat_1(A) -> m2_cat_1(k19_cat_2(A,B,C,D,E,F),k11_cat_2(A,B),k11_cat_2(C,D)))) # label(dt_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5824 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> k15_cat_1(B) = k8_cat_2(A,B))))) # label(d5_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5825 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(C),k14_cat_2(A,B,C,D,E),F) = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(C),D,k13_cat_2(A,B,k10_cat_1(A,E),F)))))))))))))) # label(t47_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5826 (all A all B all C all D all E (v2_cat_1(A) & v2_cat_1(B) & v2_cat_1(C) & m2_cat_1(E,A,C) & m2_cat_1(D,A,B) & l1_cat_1(C) & l1_cat_1(B) & l1_cat_1(A) -> k13_funct_3(D,E) = k18_cat_2(A,B,C,D,E))) # label(redefinition_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5827 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> -v1_xboole_0(k3_tarski(a_2_0_cat_2(A,B))) & m1_subset_1(k3_tarski(a_2_0_cat_2(A,B)),k1_zfmisc_1(u2_cat_1(A))))))) # label(t28_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5828 (all A all B all C (v2_cat_1(B) & l1_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(A) & v2_cat_1(A) -> (all D (m1_subset_1(D,C) <-> m2_cat_2(D,A,B,C))))) # label(redefinition_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5829 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,B),C) & m2_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) -> v1_funct_1(k3_funct_5(D)) & m2_relset_1(k3_funct_5(D),A,k1_fraenkel(B,C)) & v1_funct_2(k3_funct_5(D),A,k1_fraenkel(B,C)))))))))) # label(t1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5830 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_cat_1(G,B,C,D) -> (D = F & C = E -> m1_cat_1(G,A,E,F) | k1_xboole_0 = k6_cat_1(B,C,D)))))))))))))))) # label(t16_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5831 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> (exists C m1_cat_2(C,A,B)))) # label(existence_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5832 (all A all B all C all D all E all F (-v1_xboole_0(C) & m1_fraenkel(D,B,C) & v1_funct_2(E,A,D) & m1_subset_1(F,A) & m1_relset_1(E,A,D) & v1_funct_1(E) & -v1_xboole_0(A) -> k1_funct_1(E,F) = k1_cat_2(A,B,C,D,E,F))) # label(redefinition_k1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5833 (all A all B all C all D all E all F (-v1_xboole_0(A) & -v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(F,B,D) & v1_funct_2(F,B,D) & v1_funct_1(F) & m1_relset_1(E,A,C) & -v1_xboole_0(D) -> m2_relset_1(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_2(k9_cat_2(A,B,C,D,E,F),k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & v1_funct_1(k9_cat_2(A,B,C,D,E,F)))) # label(dt_k9_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5834 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> (all E (m1_subset_1(E,u2_cat_1(A)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (F = D & k2_cat_1(B,D) = k3_cat_1(B,C) & C = E -> k4_cat_1(B,C,D) = k4_cat_1(A,E,F)))))))))))))) # label(t17_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5835 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k3_cat_1(B,E) = k2_cat_1(B,F) & k3_cat_1(A,C) = k2_cat_1(A,D) -> k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) = k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F))))))))))))))) # label(t39_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5836 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k8_cat_2(A,B)),C) = C)))))) # label(t22_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5837 (all A (v2_cat_1(A) & l1_cat_1(A) -> (exists B m3_cat_2(B,A)))) # label(existence_m3_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5838 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> m1_subset_1(k1_domain_1(u2_cat_1(A),u2_cat_1(B),C,D),u2_cat_1(k11_cat_2(A,B))))))))))) # label(t36_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5839 (all A all B all C all D (-v1_xboole_0(B) & -v1_xboole_0(C) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(A) -> k5_funct_5(D) = k3_cat_2(A,B,C,D))) # label(redefinition_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5840 $T # label(t11_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5841 (all A all B (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) -> l1_cat_1(k11_cat_2(A,B)) & v2_cat_1(k11_cat_2(A,B)))) # label(dt_k11_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5842 (all A all B all C all D (v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k3_cat_2(A,B,C,D)) & v1_funct_2(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)) & m2_relset_1(k3_cat_2(A,B,C,D),B,k1_fraenkel(A,C)))) # label(dt_k3_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5843 $T # label(t9_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5844 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(B),u1_cat_1(A),k12_cat_1(B,A,k4_cat_2(B,A,C)),D))))))))) # label(t7_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5845 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (v9_cat_1(k8_cat_2(A,B),B,A) <-> (all C (m1_subset_1(C,u1_cat_1(B)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(A)) -> (D = F & C = E -> k6_cat_1(A,E,F) = k6_cat_1(B,C,D))))))))))))))) # label(t25_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5846 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(A)) -> (all E (m1_subset_1(E,u2_cat_1(B)) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,D,F)) = k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E)) -> k13_cat_2(A,B,k4_cat_1(A,C,D),k4_cat_1(B,E,F)) = k4_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,E),k13_cat_2(A,B,D,F))))))))))))))) # label(t40_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5847 (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(B,A),C) & v1_funct_2(D,k2_zfmisc_1(B,A),C) & v1_funct_1(D) -> v1_funct_1(k5_funct_5(D)) & v1_funct_2(k5_funct_5(D),A,k1_fraenkel(B,C)) & m2_relset_1(k5_funct_5(D),A,k1_fraenkel(B,C)))))))))) # label(t2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5848 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) -> (all E (v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) & m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_1(E) -> ((exists F ((all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(B)) -> k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,G) = k15_cat_2(B,A,C,F,G) & k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,H) = k14_cat_2(B,A,C,F,H))))) & m2_cat_1(F,k11_cat_2(B,A),C))) -> (all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F))))))))))))))))) # label(t53_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5849 (all A all B all C all D all E (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C) & m2_cat_1(D,A,B) & m2_cat_1(E,A,C) & v2_cat_1(B) & v2_cat_1(A) -> m2_cat_1(k18_cat_2(A,B,C,D,E),A,k11_cat_2(B,C)))) # label(dt_k18_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5850 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k6_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,E),k12_cat_2(A,B,D,F)) = k2_zfmisc_1(k6_cat_1(A,C,D),k6_cat_1(B,E,F)))))))))))))) # label(t42_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5851 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,B) -> (all F (v1_funct_2(F,k2_zfmisc_1(A,B),C) & m2_relset_1(F,k2_zfmisc_1(A,B),C) & v1_funct_1(F) -> k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)) = k8_funct_2(A,C,k1_cat_2(B,A,C,k1_fraenkel(A,C),k3_cat_2(A,B,C,F),E),D))))))))))))) # label(t4_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5852 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) & -v1_xboole_0(B) & -v1_xboole_0(A) -> v1_funct_1(k10_cat_2(A,B,C,D)) & m2_relset_1(k10_cat_2(A,B,C,D),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)))) # label(dt_k10_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5853 (all A all B all C all D all E (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & m1_subset_1(E,u1_cat_1(A)) & m2_cat_1(D,k11_cat_2(A,B),C) & l1_cat_1(C) & v2_cat_1(A) -> m2_cat_1(k14_cat_2(A,B,C,D,E),B,C))) # label(dt_k14_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5854 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(k11_cat_2(A,B))) -> (exists D (m1_subset_1(D,u2_cat_1(A)) & (exists E (k13_cat_2(A,B,D,E) = C & m1_subset_1(E,u2_cat_1(B)))))))))))) # label(t37_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5855 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> r1_tarski(u2_cat_1(B),u2_cat_1(A)))))) # label(t13_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5856 (all A all B (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) -> v2_cat_1(k11_cat_2(A,B)) & v1_cat_1(k11_cat_2(A,B)))) # label(fc2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5857 $T # label(t10_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5858 (all A all B all C all D (v2_cat_1(A) & v2_cat_1(B) & m1_subset_1(C,u2_cat_1(A)) & m1_subset_1(D,u2_cat_1(B)) & l1_cat_1(B) & l1_cat_1(A) -> k13_cat_2(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k13_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5859 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(A)) -> (all E (m1_cat_1(E,A,C,D) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> (all H (m1_cat_1(H,B,F,G) -> -(k6_cat_1(B,F,G) != k1_xboole_0 & -m1_cat_1(k13_cat_2(A,B,E,H),k11_cat_2(A,B),k12_cat_2(A,B,C,F),k12_cat_2(A,B,D,G)) & k1_xboole_0 != k6_cat_1(A,C,D)))))))))))))))))) # label(t43_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5860 $T # label(dt_k5_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5861 (all A all B all C all D (-v1_xboole_0(A) & -v1_xboole_0(B) & v1_funct_2(D,k2_zfmisc_1(A,B),C) & m1_relset_1(D,k2_zfmisc_1(A,B),C) & v1_funct_1(D) & -v1_xboole_0(C) -> k2_cat_2(A,B,C,D) = k3_funct_5(D))) # label(redefinition_k2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5862 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(A),k8_cat_2(A,B),C) = C)))))) # label(t21_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5863 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(A),k16_cat_2(A,B),k13_cat_2(A,B,C,D)) = C)))))))) # label(t58_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5864 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> k16_cat_2(A,B) = k9_funct_3(u2_cat_1(A),u2_cat_1(B)))))) # label(d10_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5865 $T # label(t8_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5866 $T # label(t49_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5867 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> k13_cat_2(A,B,k10_cat_1(A,C),k10_cat_1(B,D)) = k10_cat_1(k11_cat_2(A,B),k12_cat_2(A,B,C,D)))))))))) # label(t41_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5868 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m1_subset_1(C,u2_cat_1(B)) -> m1_subset_1(C,u2_cat_1(A)))))))) # label(t14_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5869 $T # label(t5_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5870 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m3_cat_2(B,A) -> m2_cat_1(k8_cat_2(A,B),B,A))) # label(dt_k8_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5871 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> m2_cat_1(k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)),B,C))))))))))) # label(t44_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5872 (all A (l1_cat_1(A) & v2_cat_1(A) -> (exists B (m3_cat_2(B,A) & v1_cat_1(B) & v2_cat_1(B))))) # label(rc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5873 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> (all C (m1_cat_2(C,A,B) -> -v1_xboole_0(C))))) # label(dt_m1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5874 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)) = k8_funct_2(u1_cat_1(A),u1_cat_1(C),k12_cat_1(A,C,k15_cat_2(A,B,C,D,F)),E))))))))))))) # label(t51_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5875 $T # label(t56_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5876 (all A all B all C all D all E all F (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & l1_cat_1(C) & v2_cat_1(D) & m2_cat_1(F,B,D) & m2_cat_1(E,A,C) & l1_cat_1(D) & v2_cat_1(C) & v2_cat_1(B) -> k19_cat_2(A,B,C,D,E,F) = k15_funct_3(E,F))) # label(redefinition_k19_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5877 (all A all B (l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(A) -> m1_cat_2(k7_cat_2(A,B),A,B))) # label(dt_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5878 (all A all B all C all D all E all F (-v1_xboole_0(A) & l1_cat_1(B) & l1_cat_1(C) & v1_funct_1(E) & m1_subset_1(F,A) & m1_relset_1(E,A,D) & v1_funct_2(E,A,D) & m1_cat_2(D,B,C) & v2_cat_1(C) & v2_cat_1(B) -> k1_funct_1(E,F) = k6_cat_2(A,B,C,D,E,F))) # label(redefinition_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5879 (all A all B (l1_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & v2_cat_1(A) -> m2_cat_1(k16_cat_2(A,B),k11_cat_2(A,B),A))) # label(dt_k16_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5880 $T # label(t20_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5881 (all A all B (v2_cat_1(B) & l1_cat_1(B) & l1_cat_1(A) & v2_cat_1(A) -> -v1_xboole_0(k5_cat_2(A,B)))) # label(fc1_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5882 (all A all B all C all D (v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(C,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> m1_subset_1(k12_cat_2(A,B,C,D),u1_cat_1(k11_cat_2(A,B))))) # label(dt_k12_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5883 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)) = k15_cat_2(A,B,C,D,E))))))))))) # label(d9_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5884 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k2_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k2_cat_1(A,C),k2_cat_1(B,D)) & k3_cat_1(k11_cat_2(A,B),k13_cat_2(A,B,C,D)) = k12_cat_2(A,B,k3_cat_1(A,C),k3_cat_1(B,D)))))))))) # label(t38_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5885 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> g1_cat_1(k2_zfmisc_1(u1_cat_1(A),u1_cat_1(B)),k2_zfmisc_1(u2_cat_1(A),u2_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u3_cat_1(A),u3_cat_1(B)),k9_cat_2(u2_cat_1(A),u2_cat_1(B),u1_cat_1(A),u1_cat_1(B),u4_cat_1(A),u4_cat_1(B)),k10_cat_2(u2_cat_1(A),u2_cat_1(B),u5_cat_1(A),u5_cat_1(B)),k9_cat_2(u1_cat_1(A),u1_cat_1(B),u2_cat_1(A),u2_cat_1(B),u6_cat_1(A),u6_cat_1(B))) = k11_cat_2(A,B))))) # label(d7_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5886 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(B)) -> m2_cat_1(k1_funct_1(k5_funct_5(D),k10_cat_1(B,E)),A,C))))))))))) # label(t45_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5887 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> m2_cat_1(k9_cat_2(u2_cat_1(A),u2_cat_1(C),u2_cat_1(B),u2_cat_1(D),E,F),k11_cat_2(A,C),k11_cat_2(B,D)))))))))))))) # label(t65_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5888 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> k1_funct_1(k3_funct_5(D),k10_cat_1(A,E)) = k14_cat_2(A,B,C,D,E))))))))))) # label(d8_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.84 5889 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (l1_cat_1(D) & v2_cat_1(D) -> (all E (m2_cat_1(E,A,B) -> (all F (m2_cat_1(F,C,D) -> (all G (m1_subset_1(G,u1_cat_1(A)) -> (all H (m1_subset_1(H,u1_cat_1(C)) -> k12_cat_2(B,D,k8_funct_2(u1_cat_1(A),u1_cat_1(B),k12_cat_1(A,B,E),G),k8_funct_2(u1_cat_1(C),u1_cat_1(D),k12_cat_1(C,D,F),H)) = k8_funct_2(u1_cat_1(k11_cat_2(A,C)),u1_cat_1(k11_cat_2(B,D)),k12_cat_1(k11_cat_2(A,C),k11_cat_2(B,D),k19_cat_2(A,C,B,D,E,F)),k12_cat_2(A,C,G,H)))))))))))))))))) # label(t66_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5890 $T # label(t57_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5891 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (l1_cat_1(C) & v2_cat_1(C) -> (all D (v1_funct_1(D) & m2_relset_1(D,u1_cat_1(A),k7_cat_2(B,C)) & v1_funct_2(D,u1_cat_1(A),k7_cat_2(B,C)) -> (all E (m2_relset_1(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_2(E,u1_cat_1(B),k7_cat_2(A,C)) & v1_funct_1(E) -> -((all F (m1_subset_1(F,u1_cat_1(A)) -> (all G (m1_subset_1(G,u1_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,F),k10_cat_1(B,G)) = k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,G),k10_cat_1(A,F)))))) & (all F (m2_cat_1(F,k11_cat_2(B,A),C) -> -(all G (m1_subset_1(G,u2_cat_1(B)) -> (all H (m1_subset_1(H,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,G)),H),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,H)),G)) = k8_funct_2(u2_cat_1(k11_cat_2(B,A)),u2_cat_1(C),F,k13_cat_2(B,A,G,H)))))))) & (all F (m1_subset_1(F,u2_cat_1(B)) -> (all G (m1_subset_1(G,u2_cat_1(A)) -> k4_cat_1(C,k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k2_cat_1(A,G)),F),k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k3_cat_1(B,F)),G)) = k4_cat_1(C,k8_funct_2(u2_cat_1(A),u2_cat_1(C),k6_cat_2(u1_cat_1(B),A,C,k7_cat_2(A,C),E,k2_cat_1(B,F)),G),k8_funct_2(u2_cat_1(B),u2_cat_1(C),k6_cat_2(u1_cat_1(A),B,C,k7_cat_2(B,C),D,k3_cat_1(A,G)),F))))))))))))))))) # label(t52_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5892 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> m2_cat_1(k15_cat_1(B),B,A))))) # label(t19_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5893 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & l1_cat_1(B) & m1_cat_2(C,A,B) & v2_cat_1(B) -> (all D (m2_cat_2(D,A,B,C) -> m2_cat_1(D,A,B))))) # label(dt_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5894 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> k8_funct_2(u2_cat_1(B),u2_cat_1(A),k4_cat_2(B,A,C),D) = k10_cat_1(A,C))))))))) # label(t6_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5895 (all A all B all C all D all E all F (-v1_xboole_0(A) & l1_cat_1(C) & m1_cat_2(D,B,C) & m1_relset_1(E,A,D) & m1_subset_1(F,A) & v1_funct_2(E,A,D) & v1_funct_1(E) & v2_cat_1(C) & l1_cat_1(B) & v2_cat_1(B) -> m2_cat_2(k6_cat_2(A,B,C,D,E,F),B,C,D))) # label(dt_k6_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5896 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (all D (m2_cat_1(D,k11_cat_2(A,B),C) -> (all E (m1_subset_1(E,u1_cat_1(A)) -> (all F (m1_subset_1(F,u1_cat_1(B)) -> k8_funct_2(u1_cat_1(B),u1_cat_1(C),k12_cat_1(B,C,k14_cat_2(A,B,C,D,E)),F) = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(C),k12_cat_1(k11_cat_2(A,B),C,D),k12_cat_2(A,B,E,F)))))))))))))) # label(t48_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5897 (all A all B (v2_cat_1(A) & l1_cat_1(B) & v2_cat_1(B) & l1_cat_1(A) -> k5_cat_2(A,B) = k7_cat_2(A,B))) # label(redefinition_k7_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5898 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> C = k8_funct_2(u1_cat_1(k11_cat_2(A,B)),u1_cat_1(A),k12_cat_1(k11_cat_2(A,B),A,k16_cat_2(A,B)),k12_cat_2(A,B,C,D)))))))))) # label(t59_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5899 (all A all B all C all D all E (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(C) & l1_cat_1(C) & m1_subset_1(E,u1_cat_1(B)) & m2_cat_1(D,k11_cat_2(A,B),C) & l1_cat_1(B) & v2_cat_1(B) -> m2_cat_1(k15_cat_2(A,B,C,D,E),A,C))) # label(dt_k15_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5900 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,u2_cat_1(B)) -> D = k8_funct_2(u2_cat_1(k11_cat_2(A,B)),u2_cat_1(B),k17_cat_2(A,B),k13_cat_2(A,B,C,D)))))))))) # label(t60_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5901 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m1_subset_1(C,u1_cat_1(A)) -> (all D (m1_subset_1(D,u1_cat_1(B)) -> m1_subset_1(k1_domain_1(u1_cat_1(A),u1_cat_1(B),C,D),u1_cat_1(k11_cat_2(A,B))))))))))) # label(t34_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5902 (all A all B all C (l1_cat_1(A) & v2_cat_1(B) & m1_cat_2(C,A,B) & l1_cat_1(B) & v2_cat_1(A) -> (exists D m2_cat_2(D,A,B,C)))) # label(existence_m2_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5903 (all A (l1_cat_1(A) & v2_cat_1(A) -> m3_cat_2(A,A))) # label(t18_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5904 (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) -> k8_funct_2(B,C,k1_cat_2(A,B,C,k1_fraenkel(B,C),k2_cat_2(A,B,C,F),D),E) = k8_funct_2(k2_zfmisc_1(A,B),C,F,k1_domain_1(A,B,D,E)))))))))))))) # label(t3_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5905 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (r1_cat_2(B,A) <-> v9_cat_1(k8_cat_2(A,B),B,A)))))) # label(t27_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5906 $T # label(t46_cat_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5907 (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) -> (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]. 183.69/184.85 5908 (all A all B (l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) & -v3_struct_0(A) -> v10_lattices(k8_filter_0(A,B)) & l3_lattices(k8_filter_0(A,B)) & -v3_struct_0(k8_filter_0(A,B)))) # label(dt_k8_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5909 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_0(A) -> v11_lattices(A))) # label(t39_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5910 (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(k4_filter_0(A,B,C),u1_struct_0(A)))) # label(dt_k4_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5911 (all A all B (l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & v10_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k2_filter_0(A,B),A))) # label(dt_k2_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5912 (all A (l3_lattices(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)) -> (r2_hidden(k3_lattices(A,C,D),B) <-> r2_hidden(D,B) | r2_hidden(C,B)))))) <-> v2_filter_0(B,A)))))) # label(d6_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5913 (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]. 183.69/184.85 5914 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v10_lattices(A) & l3_lattices(A) & v17_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B))) & v17_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v10_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t75_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5915 (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))) -> (l3_lattices(A) & r2_hidden(k5_lattices(A),B) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> u1_struct_0(A) = k3_filter_0(A,B) & k1_filter_0(A) = k3_filter_0(A,B)))))) # label(t31_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5916 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (B != k1_filter_0(A) & v2_filter_0(B,A) <-> v1_filter_0(B,A)))))) # label(t58_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5917 (exists A (v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v7_lattices(A) & v3_filter_0(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5918 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> m1_filter_0(k1_filter_0(A),A))) # label(dt_k1_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5919 $T # label(t28_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5920 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(u1_struct_0(A) = k2_filter_0(A,B) & -(all C (m1_subset_1(C,u1_struct_0(A)) -> B = k4_lattices(A,B,C)))))))) # label(t23_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5921 $T # label(t16_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5922 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_lattices(A) -> k8_filter_0(A,k1_filter_0(A)) = A)) # label(t62_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5923 $T # label(t79_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5924 (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,C,B),D) & r2_hidden(k3_lattices(A,B,C),D)))))))))) # label(t10_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5925 (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)) -> (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]. 183.69/184.85 5926 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(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]. 183.69/184.85 5927 (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)) -> 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]. 183.69/184.85 5928 (all A all B (v10_lattices(A) & l3_lattices(A) & m1_filter_0(B,A) & v3_filter_0(A) & -v3_struct_0(A) -> v8_relat_2(k11_filter_0(A,B)) & 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)) & v3_relat_2(k11_filter_0(A,B)))) # label(dt_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5929 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_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]. 183.69/184.85 5930 (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,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]. 183.69/184.85 5931 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (all C (-v3_struct_0(C) & v10_lattices(C) & l3_lattices(C) -> (k8_filter_0(A,B) = C <-> (exists D (m2_relset_1(D,k2_zfmisc_1(B,B),B) & (exists E (v1_funct_2(E,k2_zfmisc_1(B,B),B) & m2_relset_1(E,k2_zfmisc_1(B,B),B) & E = k1_realset1(u1_lattices(A),B) & C = g3_lattices(B,D,E) & D = k1_realset1(u2_lattices(A),B) & v1_funct_1(E))) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D)))))))))) # label(d10_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5932 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(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]. 183.69/184.85 5933 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k1_filter_0(A) = u1_struct_0(A))) # label(d2_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5934 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(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)) -> 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]. 183.69/184.85 5935 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_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]. 183.69/184.85 5936 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & -v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,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]. 183.69/184.85 5937 (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]. 183.69/184.85 5938 (all A all B (-v3_struct_0(A) & l3_lattices(A) & m1_filter_0(B,A) & v3_filter_0(A) & v10_lattices(A) -> k11_filter_0(A,B) = k10_filter_0(A,B))) # label(redefinition_k11_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5939 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(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]. 183.69/184.85 5940 (all A (v10_lattices(A) & l3_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]. 183.69/184.85 5941 $T # label(t25_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5942 (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) -> 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]. 183.69/184.85 5943 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> B = k3_filter_0(A,B))))) # label(t26_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5944 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v17_lattices(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]. 183.69/184.85 5945 (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,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]. 183.69/184.85 5946 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (v1_relat_1(C) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(k9_filter_0(A,D,E),B) <-> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E),C)))))) & r1_tarski(k3_relat_1(C),u1_struct_0(A)) <-> C = k10_filter_0(A,B)))))))) # label(d12_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5947 (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)) -> 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]. 183.69/184.85 5948 (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 (m1_filter_0(D,A) -> -(v1_filter_0(D,A) & (-r2_hidden(C,D) & r2_hidden(B,D) | -r2_hidden(B,D) & r2_hidden(C,D))))) & B != C))))))) # label(t60_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5949 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> v14_lattices(A))) # label(t37_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5950 (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) -> k5_filter_0(A,B,C) = k6_filter_0(A,B,C))) # label(redefinition_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5951 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (-v3_struct_0(A) & v15_lattices(A) & v16_lattices(A) & v10_lattices(A) & l3_lattices(A) & v12_lattices(A) & -v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> v10_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v15_lattices(k8_filter_0(A,k2_filter_0(A,B))) & v16_lattices(k8_filter_0(A,k2_filter_0(A,B))) & l3_lattices(k8_filter_0(A,k2_filter_0(A,B))) & -v3_struct_0(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t74_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5952 (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 & B = E -> k4_lattices(A,B,C) = k4_lattices(k8_filter_0(A,D),E,F) & k3_lattices(A,B,C) = k3_lattices(k8_filter_0(A,D),E,F)))))))))))))) # label(t64_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5953 (all A (l3_lattices(A) & v10_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]. 183.69/184.85 5954 (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) -> u1_struct_0(A) = k3_relat_1(k10_filter_0(A,B))))))) # label(t85_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5955 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(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]. 183.69/184.85 5956 (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]. 183.69/184.85 5957 (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]. 183.69/184.85 5958 (all A (-v3_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_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(C,E,D,D) & r1_filter_0(A,B,F,F))))))))))))) # label(t88_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5959 (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))) & -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]. 183.69/184.85 5960 (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)) -> (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,E,C)) & r3_lattices(A,k3_lattices(A,B,D),k3_lattices(A,C,E))))))))))))) # label(t4_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5961 $T # label(t36_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5962 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(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]. 183.69/184.85 5963 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(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) -> -(r2_hidden(B,k5_filter_0(A,C,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(F,D) & r2_hidden(E,C))))))))))))) # label(t45_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5964 (all A all B all C (v10_lattices(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) & 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]. 183.69/184.85 5965 (all A all B all C all D (m1_filter_0(D,B) & m1_filter_0(C,B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_filter_0(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & A = 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))))))))) # label(fraenkel_a_3_1_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5966 (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))) & -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),B,k3_filter_0(A,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),k3_filter_0(A,B),C)) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t47_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5967 (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)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_filter_0(E,A) -> (r2_hidden(k4_filter_0(A,C,D),E) & r2_hidden(k4_filter_0(A,B,C),E) -> r2_hidden(k4_filter_0(A,B,D),E)))))))))))) # label(t54_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5968 (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)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r3_lattices(A,B,C) & r3_lattices(A,D,E) -> 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]. 183.69/184.85 5969 (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))) & -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(k4_lattices(A,C,D),B) <-> r2_hidden(C,B) & r2_hidden(D,B))))))))))) # label(d1_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5970 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (l3_lattices(A) & v3_filter_0(A) & v10_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]. 183.69/184.85 5971 (all A all B (l3_lattices(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v10_lattices(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]. 183.69/184.85 5972 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & l3_lattices(A) & v14_lattices(A) & v10_lattices(A) -> r2_hidden(k6_lattices(A),B)))))) # label(t12_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5973 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> m1_filter_0(u1_struct_0(A),A))) # label(t15_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5974 $T # label(t86_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5975 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (all C (-v3_struct_0(C) & v10_lattices(C) & v3_filter_0(C) & l3_lattices(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]. 183.69/184.85 5976 $T # label(t43_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5977 (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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (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]. 183.69/184.85 5978 (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)) -> (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(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]. 183.69/184.85 5979 $T # label(t76_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5980 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & v17_lattices(A) -> k7_filter_0(A,B,C) = k5_filter_0(A,B,C))) # label(redefinition_k7_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5981 (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_filter_0(D,A) -> (r2_hidden(B,D) & r2_hidden(k4_filter_0(A,B,C),D) -> r2_hidden(C,D)))))))))) # label(t41_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5982 (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))) -> (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)))))) & (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]. 183.69/184.85 5983 (all A (v10_lattices(A) & l3_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]. 183.69/184.85 5984 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(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]. 183.69/184.85 5985 (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) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) -> v15_lattices(k8_filter_0(A,k2_filter_0(A,B)))))))) # label(t73_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5986 (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,C,D),E) & r2_hidden(k9_filter_0(A,B,C),E) -> r2_hidden(k9_filter_0(A,B,D),E)))))))))))) # label(t78_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5987 (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]. 183.69/184.85 5988 (all A all B (l3_lattices(A) & m1_filter_0(B,A) & v10_lattices(A) & -v3_struct_0(A) -> v1_relat_1(k10_filter_0(A,B)))) # label(dt_k10_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5989 (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]. 183.69/184.85 5990 (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]. 183.69/184.85 5991 (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)) -> k3_lattices(A,k7_lattices(A,B),C) = k4_filter_0(A,B,C))))))) # label(t55_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5992 $T # label(t21_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5993 (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) & l3_lattices(A) & v3_filter_0(A) -> v3_filter_0(k8_filter_0(A,B))))))) # label(t69_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5994 (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) -> a_3_1_filter_0(A,B,C) = k3_filter_0(A,k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t48_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.85 5995 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (u1_struct_0(A) != B & (all C (m1_filter_0(C,A) -> (r1_tarski(B,C) -> B = C | u1_struct_0(A) = C))) <-> v1_filter_0(B,A)))))) # label(d4_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 5996 (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]. 183.69/184.86 5997 (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]. 183.69/184.86 5998 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_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]. 183.69/184.86 5999 (all A all B (-v3_struct_0(A) & v17_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) -> m2_relset_1(k12_filter_0(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(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]. 183.69/184.86 6000 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> u1_struct_0(k8_filter_0(A,B)) = B & u2_lattices(k8_filter_0(A,B)) = k1_realset1(u2_lattices(A),B) & u1_lattices(k8_filter_0(A,B)) = k1_realset1(u1_lattices(A),B))))) # label(t63_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6001 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_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]. 183.69/184.86 6002 $T # label(t61_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6003 (all A all B all C (m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_0_filter_0(B,C)) <-> (exists D (r3_lattices(B,C,D) & A = D & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6004 $T # label(t17_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6005 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> -(v13_lattices(A) & (all C (m1_filter_0(C,A) -> -(r2_hidden(B,C) & v1_filter_0(C,A)))) & B != k5_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A)))))) # label(t24_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6006 (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,B,C) = k9_filter_0(A,C,B))))))) # label(t77_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6007 (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_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]. 183.69/184.86 6008 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (v13_lattices(A) -> (all B (m1_filter_0(B,A) -> -(B != u1_struct_0(A) & (all C (m1_filter_0(C,A) -> -(r1_tarski(B,C) & v1_filter_0(C,A)))))))))) # label(t22_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6009 (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) -> (r1_filter_0(A,D,B,C) -> r1_filter_0(A,D,C,B)))))))))) # label(t89_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6010 $T # label(t33_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6011 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_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]. 183.69/184.86 6012 (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 & B = E -> (r3_lattices(k8_filter_0(A,D),E,F) <-> r3_lattices(A,B,C))))))))))))))) # label(t65_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6013 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(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(B,D) -> r2_hidden(k4_filter_0(A,C,B),D)))))))))) # label(t42_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6014 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & v13_lattices(A) & l3_lattices(A) & r2_hidden(k5_lattices(A),B) & v10_lattices(A) -> B = u1_struct_0(A) & k1_filter_0(A) = B))))) # label(t32_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6015 $T # label(t35_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6016 (all A (l3_lattices(A) -> (-v3_struct_0(A) & v3_filter_0(A) & v10_lattices(A) -> -v3_struct_0(A) & v6_lattices(A) & v10_lattices(A) & v12_lattices(A) & v11_lattices(A) & v9_lattices(A) & v8_lattices(A) & v7_lattices(A) & v5_lattices(A) & v4_lattices(A)))) # label(cc1_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6017 (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 (-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]. 183.69/184.86 6018 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(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))) -> (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]. 183.69/184.86 6019 (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) & v11_lattices(A) -> m1_filter_0(k6_filter_0(A,B,C),A))) # label(dt_k6_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6020 (all A all B (v10_lattices(A) & m1_filter_0(B,A) & l3_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_0(A,B)) & v5_lattices(k8_filter_0(A,B)) & v6_lattices(k8_filter_0(A,B)) & v7_lattices(k8_filter_0(A,B)) & v8_lattices(k8_filter_0(A,B)) & v9_lattices(k8_filter_0(A,B)) & v10_lattices(k8_filter_0(A,B)) & v4_lattices(k8_filter_0(A,B)) & v3_lattices(k8_filter_0(A,B)))) # label(fc2_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6021 (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) -> 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]. 183.69/184.86 6022 (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) & l3_lattices(A) & v3_filter_0(A) -> r8_relat_2(k10_filter_0(A,B),u1_struct_0(A))))))) # label(t83_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6023 (all A (v17_lattices(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (B != u1_struct_0(A) & (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]. 183.69/184.86 6024 (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) <-> k4_lattices(A,B,k7_lattices(A,C)) = k5_lattices(A)))))))) # label(t56_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6025 (all A all B all C all D (v10_lattices(B) & l3_lattices(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) & -v3_struct_0(B) -> (r2_hidden(A,a_3_0_filter_0(B,C,D)) <-> (exists E exists F (m1_subset_1(E,u1_struct_0(B)) & k4_lattices(B,E,F) = A & r2_hidden(F,D) & r2_hidden(E,C) & m1_subset_1(F,u1_struct_0(B))))))) # label(fraenkel_a_3_0_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6026 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (-v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & v10_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]. 183.69/184.86 6027 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (l3_lattices(A) & v13_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k1_filter_0(A) = k2_filter_0(A,k5_lattices(A))))) # label(t20_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6028 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> v8_relat_2(k10_filter_0(A,B)) & 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)) & v3_relat_2(k10_filter_0(A,B))))))) # label(t84_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6029 (all A all B all C (v10_lattices(A) & m1_filter_0(B,A) & m1_filter_0(C,A) & l3_lattices(A) & v17_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]. 183.69/184.86 6030 (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))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> k5_filter_0(A,B,C) = a_3_0_filter_0(A,B,C))))))) # label(d9_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6031 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v3_filter_0(A))) # label(t40_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6032 $T # label(t8_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6033 (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,D,C) & r3_lattices(A,B,C) -> r3_lattices(A,k3_lattices(A,B,D),C)))))))))) # label(t6_filter_0) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6034 (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,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]. 183.69/184.86 6035 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (D = C -> r1_tarski(k1_connsp_1(B,D),k1_connsp_1(A,C))))))))))) # label(t14_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6036 (all A all B (m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> m1_subset_1(k1_connsp_2(A,B),k1_zfmisc_1(u1_struct_0(A))))) # label(dt_k1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6037 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_connsp_2(A,B)))))) # label(d4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6038 $T # label(t1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6039 (all A (l1_pre_topc(A) & v2_pre_topc(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))) -> (m1_connsp_2(C,A,B) <-> m2_connsp_2(C,A,k1_struct_0(A,B))))))))) # label(t10_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6040 (all A all B (v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists C m1_connsp_2(C,A,B)))) # label(existence_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6041 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v3_pre_topc(B,A) & r2_hidden(C,B) -> m1_connsp_2(B,A,C)))))))) # label(t5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6042 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (v1_connsp_2(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (r3_connsp_1(A,B) -> v3_pre_topc(B,A))))))) # label(t21_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6043 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (-v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(C,A) & r2_hidden(B,C) & (all D (m1_subset_1(D,u1_struct_0(k3_pre_topc(A,C))) -> -(D = B & r2_hidden(B,k1_tops_1(k3_pre_topc(A,C),k1_connsp_1(k3_pre_topc(A,C),D))))))))) <-> r1_connsp_2(A,B)))))) # label(t20_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6044 (all A (v2_pre_topc(A) & l1_pre_topc(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))) -> (m1_connsp_2(C,A,B) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r1_tarski(D,C) & r2_hidden(B,D)))))))))) # label(t8_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6045 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r1_tarski(k1_connsp_1(A,B),k1_connsp_2(A,B)))))) # label(t33_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6046 (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))) -> (m2_connsp_2(C,A,B) <-> r1_tarski(B,k1_tops_1(A,C))))))))) # label(d2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6047 (all A all B (v2_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> (exists C m2_connsp_2(C,A,B)))) # label(existence_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6048 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (v1_connsp_2(k3_pre_topc(A,B)) <-> v2_connsp_2(B,A)))))) # label(d6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6049 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_pre_topc(A) -> (all C (m2_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6050 $T # label(t16_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6051 $T # label(t29_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6052 $T # label(t17_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6053 $T # label(t15_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6054 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (r2_connsp_2(A,B,C) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -(D = B & (all E (m1_subset_1(E,u1_struct_0(k3_pre_topc(A,D))) -> -(r1_connsp_2(k3_pre_topc(A,D),E) & E = C))))))))))))) # label(d5_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6055 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v4_pre_topc(C,A) & r2_hidden(B,C) & r1_tarski(C,k1_connsp_2(A,B)) -> k1_connsp_2(A,B) = C))))))) # label(t31_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6056 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> -(r2_hidden(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(D,B) & m1_connsp_2(D,A,C))))))) <-> v3_pre_topc(B,A)))))) # label(t9_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6057 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (F = C & E = D & m1_connsp_2(E,A,F) -> m1_connsp_2(D,k3_pre_topc(A,B),C)))))))))))))) # label(t12_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6058 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k1_connsp_2(A,B) = C <-> (exists D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & C = k6_setfam_1(u1_struct_0(A),D) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,E) & v4_pre_topc(E,A) & v3_pre_topc(E,A) <-> r2_hidden(E,D))))))))))))) # label(d7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6059 (all A (v2_pre_topc(A) & l1_pre_topc(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))) -> (m1_connsp_2(C,A,B) & m1_connsp_2(D,A,B) -> m1_connsp_2(k4_subset_1(u1_struct_0(A),C,D),A,B)))))))))) # label(t3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6060 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k1_connsp_2(A,B)))))) # label(t30_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6061 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,C) & v4_pre_topc(B,A) & v3_pre_topc(C,A) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_tarski(B,D) & r1_tarski(k6_pre_topc(A,D),C) & v3_pre_topc(D,A)))) & k2_pre_topc(A) != C & k1_xboole_0 != B))))) <-> v5_compts_1(A)))) # label(t26_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6062 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(m1_connsp_2(C,A,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> -(v3_pre_topc(D,A) & r1_tarski(D,C) & m1_connsp_2(D,A,B))))))))))) # label(t7_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6063 $T # label(t2_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6064 (all A (l1_pre_topc(A) & v2_pre_topc(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))) -> (m1_connsp_2(D,A,B) & m1_connsp_2(C,A,B) <-> m1_connsp_2(k5_subset_1(u1_struct_0(A),C,D),A,B)))))))))) # label(t4_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6065 (all A all B (v2_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & l1_pre_topc(A) & -v3_struct_0(A) -> (all C (m1_connsp_2(C,A,B) -> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))))))) # label(dt_m1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6066 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (v5_compts_1(A) & v1_connsp_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 != k1_xboole_0 & v4_pre_topc(C,A) & r1_xboole_0(B,C) & v2_connsp_1(B,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))) -> -(v2_connsp_1(E,A) & v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(D,E) & v2_connsp_1(D,A)))))) & v2_connsp_1(C,A) & v4_pre_topc(B,A) & B != k1_xboole_0)))))))) # label(t27_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6067 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(k1_xboole_0 = C & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(B,D) & v4_pre_topc(D,A) & v3_pre_topc(D,A) <-> r2_hidden(D,C))))))))))) # label(t28_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6068 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (r1_connsp_2(A,B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(C) -> (v3_pre_topc(C,A) & r2_hidden(B,C) -> r2_connsp_2(A,C,B))))))))) # label(t22_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6069 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (v1_connsp_2(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(k3_pre_topc(A,B)))) -> -(v2_connsp_1(C,k3_pre_topc(A,B)) & v3_pre_topc(C,k3_pre_topc(A,B)) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(D,A) & k5_subset_1(u1_struct_0(A),B,D) = C & v2_connsp_1(D,A)))))))))))) # label(t25_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6070 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v4_pre_topc(k1_connsp_2(A,B),A))))) # label(t32_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6071 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (m1_connsp_2(B,A,C) -> r2_hidden(C,B)))))))) # label(t6_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6072 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v1_connsp_2(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> v2_connsp_2(B,A))))))) # label(t23_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6073 (all A (l1_pre_topc(A) & v2_pre_topc(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))) -> (r4_connsp_1(A,C,D) & r2_hidden(B,D) & m1_connsp_2(C,A,B) -> m1_connsp_2(D,A,B)))))) <-> r1_connsp_2(A,B)))))) # label(t19_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6074 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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(D,C) & v2_connsp_1(D,A) & m1_connsp_2(D,A,B)))) & m1_connsp_2(C,A,B)))) <-> r1_connsp_2(A,B)))))) # label(d3_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6075 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,u1_struct_0(k3_pre_topc(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,B)))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> (v3_pre_topc(B,A) & m1_connsp_2(D,k3_pre_topc(A,B),C) & C = F & D = E -> m1_connsp_2(E,A,F)))))))))))))) # label(t11_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6076 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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_tops_1(A,C)) <-> m1_connsp_2(C,A,B)))))))) # label(d1_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6077 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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))) -> (r4_connsp_1(A,B,C) & v3_pre_topc(B,A) -> v3_pre_topc(C,A)))))) <-> v1_connsp_2(A)))) # label(t24_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6078 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) & r3_connsp_1(A,B) -> r4_connsp_1(A,C,B)))))))) # label(t13_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6079 $T # label(t18_connsp_2) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6080 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> u1_struct_0(A) = k3_relat_1(k9_filter_1(A)) & k2_relat_1(k9_filter_1(A)) = u1_struct_0(A) & u1_struct_0(A) = k1_relat_1(k9_filter_1(A)))) # label(t33_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6081 (all A all B all C (m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> m1_filter_0(k1_filter_1(A,B,C),A))) # label(dt_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6082 (all A (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> -v3_struct_0(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & v17_lattices(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)))))) # label(t21_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6083 (all A all B (-v3_struct_0(A) & l3_lattices(A) & -v3_struct_0(B) & l3_lattices(B) -> l3_lattices(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)))) # label(dt_k8_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6084 (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 (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]. 183.69/184.86 6085 (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,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) -> (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) -> (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]. 183.69/184.86 6086 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(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) -> (r6_binop_1(A,C,D) & r6_binop_1(B,E,F) <-> 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]. 183.69/184.86 6087 (all A all B all C (m1_filter_0(C,A) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k1_filter_1(A,B,B) = B)) # label(idempotence_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6088 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (v10_lattices(k8_filter_1(A,B)) & v16_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v15_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B)) <-> -v3_struct_0(A) & l3_lattices(A) & l3_lattices(B) & v16_lattices(B) & v15_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & v16_lattices(A) & v15_lattices(A) & v10_lattices(A)))))) # label(t46_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6089 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_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]. 183.69/184.86 6090 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> k1_lattice2(k8_filter_1(A,B)) = k8_filter_1(k1_lattice2(A),k1_lattice2(B)))))) # label(t49_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6091 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (l3_lattices(B) & -v3_struct_0(B) -> k8_filter_1(A,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))))))) # label(d7_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6092 (all A all B (m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(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]. 183.69/184.86 6093 (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)) -> (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) -> (all D (m1_subset_1(D,u1_struct_0(k5_filter_1(A,B))) -> ((all E (v8_relat_2(E) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(E,u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(E) -> (k10_filter_0(A,B) = E -> D = k2_filter_1(u1_struct_0(A),E,C)))) <-> k6_filter_1(A,B,C) = D)))))))))) # label(d6_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6094 (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 (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]. 183.69/184.86 6095 (all A all B all C all D (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v10_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l3_lattices(B) & -v3_struct_0(B) -> k10_filter_1(A,B,C,D) = k4_tarski(C,D))) # label(redefinition_k10_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6096 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (v12_lattices(A) & v12_lattices(B) <-> v12_lattices(k8_filter_1(A,B))))))) # label(t38_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6097 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (m1_filter_0(B,A) -> (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all C (v3_lattices(C) & l3_lattices(C) & v10_lattices(C) & -v3_struct_0(C) -> ((all D (v3_relat_2(D) & v8_relat_2(D) & v1_partfun1(D,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) -> (D = k10_filter_0(A,B) -> 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))) = C))) <-> C = k5_filter_1(A,B))))))))) # label(d5_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.86 6098 (all A (-v1_xboole_0(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,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]. 183.69/184.86 6099 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(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)) & k6_filter_1(A,B,k3_lattices(A,C,D)) = k3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D)))))))))) # label(t15_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6100 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v15_lattices(k8_filter_1(A,B)) <-> v15_lattices(B) & v15_lattices(A)))))) # label(t42_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6101 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (r4_wellord1(k9_filter_1(A),k9_filter_1(B)) <-> r1_filter_1(A,B)))))) # label(d9_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6102 (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,k4_lattices(A,B,C),k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C))) = k9_filter_0(A,B,C))))))) # label(t51_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6103 (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]. 183.69/184.87 6104 (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_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (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) -> ((all E all F all G all H (r2_hidden(E,k8_eqrel_1(A,B)) & r2_hidden(G,E) & r2_hidden(H,F) & r2_hidden(F,k8_eqrel_1(A,B)) -> k6_eqrel_1(A,B,k1_binop_1(C,G,H)) = k1_binop_1(D,E,F))) <-> k4_filter_1(A,B,C) = D)))))))))) # label(d4_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6105 (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) -> (v1_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B)) <-> v1_binop_1(D,B) & v1_binop_1(C,A)))))))))) # label(t23_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6106 (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)) -> 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]. 183.69/184.87 6107 (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 (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]. 183.69/184.87 6108 (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)) -> (-v3_struct_0(A) & v15_lattices(A) & -v3_struct_0(B) & l3_lattices(B) & v15_lattices(B) & v10_lattices(B) & l3_lattices(A) & v10_lattices(A) -> (r2_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,F)) <-> r2_lattices(A,C,D) & r2_lattices(B,E,F))))))))))))))) # label(t45_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6109 (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,B,k4_filter_0(A,C,D)) = k4_filter_0(A,k4_lattices(A,B,C),D))))))))) # label(t17_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6110 (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]. 183.69/184.87 6111 (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]. 183.69/184.87 6112 (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]. 183.69/184.87 6113 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_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,E,F),B) & r2_hidden(k9_filter_0(A,C,D),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]. 183.69/184.87 6114 (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)) -> k4_filter_0(A,C,B) = k4_filter_0(A,k3_lattices(A,B,C),B) & k4_filter_0(A,B,C) = k4_filter_0(A,B,k4_lattices(A,B,C)))))))) # label(t55_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6115 (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)) -> k10_filter_1(A,B,k3_lattices(A,C,D),k3_lattices(B,E,F)) = k3_lattices(k8_filter_1(A,B),k10_filter_1(A,B,C,E),k10_filter_1(A,B,D,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]. 183.69/184.87 6116 (all A all B all C (-v1_xboole_0(A) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_funct_2(C,A,A) & m1_relset_1(C,A,A) & v1_funct_1(C) & v8_relat_2(B) & v3_relat_2(B) -> v1_funct_1(k3_filter_1(A,B,C)) & v1_funct_2(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)) & m2_relset_1(k3_filter_1(A,B,C),k8_eqrel_1(A,B),k8_eqrel_1(A,B)))) # label(dt_k3_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6117 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> r1_filter_1(k8_filter_1(A,B),k8_filter_1(B,A)))))) # label(t50_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6118 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> (l3_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B)) -> v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A)))))) # label(t35_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6119 (all A all B all C all D (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(B,B),B) & m1_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> v1_funct_1(k7_filter_1(A,B,C,D)) & 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)) & 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)))) # label(dt_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6120 (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]. 183.69/184.87 6121 (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)) -> 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]. 183.69/184.87 6122 (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) -> (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]. 183.69/184.87 6123 (all A (l3_lattices(A) & v10_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]. 183.69/184.87 6124 (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)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_filter_0(A,B,k9_filter_0(A,B,C)) = C)))))) # label(t54_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6125 (all A all B (-v3_struct_0(A) & v10_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & l3_lattices(A) -> r1_filter_1(A,A))) # label(reflexivity_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6126 (all A (v3_filter_0(A) & l3_lattices(A) & v10_lattices(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]. 183.69/184.87 6127 (all A (-v1_xboole_0(A) -> (all B (v1_relat_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) -> (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]. 183.69/184.87 6128 (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)) -> (r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k9_filter_1(A)) <-> r3_lattices(A,B,C)))))))) # label(t32_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6129 (all A all B all C (-v3_struct_0(A) & m1_subset_1(C,u1_struct_0(A)) & m1_filter_0(B,A) & l3_lattices(A) & v10_lattices(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]. 183.69/184.87 6130 (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]. 183.69/184.87 6131 (all A all B all C all D (v10_lattices(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) & -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]. 183.69/184.87 6132 (all A all B (v10_lattices(A) & v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & -v3_struct_0(A) -> -v3_struct_0(k8_filter_1(A,B)) & v3_lattices(k8_filter_1(A,B)) & v5_lattices(k8_filter_1(A,B)) & v6_lattices(k8_filter_1(A,B)) & v7_lattices(k8_filter_1(A,B)) & v8_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & v9_lattices(k8_filter_1(A,B)) & v4_lattices(k8_filter_1(A,B)))) # label(fc3_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6133 (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 (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]. 183.69/184.87 6134 (all A (-v3_struct_0(A) & v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_filter_0(B,A) -> -v3_struct_0(k5_filter_1(A,B)) & v10_lattices(k5_filter_1(A,B)) & v14_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & k6_filter_1(A,B,k6_lattices(A)) = k6_lattices(k5_filter_1(A,B)))))) # label(t19_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6135 (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 (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]. 183.69/184.87 6136 (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(B,B),B) & m2_relset_1(D,k2_zfmisc_1(B,B),B) & v1_funct_1(D) -> (v2_binop_1(k7_filter_1(A,B,C,D),k2_zfmisc_1(A,B)) <-> v2_binop_1(D,B) & v2_binop_1(C,A)))))))))) # label(t24_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6137 (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)) -> (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]. 183.69/184.87 6138 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_filter_0(B,A) -> (v13_lattices(A) -> v13_lattices(k5_filter_1(A,B)) & l3_lattices(k5_filter_1(A,B)) & k6_filter_1(A,B,k5_lattices(A)) = k5_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]. 183.69/184.87 6139 (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_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(A,C,D) & r3_lattices(B,E,F)))))))))))))) # label(t37_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6140 (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)) -> (r2_hidden(k4_filter_0(A,C,D),B) <-> r3_lattices(k5_filter_1(A,B),k6_filter_1(A,B,C),k6_filter_1(A,B,D))))))))))) # label(t16_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6141 (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) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & m2_relset_1(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) -> (r3_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F)) <-> r3_binop_1(B,D,F) & r3_binop_1(A,C,E)))))))))))))) # label(t27_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6142 (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 (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]. 183.69/184.87 6143 (all A all B (-v1_xboole_0(A) & v1_relat_1(B) -> (all C (m2_filter_1(C,A,B) -> v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A))))) # label(dt_m2_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6144 (all A all B all C (-v1_xboole_0(A) & m1_relset_1(B,A,A) & m1_subset_1(C,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> k6_eqrel_1(A,B,C) = k2_filter_1(A,B,C))) # label(redefinition_k2_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6145 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & v13_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & v13_lattices(B) & l3_lattices(B) & l3_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]. 183.69/184.87 6146 (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 (m2_relset_1(E,k2_zfmisc_1(A,A),A) & v1_funct_2(E,k2_zfmisc_1(A,A),A) & 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) -> (r2_binop_1(B,D,F) & r2_binop_1(A,C,E) <-> r2_binop_1(k2_zfmisc_1(A,B),k1_domain_1(A,B,C,D),k7_filter_1(A,B,E,F))))))))))))))) # label(t26_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6147 (all A (l3_lattices(A) & v3_filter_0(A) & v10_lattices(A) & -v3_struct_0(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]. 183.69/184.87 6148 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> (all D (v1_funct_2(D,k2_zfmisc_1(A,A),A) & m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) -> (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 (v1_funct_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(F,k2_zfmisc_1(B,B),B) & v1_funct_1(F) -> (r4_binop_1(B,E,F) & r4_binop_1(A,C,D) <-> 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]. 183.69/184.87 6149 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v13_lattices(k8_filter_1(A,B)) <-> v13_lattices(B) & v13_lattices(A)))))) # label(t40_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6150 (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]. 183.69/184.87 6151 (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 (-v3_struct_0(C) & l3_lattices(C) & v10_lattices(C) -> (r1_filter_1(B,C) & r1_filter_1(A,B) -> r1_filter_1(A,C)))))))) # label(t34_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6152 (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]. 183.69/184.87 6153 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) -> (v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & -v3_struct_0(B) & v10_lattices(B) & l3_lattices(B) & v17_lattices(B) & -v3_struct_0(A) <-> v17_lattices(k8_filter_1(A,B)) & l3_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B))))))) # label(t47_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6154 (all A all B (-v3_struct_0(A) & -v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) & l3_lattices(A) & v10_lattices(A) -> (r1_filter_1(A,B) -> r1_filter_1(B,A)))) # label(symmetry_r1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6155 (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)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k4_lattices(A,B,k7_lattices(A,C)) = k7_lattices(A,k4_filter_0(A,B,C)) & k9_filter_0(A,B,k7_lattices(A,C)) = k7_lattices(A,k9_filter_0(A,B,C)) & k7_lattices(A,k9_filter_0(A,B,C)) = k9_filter_0(A,k7_lattices(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)))))))) # label(t52_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6156 (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) -> (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]. 183.69/184.87 6157 (all A all B all C (v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(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) & v8_relat_2(B) & -v1_xboole_0(A) -> v1_funct_1(k4_filter_1(A,B,C)) & 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)) & 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)))) # label(dt_k4_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6158 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m2_relset_1(C,k2_zfmisc_1(A,A),A) -> (all D (m2_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(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_2(F,k2_zfmisc_1(B,B),B) & m2_relset_1(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]. 183.69/184.87 6159 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v3_filter_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]. 183.69/184.87 6160 (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_filter_0(B) & v3_filter_0(A) <-> v3_filter_0(k8_filter_1(A,B))))))) # label(t48_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6161 (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 (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]. 183.69/184.87 6162 (all A (v10_lattices(A) & l3_lattices(A) & v3_filter_0(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)) -> (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]. 183.69/184.87 6163 (all A all B all C (v10_lattices(A) & l3_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) & -v3_struct_0(A) -> k1_filter_1(A,C,B) = k1_filter_1(A,B,C))) # label(commutativity_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6164 (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 (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> (m1_filter_1(C,A,B) -> (all 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)) & v1_funct_1(D) -> (k3_filter_1(A,B,C) = D <-> (all E all F (r2_hidden(F,E) & r2_hidden(E,k8_eqrel_1(A,B)) -> k1_funct_1(D,E) = k6_eqrel_1(A,B,k1_funct_1(C,F)))))))))))))) # label(d3_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6165 (all A (-v1_xboole_0(A) -> (all B (v3_relat_2(B) & m2_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_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]. 183.69/184.87 6166 (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,B) = k2_filter_0(A,C) -> C = B))))))) # label(t2_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6167 (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) -> k1_domain_1(A,B,k2_binop_1(A,A,A,G,C,D),k2_binop_1(B,B,B,H,E,F)) = 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)))))))))))))))))) # label(t22_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6168 (all A all B all C (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(C,A) & m1_filter_0(B,A) -> k1_filter_1(A,B,C) = k3_xboole_0(B,C))) # label(redefinition_k1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6169 (all A (v10_lattices(A) & l3_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]. 183.69/184.87 6170 (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 (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]. 183.69/184.87 6171 (all A all B (-v3_struct_0(A) & l3_lattices(B) & -v3_struct_0(B) & l3_lattices(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]. 183.69/184.87 6172 (all A (-v1_xboole_0(A) -> (all B (v1_relat_1(B) -> (all C (v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C) -> ((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)))))) <-> m1_filter_1(C,A,B)))))))) # label(d1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6173 (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]. 183.69/184.87 6174 (all A all B (v1_relat_1(B) & -v1_xboole_0(A) -> (all C (m1_filter_1(C,A,B) -> v1_funct_2(C,A,A) & m2_relset_1(C,A,A) & v1_funct_1(C))))) # label(dt_m1_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6175 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (v10_lattices(B) & l3_lattices(B) & -v3_struct_0(B) -> (-v3_struct_0(A) & v10_lattices(A) & v14_lattices(A) & v10_lattices(B) & v14_lattices(B) & l3_lattices(B) & -v3_struct_0(B) & l3_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]. 183.69/184.87 6176 (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]. 183.69/184.87 6177 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) & v3_relat_2(B) -> 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]. 183.69/184.87 6178 (all A all B all C all D (v1_funct_1(C) & 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_2(C,k2_zfmisc_1(A,A),A) -> k3_funct_4(C,D) = k7_filter_1(A,B,C,D))) # label(redefinition_k7_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6179 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(B) -> (v10_lattices(A) & l3_lattices(B) & v11_lattices(B) & v10_lattices(B) & -v3_struct_0(B) & l3_lattices(A) & v11_lattices(A) & -v3_struct_0(A) <-> l3_lattices(k8_filter_1(A,B)) & v11_lattices(k8_filter_1(A,B)) & v10_lattices(k8_filter_1(A,B)) & -v3_struct_0(k8_filter_1(A,B))))))) # label(t39_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6180 (all A (-v3_struct_0(A) & l3_lattices(A) & v3_filter_0(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,k4_filter_0(A,B,C),k4_filter_0(A,B,k3_lattices(A,C,D))) & 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)))))))))) # label(t56_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6181 (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]. 183.69/184.87 6182 (all A all B (l3_lattices(B) & v10_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)) & r3_lattices(B,C,D) & k1_domain_1(u1_struct_0(B),u1_struct_0(B),C,D) = A & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_1_0_filter_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6183 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v3_compts_1(A) -> v4_pre_topc(k1_struct_0(A,B),A)))))) # label(t10_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6184 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (v9_metric_1(A) -> r2_hidden(k9_metric_1(A,B,C),k4_pcomps_1(A))))))))) # label(t33_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6185 (all A (l1_metric_1(A) -> r2_hidden(u1_struct_0(A),k4_pcomps_1(A)))) # label(t34_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6186 (all A l1_pre_topc(k2_pcomps_1(A))) # label(dt_k2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6187 (all A (l1_metric_1(A) -> g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A)) = k5_pcomps_1(A))) # label(d6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6188 (all A (l1_metric_1(A) -> v2_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))) & l1_pre_topc(g1_pre_topc(u1_struct_0(A),k4_pcomps_1(A))))) # label(t37_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6189 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_pre_topc(A,B) & (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(v1_tops_2(C,A) & r1_pre_topc(A,C) & v1_pcomps_1(C,A) & r1_setfam_1(C,B)))) & v1_tops_2(B,A)))) <-> v2_pcomps_1(A)))) # label(d4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6190 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_tarski(a_3_1_pcomps_1(A,B,C),B))))))) # label(t11_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6191 (all A k1_pcomps_1(A) = u1_pre_topc(k2_pcomps_1(A))) # label(t7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6192 $T # label(t32_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6193 (all A (l1_metric_1(A) -> v1_pre_topc(k5_pcomps_1(A)) & v2_pre_topc(k5_pcomps_1(A)))) # label(fc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6194 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> ((exists E (r2_hidden(E,B) & k6_pre_topc(A,E) = D & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_hidden(D,C)))) <-> k3_pcomps_1(A,B) = C))))))) # label(d3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6195 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> v1_pcomps_1(k3_pcomps_1(A,B),A)))))) # label(t21_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6196 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (v2_compts_1(A) -> v2_pcomps_1(A)))) # label(t25_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6197 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k1_tarski(B) = C -> k3_pcomps_1(A,C) = k1_tarski(k6_pre_topc(A,B))))))))) # label(t16_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6198 (all A (v2_pre_topc(k2_pcomps_1(A)) & v1_pre_topc(k2_pcomps_1(A)))) # label(fc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6199 (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)))) -> (k1_xboole_0 = B -> k3_pcomps_1(A,B) = k1_xboole_0))))) # label(t15_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6200 (exists A (v2_pre_topc(A) & v3_pcomps_1(A) & v1_pre_topc(A) & -v3_struct_0(A) & l1_pre_topc(A))) # label(rc3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.87 6201 (all A (m1_subset_1(A,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(A,f2_s1_pcomps_1) -> r2_hidden(f4_s1_pcomps_1(A),f3_s1_pcomps_1)))) -> (exists A (m2_relset_1(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(f1_s1_pcomps_1))) -> (r2_hidden(B,f2_s1_pcomps_1) -> f4_s1_pcomps_1(B) = k1_funct_1(A,B)))) & v1_funct_2(A,f2_s1_pcomps_1,f3_s1_pcomps_1) & v1_funct_1(A))) # label(s1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6202 (all A all B (-v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> v1_metric_1(k6_pcomps_1(A,B)) & v6_metric_1(k6_pcomps_1(A,B)) & v8_metric_1(k6_pcomps_1(A,B)) & l1_metric_1(k6_pcomps_1(A,B)) & v9_metric_1(k6_pcomps_1(A,B)) & v7_metric_1(k6_pcomps_1(A,B)) & -v3_struct_0(k6_pcomps_1(A,B)))) # label(dt_k6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6203 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> v2_tops_2(k3_pcomps_1(A,B),A))))) # label(t14_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6204 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_setfam_1(B,k3_pcomps_1(A,B)))))) # label(t20_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6205 $T # label(t6_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6206 (all A (-v3_struct_0(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_pre_topc(A,B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(D,B) & r2_hidden(C,D)))))))))) # label(t5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6207 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (v1_xreal_0(D) -> -(v9_metric_1(A) & r2_hidden(B,k9_metric_1(A,C,D)) & (all E (m1_subset_1(E,k1_numbers) -> -(-r1_xreal_0(E,np__0) & r1_tarski(k9_metric_1(A,B,E),k9_metric_1(A,C,D)))))))))))))) # label(t30_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6208 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v3_compts_1(A) & v2_pcomps_1(A) -> v5_compts_1(A)))) # label(t28_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6209 (all A (-v3_struct_0(A) & l1_metric_1(A) -> -v3_struct_0(k5_pcomps_1(A)) & v1_pre_topc(k5_pcomps_1(A)) & v2_pre_topc(k5_pcomps_1(A)))) # label(fc4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6210 (all A (v7_metric_1(A) & l1_metric_1(A) & v9_metric_1(A) & v8_metric_1(A) & v6_metric_1(A) & -v3_struct_0(A) -> v3_compts_1(k5_pcomps_1(A)))) # label(t38_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6211 (exists A (l1_pre_topc(A) & v2_pre_topc(A) & v3_compts_1(A) & v1_pre_topc(A) & -v3_struct_0(A))) # label(rc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6212 (all A v2_compts_1(k2_pcomps_1(k1_tarski(A)))) # label(t9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6213 (all A all B (l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> m1_subset_1(k3_pcomps_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6214 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) & v1_pcomps_1(C,A) -> v1_pcomps_1(B,A)))))))) # label(t12_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6215 (all A (-v3_struct_0(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(k1_zfmisc_1(u1_struct_0(A)))) -> k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),k3_pcomps_1(A,B),k3_pcomps_1(A,C)) = k3_pcomps_1(A,k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C)))))))) # label(t18_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6216 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (k4_pcomps_1(A) = B <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_numbers) -> -(-r1_xreal_0(E,np__0) & r1_tarski(k9_metric_1(A,D,E),C)))) & r2_hidden(D,C)))))))))))) # label(d5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6217 (all A A = u1_struct_0(k2_pcomps_1(A))) # label(t8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6218 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> (r1_pcomps_1(A,B) -> g1_metric_1(A,B) = k6_pcomps_1(A,B)))))) # label(d8_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6219 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_numbers) -> (all C (m1_subset_1(C,k1_numbers) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (all F (m1_subset_1(F,u1_struct_0(A)) -> -(r2_hidden(D,k5_subset_1(u1_struct_0(A),k9_metric_1(A,E,B),k9_metric_1(A,F,C))) & (all G (m1_subset_1(G,k1_numbers) -> -(r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,F,C)) & r1_tarski(k9_metric_1(A,D,G),k9_metric_1(A,E,B))))) & v9_metric_1(A)))))))))))))) # label(t31_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6220 (all A all B all C all D (l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> ((exists E (-r1_xboole_0(E,D) & r2_hidden(E,C) & A = E & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_3_0_pcomps_1(B,C,D))))) # label(fraenkel_a_3_0_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6221 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) -> k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t23_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6222 $T # label(t3_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6223 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> k6_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)) = k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t19_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6224 (all A all B all C all D (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) -> ((exists E (A = E & -r1_xboole_0(E,D) & r2_hidden(E,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))))) <-> r2_hidden(A,a_3_1_pcomps_1(B,C,D))))) # label(fraenkel_a_3_1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6225 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> ((exists B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & u1_pre_topc(A) = k4_pcomps_1(k6_pcomps_1(u1_struct_0(A),B)) & r1_pcomps_1(u1_struct_0(A),B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers))) <-> v3_pcomps_1(A)))) # label(d9_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6226 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (v3_compts_1(A) & v2_pcomps_1(A) -> v4_compts_1(A)))) # label(t27_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6227 (all A all B (m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_funct_1(B) -> (v8_metric_1(g1_metric_1(A,B)) & l1_metric_1(g1_metric_1(A,B)) & v9_metric_1(g1_metric_1(A,B)) & v7_metric_1(g1_metric_1(A,B)) & v6_metric_1(g1_metric_1(A,B)) <-> r1_pcomps_1(A,B)))) # label(t39_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6228 (all A (-v1_xboole_0(A) -> v1_pre_topc(k2_pcomps_1(A)) & v2_pre_topc(k2_pcomps_1(A)) & -v3_struct_0(k2_pcomps_1(A)))) # label(fc2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6229 (all A (l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> (exists D (v3_pre_topc(D,A) & v1_finset_1(a_3_0_pcomps_1(A,B,D)) & r2_hidden(C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))))) <-> v1_pcomps_1(B,A)))))) # label(d2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6230 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (exists C (m1_subset_1(C,k1_numbers) & -r1_xreal_0(C,np__0) & r1_tarski(k9_metric_1(A,B,C),u1_struct_0(A)))))))) # label(t29_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6231 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,k4_pcomps_1(A)) & r2_hidden(B,k4_pcomps_1(A)) -> r2_hidden(k5_subset_1(u1_struct_0(A),B,C),k4_pcomps_1(A))))))))) # label(t35_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6232 $T # label(t4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6233 (all A all B (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m2_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) -> ((all C (m1_subset_1(C,A) -> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> (np__0 = k1_metric_1(A,A,B,C,D) -> C = D) & (D = C -> np__0 = k1_metric_1(A,A,B,C,D)) & k1_metric_1(A,A,B,C,D) = k1_metric_1(A,A,B,D,C) & r1_xreal_0(k1_metric_1(A,A,B,C,E),k3_real_1(k1_metric_1(A,A,B,C,D),k1_metric_1(A,A,B,D,E))))))))) <-> r1_pcomps_1(A,B)))) # label(d7_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6234 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> r1_tarski(k5_setfam_1(u1_struct_0(A),B),k5_setfam_1(u1_struct_0(A),k3_pcomps_1(A,B))))))) # label(t22_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6235 (all A (l1_metric_1(A) -> m1_subset_1(k4_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) # label(dt_k4_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6236 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (v1_xreal_0(C) -> (all D (v1_xreal_0(D) -> (r1_xreal_0(C,D) -> r1_tarski(k9_metric_1(A,B,C),k9_metric_1(A,B,D))))))))))) # label(t1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6237 (all A m1_subset_1(k1_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(A)))) # label(dt_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6238 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_finset_1(B) -> v1_pcomps_1(B,A)))))) # label(t13_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6239 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(B,A) & r1_xboole_0(B,C) & (all D (m1_subset_1(D,u1_struct_0(A)) -> -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,F) & r1_xboole_0(E,F) & r1_tarski(B,E) & v3_pre_topc(F,A) & v3_pre_topc(E,A)))))) & r2_hidden(D,C)))) & (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))) -> -(v3_pre_topc(E,A) & r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(D,E) & v3_pre_topc(D,A)))))) & v4_pre_topc(C,A) & v2_pcomps_1(A)))))))) # label(t26_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6240 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (v1_pcomps_1(B,A) & v2_tops_2(B,A) -> v4_pre_topc(k5_setfam_1(u1_struct_0(A),B),A)))))) # label(t24_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6241 (all A k1_zfmisc_1(A) = k1_pcomps_1(A)) # label(redefinition_k1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6242 (exists A (l1_pre_topc(A) & -v3_struct_0(A) & v2_pre_topc(A) & v2_pcomps_1(A))) # label(rc1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6243 (all A (l1_metric_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,k4_pcomps_1(A)) -> r2_hidden(k5_setfam_1(u1_struct_0(A),B),k4_pcomps_1(A))))))) # label(t36_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6244 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(k1_xboole_0 = k6_pre_topc(A,B) & B != k1_xboole_0) & -(k1_xboole_0 = B & k1_xboole_0 != k6_pre_topc(A,B)))))) # label(t2_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6245 (all A (l1_metric_1(A) -> l1_pre_topc(k5_pcomps_1(A)))) # label(dt_k5_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6246 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (r1_tarski(B,C) -> r1_tarski(k3_pcomps_1(A,B),k3_pcomps_1(A,C))))))))) # label(t17_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6247 (all A g1_pre_topc(A,k1_pcomps_1(A)) = k2_pcomps_1(A)) # label(d1_pcomps_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6248 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v3_pre_topc(C,A) & v3_pre_topc(D,B) -> v3_pre_topc(k7_borsuk_1(A,B,C,D),k6_borsuk_1(A,B))))))))))) # label(t46_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6249 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) -> k2_funcop_1(B,C) = k1_borsuk_1(A,B,C))) # label(redefinition_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6250 $T # label(t1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6251 $T # label(t8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6252 $T # label(t3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6253 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k1_funct_1(k1_funct_3(k9_funct_3(B,C)),A) = k2_funct_2(k2_zfmisc_1(B,C),B,k9_funct_3(B,C),A))) # label(t9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6254 (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 (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) -> k5_setfam_1(B,k2_funct_2(k1_zfmisc_1(A),k1_zfmisc_1(B),k2_funct_3(A,B,C),D)) = k2_funct_2(A,B,C,k5_setfam_1(A,D)))))))) # label(t16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6255 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) & v2_pre_topc(A) -> v5_pre_topc(k17_borsuk_1(A,B),A,k16_borsuk_1(A,B)) & m2_relset_1(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & v1_funct_2(k17_borsuk_1(A,B),u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B))) & v1_funct_1(k17_borsuk_1(A,B)))) # label(dt_k17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6256 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> k18_borsuk_1(A,B,C) = k2_xboole_0(C,a_2_3_borsuk_1(A,B)))))))) # label(d12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6257 (all A all B all C all D all E (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & l1_pre_topc(B) & l1_pre_topc(C) & v1_funct_1(D) & v5_pre_topc(D,A,B) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v5_pre_topc(E,B,C) & v1_funct_1(E) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v2_pre_topc(C) & -v3_struct_0(C) & v2_pre_topc(B) & v2_pre_topc(A) -> v1_funct_1(k4_borsuk_1(A,B,C,D,E)) & v5_pre_topc(k4_borsuk_1(A,B,C,D,E),A,C) & m2_relset_1(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v1_funct_2(k4_borsuk_1(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)))) # label(dt_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6258 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(A) -> v2_pre_topc(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & -v3_struct_0(k6_borsuk_1(A,B)))) # label(fc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6259 (all A all B all C (l1_struct_0(A) & m1_subset_1(C,u1_struct_0(B)) & l1_struct_0(B) & -v3_struct_0(B) -> v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k3_borsuk_1(A,B,C)))) # label(dt_k3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6260 (all A all B (v2_pre_topc(A) & m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> v2_pre_topc(k16_borsuk_1(A,B)) & v1_pre_topc(k16_borsuk_1(A,B)) & -v3_struct_0(k16_borsuk_1(A,B)))) # label(fc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6261 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> r1_tarski(k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)),C))))))) # label(t53_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6262 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(D,k18_borsuk_1(A,B,C)) & -r2_hidden(D,C) & (all E (m1_subset_1(E,u1_struct_0(A)) -> -(-r2_hidden(E,k2_pre_topc(B)) & k1_struct_0(A,E) = D)))))))))))) # label(t74_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6263 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_borsuk_1(B,A) -> m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B))))) # label(dt_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6264 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_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)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),E) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) -> D = E | r2_hidden(D,u1_struct_0(B))))))))))))) # label(t78_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6265 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> k3_tarski(a_2_0_borsuk_1(A,B)) = k3_tarski(k5_setfam_1(A,B)))) # label(t17_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6266 $T # label(t43_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6267 (all A all 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) != k1_xboole_0 -> C = k1_funct_1(k1_funct_3(k9_funct_3(A,B)),k12_mcart_1(A,B,C,D)) & D = k1_funct_1(k1_funct_3(k10_funct_3(A,B)),k12_mcart_1(A,B,C,D))))))) # label(t13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6268 (all A all B all C r1_tarski(k9_relat_1(k2_funcop_1(A,B),C),k1_tarski(B))) # label(t6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6269 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) -> (all C (v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) -> (k16_borsuk_1(A,B) = C <-> u1_pre_topc(C) = a_2_2_borsuk_1(A,B) & B = u1_struct_0(C)))))))) # label(d10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6270 (all A all B all C all D all E (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & m1_connsp_2(E,B,C) & v1_funct_1(D) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> m2_connsp_2(k5_borsuk_1(A,B,C,D,E),A,k5_pre_topc(A,B,D,k1_struct_0(B,C))))) # label(dt_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6271 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C)) = k1_tops_1(k6_borsuk_1(A,B),C))))))) # label(t55_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6272 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (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(B))) -> (r1_compts_1(k6_borsuk_1(A,B),C,k7_borsuk_1(A,B,D,E)) -> (D != k1_xboole_0 -> r1_compts_1(B,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),E)) & (E != k1_xboole_0 -> r1_compts_1(A,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),D))))))))))))) # label(t62_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6273 (all A all B (l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(A) & -v3_struct_0(A) -> m2_relset_1(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))) & v1_funct_2(k12_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A))) & v1_funct_1(k12_borsuk_1(A,B)))) # label(dt_k12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6274 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),k11_borsuk_1(A,B,C))))))))) # label(t54_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6275 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,C) -> k8_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k1_domain_1(A,C,E,F)) = k1_domain_1(B,C,k8_funct_2(A,B,D,E),F))))))))))))) # label(t21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6276 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_borsuk_1(B,A) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (all D (m2_connsp_2(D,A,k5_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),k1_struct_0(k16_borsuk_1(A,B),C))) -> m1_connsp_2(k4_pre_topc(A,k16_borsuk_1(A,B),k17_borsuk_1(A,B),D),k16_borsuk_1(A,B),C))))))))) # label(t81_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6277 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_pre_topc(B,A) & -v3_struct_0(B) & v1_borsuk_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B))))) # label(rc4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6278 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> k2_borsuk_1(u1_struct_0(A),B) = k17_borsuk_1(A,B))))) # label(d11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6279 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> k13_borsuk_1(A,B) = k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B))))))) # label(d8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6280 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) -> m2_relset_1(k1_borsuk_1(A,B,C),B,A) & v1_funct_2(k1_borsuk_1(A,B,C),B,A) & v1_funct_1(k1_borsuk_1(A,B,C)))) # label(dt_k1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6281 $T # label(t2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6282 (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,A,B) & v1_funct_2(E,A,B) & v1_funct_1(E) -> (all F (v1_funct_2(F,B,C) & m2_relset_1(F,B,C) & v1_funct_1(F) -> r1_tarski(k3_funct_2(A,B,E,k6_domain_1(B,D)),k3_funct_2(A,C,k7_funct_2(A,B,C,E,F),k6_domain_1(C,k8_funct_2(B,C,F,D)))))))))))))))) # label(t20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6283 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v2_borsuk_1(C,B) & m1_borsuk_1(C,B) -> (r2_borsuk_1(A,B) -> r2_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t85_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6284 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(A)) -> ((all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (r2_hidden(D,B) -> r1_xboole_0(D,C) | r1_tarski(D,C)))) -> k3_funct_2(A,B,k2_borsuk_1(A,B),k2_funct_2(A,B,k2_borsuk_1(A,B),C)) = C))))))) # label(t33_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6285 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (k7_borsuk_1(A,B,C,D) != k1_xboole_0 -> D = k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) & C = k8_funct_2(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),k7_borsuk_1(A,B,C,D))))))))))) # label(t65_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6286 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C) = k1_xboole_0 | k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C) = k1_xboole_0 -> C = k1_xboole_0))))))) # label(t61_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6287 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> r2_hidden(C,k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),C)))))))) # label(t70_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6288 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> (exists D (m1_subset_1(D,A) & k8_funct_2(A,B,k2_borsuk_1(A,B),D) = C)))))))) # label(t32_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6289 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_zfmisc_1(A),B) -> C = k3_funct_2(A,B,k2_borsuk_1(A,B),k6_domain_1(B,C)))))))) # label(t30_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6290 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_borsuk_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> v4_pre_topc(C,A))))))))) # label(d14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6291 $T # label(t22_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6292 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -((all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(r2_hidden(E,C) & D = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),E)))) & r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),C)))))))))) # label(t58_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6293 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & -v3_struct_0(B) -> m1_borsuk_1(k19_borsuk_1(A,B,C),A))) # label(dt_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6294 (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))) -> (D = C -> (v6_compts_1(C,A) <-> v6_compts_1(D,B))))))))))) # label(t42_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6295 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (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)) & v5_pre_topc(D,B,A) -> (all E (m1_connsp_2(E,A,C) -> m2_connsp_2(k5_pre_topc(B,A,D,E),B,k5_pre_topc(B,A,D,k1_struct_0(A,C))))))))))))) # label(t38_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6296 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) -> (exists D ((exists E (k8_borsuk_1(A,B,D,E) = C & m1_subset_1(E,u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(A)))))))))) # label(t50_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6297 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_funct_1(k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))))))))))) # label(t80_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6298 (all A all B all C (v1_funct_1(C) & v1_relat_1(C) -> (r1_tarski(A,k10_relat_1(C,B)) -> r1_tarski(k9_relat_1(C,A),B)))) # label(t5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6299 (all A all B (v2_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_funct_2(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))) & m2_relset_1(k13_borsuk_1(A,B),k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B))) & v1_funct_1(k13_borsuk_1(A,B)))) # label(dt_k13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6300 $T # label(t11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6301 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) & m1_pre_topc(B,A) & -v3_struct_0(B) -> m1_eqrel_1(k18_borsuk_1(A,B,C),u1_struct_0(A)) & -v1_xboole_0(k18_borsuk_1(A,B,C)))) # label(dt_k18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6302 (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) & v1_borsuk_1(B,A))))) # label(rc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6303 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> r1_tarski(k5_pre_topc(A,B,C,k1_tops_1(B,D)),k1_tops_1(A,k5_pre_topc(A,B,C,D))))))))))) # label(t37_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6304 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) -> (all E (m1_subset_1(E,B) -> (all F (m1_subset_1(F,C) -> k12_mcart_1(A,C,k3_funct_2(A,B,D,k6_domain_1(B,E)),k6_domain_1(C,F)) = k3_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k6_domain_1(k2_zfmisc_1(B,C),k1_domain_1(B,C,E,F))))))))))))))) # label(t24_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6305 (all A all B (-v1_xboole_0(A) & m1_eqrel_1(B,A) & -v1_xboole_0(B) -> m2_relset_1(k2_borsuk_1(A,B),A,B) & v1_funct_2(k2_borsuk_1(A,B),A,B) & v1_funct_1(k2_borsuk_1(A,B)))) # label(dt_k2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6306 $T # label(d4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.69/184.88 6307 (all A all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (k5_setfam_1(A,B) = A -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (D = k3_tarski(C) -> r1_tarski(k3_subset_1(A,D),k3_tarski(k3_subset_1(B,C))))))))))) # label(t18_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6308 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(k16_borsuk_1(A,B))) -> (exists D (m1_subset_1(D,u1_struct_0(A)) & C = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,B)),k17_borsuk_1(A,B),D))))))))) # label(t71_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6309 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> k11_borsuk_1(A,B,C) = a_3_1_borsuk_1(A,B,C))))))) # label(d6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6310 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B m1_borsuk_1(B,A)))) # label(existence_m1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6311 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (v1_pre_topc(C) & l1_pre_topc(C) & v2_pre_topc(C) -> (u1_pre_topc(C) = a_3_0_borsuk_1(A,B,C) & u1_struct_0(C) = k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)) <-> C = k6_borsuk_1(A,B)))))))) # label(d5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6312 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> k1_funct_1(k17_borsuk_1(B,C),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D)))))))))) # label(t76_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6313 (all A all B all C (v2_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & v1_borsuk_1(B,A) & l1_pre_topc(A) & -v3_struct_0(A) -> v1_pre_topc(k21_borsuk_1(A,B,C)) & m1_pre_topc(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))) & v1_borsuk_1(k21_borsuk_1(A,B,C),k16_borsuk_1(A,k20_borsuk_1(A,B,C))))) # label(dt_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6314 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> m1_subset_1(k3_tarski(C),k1_zfmisc_1(A)))))))) # label(t25_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6315 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_setfam_1(B) & m1_eqrel_1(B,A))))) # label(rc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6316 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) -> ((all D (m1_subset_1(D,A) -> r2_hidden(D,k8_funct_2(A,B,C,D)))) <-> k2_borsuk_1(A,B) = C))))))) # label(d1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6317 (all A (l1_struct_0(A) & -v3_struct_0(A) -> v1_setfam_1(k15_borsuk_1(A)) & -v1_xboole_0(k15_borsuk_1(A)))) # label(fc3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6318 (all A all B all C (-v3_struct_0(A) & m1_pre_topc(B,A) & m1_borsuk_1(C,B) & v1_borsuk_1(B,A) & -v3_struct_0(B) & l1_pre_topc(A) & v2_pre_topc(A) -> k18_borsuk_1(A,B,C) = k19_borsuk_1(A,B,C))) # label(redefinition_k19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6319 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> (exists F ((exists G (m1_subset_1(G,k1_zfmisc_1(B)) & k12_mcart_1(A,B,F,G) = E)) & m1_subset_1(F,k1_zfmisc_1(A)))) & r1_tarski(E,C))) -> r1_tarski(k2_zfmisc_1(k1_setfam_1(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k3_tarski(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.88 6320 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(A)) -> (all F (m1_subset_1(F,k1_zfmisc_1(C)) -> k2_funct_2(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C),k16_funct_3(A,C,B,C,D,k6_partfun1(C)),k12_mcart_1(A,C,E,F)) = k12_mcart_1(B,C,k2_funct_2(A,B,D,E),F))))))))))))) # label(t23_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6321 (all A all B all C all D all E all F (-v3_struct_0(A) & v2_pre_topc(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) & m1_connsp_2(F,B,D) & m1_connsp_2(E,A,C) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & l1_pre_topc(A) -> m1_connsp_2(k9_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))) # label(dt_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6322 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> r1_tarski(u1_struct_0(B),u1_struct_0(A)))))) # label(t35_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6323 (all A all B all C all D all E all F (l1_pre_topc(A) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D,u1_struct_0(B)) & m2_connsp_2(E,A,C) & m1_connsp_2(F,B,D) & v2_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) & -v3_struct_0(A) -> m2_connsp_2(k10_borsuk_1(A,B,C,D,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,k1_struct_0(B,D))))) # label(dt_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6324 (all A all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> k3_xboole_0(k3_tarski(C),k3_tarski(D)) = k3_tarski(k5_subset_1(B,C,D)))))))) # label(t26_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6325 (all A all B all C all D (v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_funct_1(C) -> k14_borsuk_1(A,B,C,D) = k9_relat_1(C,D))) # label(redefinition_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6326 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) & -v1_xboole_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> k3_funct_2(A,B,k2_borsuk_1(A,B),C) = k3_tarski(C))))))) # label(t31_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6327 $T # label(t7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6328 (all A all B all C all D all E all F (-v3_struct_0(A) & v2_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_connsp_2(F,B,D) & m2_connsp_2(E,A,C) & m1_subset_1(D,u1_struct_0(B)) & l1_pre_topc(A) -> k2_zfmisc_1(E,F) = k10_borsuk_1(A,B,C,D,E,F))) # label(redefinition_k10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6329 $T # label(t40_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6330 (all A all B all C all D all E (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(C) & v2_pre_topc(C) & m1_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v5_pre_topc(E,B,C) & v1_funct_1(E) & v5_pre_topc(D,A,B) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D) & l1_pre_topc(C) & -v3_struct_0(B) -> k5_relat_1(D,E) = k4_borsuk_1(A,B,C,D,E))) # label(redefinition_k4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6331 (all A all B all C all D (v1_funct_1(C) & m1_relset_1(C,k1_pcomps_1(A),k1_pcomps_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_funct_2(C,k1_pcomps_1(A),k1_pcomps_1(B)) -> m1_subset_1(k14_borsuk_1(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(B))))) # label(dt_k14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6332 (all A all B all C all D (v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) & v2_pre_topc(A) -> k7_borsuk_1(A,B,C,D) = k2_zfmisc_1(C,D))) # label(redefinition_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6333 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) -> (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(B))) -> (k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(B),k10_funct_3(u1_struct_0(A),u1_struct_0(B)),C) = E -> v3_pre_topc(E,B)) & (k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),C) = D -> v3_pre_topc(D,A))))))))))))) # label(t59_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6334 (all A (l1_pre_topc(A) -> ((all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(k8_metric_1)))) -> (B = k1_rcomp_1(np__0,np__1) -> k3_pre_topc(k5_pcomps_1(k8_metric_1),B) = A))) <-> k22_borsuk_1 = A))) # label(d16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6335 (all A all B all C all D (l1_pre_topc(A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) -> m1_subset_1(k7_borsuk_1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))))) # label(dt_k7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6336 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D) = k1_struct_0(A,D)))))))))) # label(t77_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6337 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> v1_tops_2(k11_borsuk_1(A,B,C),k6_borsuk_1(A,B)))))))) # label(t51_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6338 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_eqrel_1(C,u1_struct_0(B)) & -v1_xboole_0(C) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (-r2_hidden(D,u1_struct_0(B)) -> r2_hidden(k1_struct_0(A,D),k18_borsuk_1(A,B,C))))))))))) # label(t75_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6339 (all A all B all C (m1_eqrel_1(C,u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) -> (r2_hidden(A,a_2_2_borsuk_1(B,C)) <-> (exists D (D = A & r2_hidden(k3_tarski(D),u1_pre_topc(B)) & m1_subset_1(D,k1_zfmisc_1(C))))))) # label(fraenkel_a_2_2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6340 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v2_borsuk_1(C,B) & m1_borsuk_1(C,B) -> (r1_borsuk_1(A,B) -> r1_borsuk_1(k16_borsuk_1(A,k20_borsuk_1(A,B,C)),k21_borsuk_1(A,B,C))))))))) # label(t84_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6341 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> -(r1_compts_1(A,C,D) & (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> -(r1_compts_1(A,E,D) & (all F -(r2_hidden(F,E) & r1_xboole_0(F,D))) & r1_tarski(E,C))))))))))))) # label(t63_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6342 (all A all B all C all D all E (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_pre_topc(B) & v5_pre_topc(D,A,B) & m1_connsp_2(E,B,C) & m1_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) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & -v3_struct_0(A) -> k10_relat_1(D,E) = k5_borsuk_1(A,B,C,D,E))) # label(redefinition_k5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6343 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & m1_eqrel_1(B,u1_struct_0(A)) -> v1_pre_topc(k16_borsuk_1(A,B)) & v2_pre_topc(k16_borsuk_1(A,B)) & l1_pre_topc(k16_borsuk_1(A,B)))) # label(dt_k16_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6344 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,A) -> (all D (m2_subset_1(D,k1_zfmisc_1(A),B) -> (r2_hidden(C,D) -> D = k8_funct_2(A,B,k2_borsuk_1(A,B),C)))))))))) # label(t29_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6345 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(k16_borsuk_1(A,k18_borsuk_1(A,B,C))),k17_borsuk_1(A,k18_borsuk_1(A,B,C)),D),u1_struct_0(k16_borsuk_1(B,C))) -> r2_hidden(D,u1_struct_0(B))))))))))) # label(t79_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6346 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (m1_borsuk_1(B,A) & v1_setfam_1(B) & v2_borsuk_1(B,A) & -v1_xboole_0(B))))) # label(rc5_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6347 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (all E (m2_connsp_2(E,A,C) -> (all F (m2_connsp_2(F,B,D) -> m2_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)))))))))))))) # label(t49_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6348 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> k1_tops_1(k6_borsuk_1(A,B),k7_borsuk_1(A,B,C,D)) = k7_borsuk_1(A,B,k1_tops_1(A,C),k1_tops_1(B,D)))))))))) # label(t47_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6349 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> v6_compts_1(k1_struct_0(A,B),A))))) # label(t41_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6350 (all A (-v1_xboole_0(A) -> (all B (m1_eqrel_1(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> (k3_tarski(C) = D -> k3_tarski(k3_subset_1(B,C)) = k3_subset_1(A,D)))))))))) # label(t27_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6351 (all A all B all C all D (l1_pre_topc(A) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) & -v3_struct_0(A) -> k4_tarski(C,D) = k8_borsuk_1(A,B,C,D))) # label(redefinition_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6352 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) -> (r2_hidden(A,a_2_0_borsuk_1(B,C)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(B)) & k3_tarski(D) = A & r2_hidden(D,C)))))) # label(fraenkel_a_2_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6353 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (all D -(r2_hidden(D,k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),C)) & (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> -(D = k2_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B)),E) & r2_hidden(E,C)))))))))))) # label(t57_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6354 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) -> (v6_compts_1(D,B) -> (all E (m2_connsp_2(E,k6_borsuk_1(B,A),k7_borsuk_1(B,A,D,k1_struct_0(A,C))) -> (exists F ((exists G (m1_connsp_2(G,A,C) & r1_tarski(k10_borsuk_1(B,A,D,C,F,G),E))) & m2_connsp_2(F,B,D)))))))))))))) # label(t67_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6355 (all A all B all C (l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) & v2_pre_topc(A) -> m1_subset_1(k11_borsuk_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))))) # label(dt_k11_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6356 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_hidden(B,k15_borsuk_1(A)) & (all C (m1_subset_1(C,u1_struct_0(A)) -> B != k1_struct_0(A,C)))))))) # label(t68_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6357 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (v3_pre_topc(C,k6_borsuk_1(A,B)) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) & k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D) = C & (all E -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (all G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) -> -(v3_pre_topc(F,A) & v3_pre_topc(G,B) & E = k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G)))))) & r2_hidden(E,D)))))))))))) # label(t45_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6358 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> (v1_tops_2(C,k6_borsuk_1(A,B)) -> v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),C),A) & v1_tops_2(k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(B),k13_borsuk_1(A,B),C),B)))))))) # label(t60_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6359 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) -> r1_tarski(C,k18_borsuk_1(A,B,C)))))))) # label(t73_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6360 (all A all B (v2_pre_topc(A) & l1_pre_topc(A) & l1_pre_topc(B) & v2_pre_topc(B) -> l1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)))) # label(dt_k6_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6361 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(A)) -> (all D (m1_subset_1(D,k1_zfmisc_1(B)) -> (k1_xboole_0 != k12_mcart_1(A,B,C,D) -> k2_funct_2(k2_zfmisc_1(A,B),A,k9_funct_3(A,B),k12_mcart_1(A,B,C,D)) = C & k2_funct_2(k2_zfmisc_1(A,B),B,k10_funct_3(A,B),k12_mcart_1(A,B,C,D)) = D))))) # label(t12_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6362 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> k2_funct_3(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(A),k9_funct_3(u1_struct_0(A),u1_struct_0(B))) = k12_borsuk_1(A,B))))) # label(d7_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6363 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> k1_xboole_0 = k1_funct_1(k12_borsuk_1(A,B),k1_xboole_0) & k1_funct_1(k13_borsuk_1(A,B),k1_xboole_0) = k1_xboole_0)))) # label(t66_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6364 (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) -> -v1_xboole_0(k8_eqrel_1(A,B)))))) # label(t28_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6365 (all A all B all C all D (v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(D) & v2_pre_topc(D) & v1_pre_topc(D) & l1_pre_topc(C) -> ((exists E (A = k5_setfam_1(u1_struct_0(D),E) & r1_tarski(E,a_2_1_borsuk_1(B,C)) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D)))))) <-> r2_hidden(A,a_3_0_borsuk_1(B,C,D))))) # label(fraenkel_a_3_0_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6366 (all A all B (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) & v2_pre_topc(A) -> (exists C (m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & -v1_xboole_0(C) & v1_relat_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_funct_1(C))))) # label(rc2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6367 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> v5_pre_topc(k3_borsuk_1(B,A,C),B,A))))))) # label(t36_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6368 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (r2_borsuk_1(A,B) <-> (exists C (v5_pre_topc(C,k6_borsuk_1(A,k22_borsuk_1),A) & m2_relset_1(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)) & (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,u1_struct_0(B)) -> (all E (m1_subset_1(E,u1_struct_0(k22_borsuk_1)) -> D = k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,E))))) & r2_hidden(k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k24_borsuk_1)),u1_struct_0(B)) & k8_funct_2(u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A),C,k8_borsuk_1(A,k22_borsuk_1,D,k23_borsuk_1)) = D)) & v1_funct_2(C,u1_struct_0(k6_borsuk_1(A,k22_borsuk_1)),u1_struct_0(A)) & v1_funct_1(C)))))))) # label(d21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6369 (all A (l1_struct_0(A) -> m1_eqrel_1(k15_borsuk_1(A),u1_struct_0(A)))) # label(dt_k15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6370 (all A (l1_struct_0(A) -> k8_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A))) = k15_borsuk_1(A))) # label(d9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6371 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k1_borsuk_1(u1_struct_0(B),u1_struct_0(A),C) = k3_borsuk_1(A,B,C))))))) # label(d3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6372 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> m1_borsuk_1(k15_borsuk_1(A),A))) # label(t82_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6373 (all A all B all C (m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) -> ((all E (r2_hidden(E,D) -> (exists F ((exists G (E = k12_mcart_1(A,B,F,G) & m1_subset_1(G,k1_zfmisc_1(B)))) & m1_subset_1(F,k1_zfmisc_1(A)))) & r1_tarski(E,C))) -> r1_tarski(k2_zfmisc_1(k3_tarski(k9_relat_1(k1_funct_3(k9_funct_3(A,B)),D)),k1_setfam_1(k9_relat_1(k1_funct_3(k10_funct_3(A,B)),D))),C)))))) # label(t14_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6374 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) -> ((all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_connsp_2(E,B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) -> (exists F (r1_tarski(k4_pre_topc(A,B,C,F),E) & m1_connsp_2(F,A,D))))))) <-> v5_pre_topc(C,A,B)))))))) # label(d2_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6375 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (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)) -> (r2_hidden(D,u1_struct_0(B)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = D))) <-> v3_borsuk_1(C,A,B)))))))) # label(d19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6376 (all A all B all C all D (-v3_struct_0(A) & v2_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & -v3_struct_0(B) & l1_pre_topc(A) -> m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))))) # label(dt_k8_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6377 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (l1_pre_topc(B) & v2_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (r1_tarski(C,D) -> r1_tarski(k11_borsuk_1(A,B,C),k11_borsuk_1(A,B,D))))))))))) # label(t52_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6378 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_eqrel_1(B,u1_struct_0(A)) & -v1_xboole_0(B) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> (all D (m2_connsp_2(D,A,C) -> (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(E,A) & r1_tarski(E,D) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(F,B) -> r1_tarski(F,E) | r1_xboole_0(F,E)))) & r1_tarski(C,E)))))))) <-> m1_borsuk_1(B,A)))))) # label(d13_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6379 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (-v1_xboole_0(C) -> (all D (v1_funct_2(D,A,B) & m2_relset_1(D,A,B) & v1_funct_1(D) -> (all E (v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) -> -((all F (m1_subset_1(F,A) -> (all G (m1_subset_1(G,A) -> (k8_funct_2(A,B,D,F) = k8_funct_2(A,B,D,G) -> k8_funct_2(A,C,E,F) = k8_funct_2(A,C,E,G)))))) & (all F (v1_funct_1(F) & m2_relset_1(F,B,C) & v1_funct_2(F,B,C) -> k7_funct_2(A,B,C,D,F) != E))))))))))))) # label(t19_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6380 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> u1_struct_0(k16_borsuk_1(A,B)) = k2_relat_1(k17_borsuk_1(A,B)))))) # label(t72_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6381 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(v1_finset_1(C) & r1_tarski(C,k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),D)) & (all E (m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> -(r1_tarski(E,D) & v1_finset_1(E) & C = k14_borsuk_1(u1_struct_0(k6_borsuk_1(A,B)),u1_struct_0(A),k12_borsuk_1(A,B),E))))))))))))) # label(t64_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6382 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m2_connsp_2(D,A,C) -> (r1_tarski(B,C) -> m2_connsp_2(D,A,B)))))))))) # label(t39_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6383 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_1(B,A) & m1_borsuk_1(C,B) & v2_borsuk_1(C,B) & m1_pre_topc(B,A) & -v3_struct_0(B) & l1_pre_topc(A) -> k21_borsuk_1(A,B,C) = k16_borsuk_1(B,C))) # label(redefinition_k21_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6384 (all A all B all C (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & v2_pre_topc(A) -> v2_borsuk_1(k20_borsuk_1(A,B,C),A) & m1_borsuk_1(k20_borsuk_1(A,B,C),A))) # label(dt_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6385 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (r1_borsuk_1(A,B) <-> (exists C (v1_funct_1(C) & v5_pre_topc(C,A,B) & v3_borsuk_1(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))))))))) # label(d20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6386 $T # label(t44_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6387 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (m1_connsp_2(E,A,C) -> (all F (m1_connsp_2(F,B,D) -> m1_connsp_2(k7_borsuk_1(A,B,E,F),k6_borsuk_1(A,B),k8_borsuk_1(A,B,C,D)))))))))))))) # label(t48_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6388 (all A all B (m1_subset_1(B,k1_zfmisc_1(A)) -> B = k3_funct_2(A,A,k6_partfun1(A),B))) # label(t4_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6389 (all A all B all C all D (v2_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(B,C)))) & l1_pre_topc(C) & l1_pre_topc(B) & v2_pre_topc(B) -> (r2_hidden(A,a_3_1_borsuk_1(B,C,D)) <-> (exists E exists F (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & r1_tarski(k7_borsuk_1(B,C,E,F),D) & v3_pre_topc(E,B) & v3_pre_topc(F,C) & k7_borsuk_1(B,C,E,F) = A))))) # label(fraenkel_a_3_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6390 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) -> (all D (m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) -> ((all E (r2_hidden(E,D) -> r1_tarski(E,C) & (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & (exists G (m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) & E = k7_borsuk_1(A,B,F,G))))))) -> r1_tarski(k7_borsuk_1(A,B,k5_setfam_1(u1_struct_0(A),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(A)),k12_borsuk_1(A,B),D)),k6_setfam_1(u1_struct_0(B),k2_funct_2(k1_pcomps_1(u1_struct_0(k6_borsuk_1(A,B))),k1_pcomps_1(u1_struct_0(B)),k13_borsuk_1(A,B),D))),C)))))))))) # label(t56_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6391 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,k1_zfmisc_1(B)) -> (r2_hidden(C,u1_pre_topc(k16_borsuk_1(A,B))) <-> r2_hidden(k3_tarski(C),u1_pre_topc(A))))))))) # label(t69_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6392 (all A all B all C (-v3_struct_0(A) & v2_pre_topc(A) & -v3_struct_0(B) & v2_borsuk_1(C,B) & m1_borsuk_1(C,B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) & l1_pre_topc(A) -> k18_borsuk_1(A,B,C) = k20_borsuk_1(A,B,C))) # label(redefinition_k20_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6393 (all A all B all C (l1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(B) & v2_pre_topc(B) -> (r2_hidden(A,a_2_1_borsuk_1(B,C)) <-> (exists D exists E (r2_hidden(E,u1_pre_topc(C)) & r2_hidden(D,u1_pre_topc(B)) & k12_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E) = A & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))))))) # label(fraenkel_a_2_1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6394 (all A all B all C all D all E all F (v2_pre_topc(A) & l1_pre_topc(A) & m1_connsp_2(F,B,D) & m1_connsp_2(E,A,C) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(C,u1_struct_0(A)) & l1_pre_topc(B) & v2_pre_topc(B) & -v3_struct_0(B) & -v3_struct_0(A) -> k2_zfmisc_1(E,F) = k9_borsuk_1(A,B,C,D,E,F))) # label(redefinition_k9_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6395 (all A all B all C (l1_pre_topc(A) & -v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & l1_pre_topc(B) & v2_pre_topc(B) & v2_pre_topc(A) & -v3_struct_0(A) -> v5_pre_topc(k3_borsuk_1(A,B,C),A,B) & v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(k3_borsuk_1(A,B,C)) & v1_relat_1(k3_borsuk_1(A,B,C)) & -v1_xboole_0(k3_borsuk_1(A,B,C)))) # label(fc1_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6396 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_borsuk_1(B,A) -> (v2_borsuk_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,B) -> v6_compts_1(C,A))))))))) # label(d15_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6397 $T # label(t34_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6398 (all A all B all C (-v3_struct_0(B) & -v3_struct_0(C) & m1_pre_topc(C,B) & l1_pre_topc(B) & v2_pre_topc(B) -> (r2_hidden(A,a_2_3_borsuk_1(B,C)) <-> (exists D (A = k1_struct_0(B,D) & -r2_hidden(D,u1_struct_0(C)) & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_3_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6399 (all A all B all C (r1_tarski(A,k2_zfmisc_1(B,C)) -> k1_funct_1(k1_funct_3(k10_funct_3(B,C)),A) = k2_funct_2(k2_zfmisc_1(B,C),C,k10_funct_3(B,C),A))) # label(t10_borsuk_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6400 (all A (-v1_xboole_0(A) & v5_grcat_1(A) -> (all B (m3_grcat_1(B,A) -> v3_grcat_1(B) & l1_grcat_1(B))))) # label(dt_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6401 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> m1_grcat_1(k13_grcat_1(A),A,A))) # label(dt_k13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6402 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k6_grcat_1(A,B) = g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)))))) # label(d10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6403 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> k12_grcat_1(A,B) = k14_grcat_1(A,B))) # label(redefinition_k14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6404 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> r1_cat_2(g1_cat_1(B,k1_grcat_1(A,B),k2_grcat_1(A,B),k3_grcat_1(A,B),k4_grcat_1(A,B),k5_grcat_1(A,B)),A))))) # label(t9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6405 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_cat_1(k32_grcat_1(A)) & v2_cat_1(k32_grcat_1(A)))) # label(fc15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6406 (exists A (-v1_xboole_0(A) & v4_grcat_1(A))) # label(rc4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6407 (all A all B all C (l1_struct_0(A) & -v3_struct_0(B) & l1_struct_0(B) & m5_grcat_1(C,A,B) & -v1_xboole_0(C) -> (all D (m6_grcat_1(D,A,B,C) -> 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))))) # label(dt_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6408 (all A (-v1_xboole_0(A) & v1_classes2(A) -> -v1_xboole_0(k31_grcat_1(A)))) # label(fc14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6409 (all A (-v1_xboole_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v5_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) -> (m4_grcat_1(A,B,C) <-> (all D (m1_subset_1(D,A) -> v2_grcat_1(D) & m1_grcat_1(D,B,C)))))))))) # label(t38_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6410 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m2_grcat_1(B,A) -> v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & -v3_struct_0(B))))) # label(dt_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6411 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) -> (all C (m4_grcat_1(C,A,B) -> (C = k18_grcat_1(A,B) <-> (all D (r2_hidden(D,C) <-> m1_grcat_1(D,A,B) & v2_grcat_1(D)))))))))) # label(d27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6412 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v4_grcat_1(k19_grcat_1(A)) & -v1_xboole_0(k19_grcat_1(A)))) # label(fc9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6413 (all A all B (-v1_xboole_0(A) & v4_grcat_1(A) & m1_subset_1(B,k20_grcat_1(A)) -> k21_grcat_1(A,B) = k9_grcat_1(B))) # label(redefinition_k21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.89 6414 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m1_subset_1(k29_grcat_1(A),k1_zfmisc_1(u1_cat_1(k28_grcat_1(A)))))) # label(dt_k29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6415 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_grcat_1(C,A,B) & v2_grcat_1(C) -> m4_grcat_1(k1_tarski(C),A,B))))))) # label(t39_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6416 (all A all B all C (v2_cat_1(B) & l1_cat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_cat_1(B))) & -v1_xboole_0(C) -> (r2_hidden(A,a_2_0_grcat_1(B,C)) <-> (exists D exists E (m1_subset_1(D,u1_cat_1(B)) & m1_subset_1(E,u1_cat_1(B)) & k6_cat_1(B,D,E) = A & r2_hidden(E,C) & r2_hidden(D,C)))))) # label(fraenkel_a_2_0_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6417 (all A (l1_grcat_1(A) -> (v3_grcat_1(A) <-> v1_grcat_1(k11_grcat_1(A),k9_grcat_1(A),k10_grcat_1(A))))) # label(d18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6418 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m2_relset_1(B,k20_grcat_1(A),A) & v1_funct_2(B,k20_grcat_1(A),A) & v1_funct_1(B) -> ((all C (m3_grcat_1(C,k20_grcat_1(A)) -> k8_funct_2(k20_grcat_1(A),A,B,C) = k22_grcat_1(A,C))) <-> k25_grcat_1(A) = B))))) # label(d33_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6419 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> v5_grcat_1(k20_grcat_1(A)) & -v1_xboole_0(k20_grcat_1(A)))) # label(dt_k20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6420 (exists A (v2_grcat_1(A) & l1_grcat_1(A))) # label(rc1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6421 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> v1_funct_1(k24_grcat_1(A)) & v1_funct_2(k24_grcat_1(A),k20_grcat_1(A),A) & m2_relset_1(k24_grcat_1(A),k20_grcat_1(A),A))) # label(dt_k24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6422 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (v1_funct_2(B,A,k20_grcat_1(A)) & m2_relset_1(B,A,k20_grcat_1(A)) & v1_funct_1(B) -> (B = k26_grcat_1(A) <-> (all C (m2_grcat_1(C,A) -> k8_funct_2(A,k20_grcat_1(A),B,C) = k23_grcat_1(A,C)))))))) # label(d34_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6423 (all A (m1_subset_1(A,f1_s2_grcat_1) -> (all B (m1_subset_1(B,f2_s2_grcat_1) -> (p1_s2_grcat_1(A,B) -> r2_hidden(f4_s2_grcat_1(A,B),f3_s2_grcat_1)))))) -> (exists A (m2_relset_1(A,k2_zfmisc_1(f1_s2_grcat_1,f2_s2_grcat_1),f3_s2_grcat_1) & (all B (m1_subset_1(B,f1_s2_grcat_1) -> (all C (m1_subset_1(C,f2_s2_grcat_1) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) <-> p1_s2_grcat_1(B,C)))))) & (all B (m1_subset_1(B,f1_s2_grcat_1) -> (all C (m1_subset_1(C,f2_s2_grcat_1) -> (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) -> f4_s2_grcat_1(B,C) = k1_funct_1(A,k4_tarski(B,C))))))) & v1_funct_1(A))) # label(s2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6424 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) -> (all C (-v3_struct_0(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (m1_grcat_1(D,B,C) -> (all E (m1_grcat_1(E,A,B) -> m1_grcat_1(k15_grcat_1(D,E),A,C))))))))))) # label(t28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6425 (all A (l1_grcat_1(A) -> v6_rlvect_1(k9_grcat_1(A)) & l1_rlvect_1(k9_grcat_1(A)) & v5_rlvect_1(k9_grcat_1(A)) & v4_rlvect_1(k9_grcat_1(A)) & -v3_struct_0(k9_grcat_1(A)))) # label(dt_k9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6426 (all A all B (l1_rlvect_1(A) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all C (m4_grcat_1(C,A,B) -> v5_grcat_1(C) & -v1_xboole_0(C))))) # label(dt_m4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6427 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k1_realset1(u5_cat_1(A),k1_grcat_1(A,B)) = k4_grcat_1(A,B))))) # label(d8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6428 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k19_grcat_1(A)))) # label(fc8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6429 (all A (l1_grcat_1(A) & v3_grcat_1(A) -> v1_grcat_1(u3_grcat_1(A),u1_grcat_1(A),u2_grcat_1(A)))) # label(t18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6430 (all A all B (v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> v3_grcat_1(k12_grcat_1(A,B)) & v2_grcat_1(k12_grcat_1(A,B)))) # label(fc5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6431 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (-v1_xboole_0(B) & v5_grcat_1(B) -> (k20_grcat_1(A) = B <-> (all C ((exists D ((exists E (v1_rlvect_1(E) & m2_grcat_1(E,A) & v2_grcat_1(C) & m1_grcat_1(C,D,E))) & m2_grcat_1(D,A) & v1_rlvect_1(D))) <-> r2_hidden(C,B)))))))) # label(d30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6432 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> m4_grcat_1(k18_grcat_1(A,B),A,B))) # label(dt_k18_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6433 (all A (v1_classes2(A) & -v1_xboole_0(A) -> u1_cat_1(k30_grcat_1(A)) = k29_grcat_1(A))) # label(t52_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6434 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(A) -> v3_grcat_1(k13_grcat_1(A)) & v2_grcat_1(k13_grcat_1(A)))) # label(fc6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6435 (all A (v1_classes2(A) & -v1_xboole_0(A) -> m3_cat_2(k32_grcat_1(A),k30_grcat_1(A)))) # label(dt_k32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6436 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & -v3_struct_0(B) -> (all C (v3_grcat_1(C) & l1_grcat_1(C) -> (B = k10_grcat_1(C) & A = k9_grcat_1(C) <-> m1_grcat_1(C,A,B)))))))) # label(d19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6437 (all A all B (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & -v3_struct_0(A) -> l1_grcat_1(k12_grcat_1(A,B)))) # label(dt_k12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6438 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k2_algstr_1,k29_grcat_1(A)))) # label(t51_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6439 (all A all B (v2_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) -> m2_relset_1(k4_grcat_1(A,B),k12_mcart_1(u2_cat_1(A),u2_cat_1(A),k1_grcat_1(A,B),k1_grcat_1(A,B)),k1_grcat_1(A,B)) & v1_funct_1(k4_grcat_1(A,B)))) # label(dt_k4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6440 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k28_grcat_1(A) = g1_cat_1(k19_grcat_1(A),k20_grcat_1(k19_grcat_1(A)),k24_grcat_1(k19_grcat_1(A)),k25_grcat_1(k19_grcat_1(A)),k27_grcat_1(k19_grcat_1(A)),k26_grcat_1(k19_grcat_1(A))))) # label(d36_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6441 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m2_grcat_1(B,A) -> k23_grcat_1(A,B) = k13_grcat_1(B))))) # label(d31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6442 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,A) & v4_grcat_1(A) -> v2_grcat_1(k23_grcat_1(A,B)) & m3_grcat_1(k23_grcat_1(A,B),k20_grcat_1(A)))) # label(dt_k23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6443 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A))) -> (all D (m1_subset_1(D,u1_cat_1(k28_grcat_1(A))) -> (all E (m2_grcat_1(E,k19_grcat_1(A)) -> v2_grcat_1(B) & m3_grcat_1(B,k20_grcat_1(k19_grcat_1(A))) & m1_subset_1(E,u1_cat_1(k28_grcat_1(A))) & m2_grcat_1(D,k19_grcat_1(A)) & v1_rlvect_1(D) & m1_subset_1(C,u2_cat_1(k28_grcat_1(A))))))))))))) # label(t47_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6444 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k6_grcat_1(k28_grcat_1(A),k29_grcat_1(A)) = k30_grcat_1(A))) # label(d38_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6445 (all A (v3_grcat_1(A) & l1_grcat_1(A) & v2_grcat_1(A) -> (all B (v2_grcat_1(B) & l1_grcat_1(B) & v3_grcat_1(B) -> (k9_grcat_1(B) = k10_grcat_1(A) -> k9_grcat_1(k15_grcat_1(B,A)) = k9_grcat_1(A) & k10_grcat_1(B) = k10_grcat_1(k15_grcat_1(B,A))))))) # label(t31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6446 (all A (l1_grcat_1(A) -> k10_grcat_1(A) = u2_grcat_1(A))) # label(d15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6447 (all A all B (-v3_struct_0(A) & l1_rlvect_1(A) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all C (m1_grcat_1(C,A,B) -> l1_grcat_1(C) & v3_grcat_1(C))))) # label(dt_m1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6448 (all A all B (p1_s1_grcat_1(A,B) & r2_hidden(B,f2_s1_grcat_1) & r2_hidden(A,f1_s1_grcat_1) -> r2_hidden(f4_s1_grcat_1(A,B),f3_s1_grcat_1))) -> (exists A ((all B all C (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) -> f4_s1_grcat_1(B,C) = k1_funct_1(A,k4_tarski(B,C)))) & (all B all C (r2_hidden(k4_tarski(B,C),k1_relat_1(A)) <-> r2_hidden(B,f1_s1_grcat_1) & p1_s1_grcat_1(B,C) & r2_hidden(C,f2_s1_grcat_1))) & m2_relset_1(A,k2_zfmisc_1(f1_s1_grcat_1,f2_s1_grcat_1),f3_s1_grcat_1) & v1_funct_1(A))) # label(s1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6449 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) -> (all D (m3_grcat_1(D,k20_grcat_1(k19_grcat_1(A))) -> (all E (m3_grcat_1(E,k20_grcat_1(k19_grcat_1(A))) -> (D = B & C = E -> (k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) -> k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)) & (k21_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D) -> k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)) & (k22_grcat_1(k19_grcat_1(A),D) = k22_grcat_1(k19_grcat_1(A),E) -> k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C)) & (k3_cat_1(k28_grcat_1(A),B) = k3_cat_1(k28_grcat_1(A),C) -> k22_grcat_1(k19_grcat_1(A),E) = k22_grcat_1(k19_grcat_1(A),D)) & (k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E) -> k2_cat_1(k28_grcat_1(A),C) = k2_cat_1(k28_grcat_1(A),B)) & (k2_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C) -> k21_grcat_1(k19_grcat_1(A),D) = k21_grcat_1(k19_grcat_1(A),E)) & (k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) -> k15_grcat_1(E,D) = k4_cat_1(k28_grcat_1(A),B,C)) & (r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A)))) -> k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)) & (k2_cat_1(k28_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B) -> r2_hidden(k4_tarski(E,D),k1_relat_1(k27_grcat_1(k19_grcat_1(A)))))))))))))))) # label(t50_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6450 (all A all B all C (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(B) & v6_rlvect_1(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)) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v4_rlvect_1(A) -> l1_grcat_1(g1_grcat_1(A,B,C)) & v2_grcat_1(g1_grcat_1(A,B,C)))) # label(dt_g1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6451 (all A all B (v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) & v4_rlvect_1(A) & -v3_struct_0(A) -> (exists C (v3_grcat_1(C) & v2_grcat_1(C) & m1_grcat_1(C,A,B))))) # label(rc3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6452 (all A (l1_struct_0(A) -> k7_grcat_1(A) = k6_partfun1(u1_struct_0(A)))) # label(d11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6453 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) & v2_cat_1(A) -> m3_cat_2(k6_grcat_1(A,B),A))) # label(dt_k6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6454 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k5_grcat_1(A,B) = k2_partfun1(u1_cat_1(A),u2_cat_1(A),u6_cat_1(A),B))))) # label(d9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6455 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) -> k10_grcat_1(B) = k22_grcat_1(A,B))) # label(redefinition_k22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6456 $T # label(d1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6457 (all A (l1_grcat_1(A) -> v4_rlvect_1(u1_grcat_1(A)) & l1_rlvect_1(u1_grcat_1(A)) & v6_rlvect_1(u1_grcat_1(A)) & v5_rlvect_1(u1_grcat_1(A)) & -v3_struct_0(u1_grcat_1(A)))) # label(dt_u1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6458 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m2_relset_1(B,k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)) & v1_funct_1(B) -> (B = k27_grcat_1(A) <-> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (all D (m3_grcat_1(D,k20_grcat_1(A)) -> (k22_grcat_1(A,D) = k21_grcat_1(A,C) <-> r2_hidden(k4_tarski(C,D),k1_relat_1(B))))))) & (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (all D (m3_grcat_1(D,k20_grcat_1(A)) -> (r2_hidden(k4_tarski(C,D),k1_relat_1(B)) -> k15_grcat_1(C,D) = k1_funct_1(B,k4_tarski(C,D)))))))))))) # label(d35_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6459 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> u1_cat_1(k6_grcat_1(A,B)) = B)))) # label(t10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6460 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k32_grcat_1(A) = k6_grcat_1(k30_grcat_1(A),k31_grcat_1(A)))) # label(d40_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6461 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (v2_grcat_1(C) & l1_grcat_1(C) -> (k9_grcat_1(C) = A & B = k10_grcat_1(C) & v1_grcat_1(k11_grcat_1(C),k9_grcat_1(C),k10_grcat_1(C)) -> m1_grcat_1(C,A,B) & v2_grcat_1(C)))))))) # label(t19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6462 (all A (l1_grcat_1(A) -> -v3_struct_0(k10_grcat_1(A)) & v4_rlvect_1(k10_grcat_1(A)) & v5_rlvect_1(k10_grcat_1(A)) & v6_rlvect_1(k10_grcat_1(A)) & l1_rlvect_1(k10_grcat_1(A)))) # label(dt_k10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6463 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> (all B (l1_rlvect_1(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,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> k2_rlvect_1(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,k2_rlvect_1(A,D,E)))))) <-> v1_grcat_1(C,A,B)))))))) # label(d13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6464 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> (exists C m5_grcat_1(C,A,B)))) # label(existence_m5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6465 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v1_cat_1(k30_grcat_1(A)) & v2_cat_1(k30_grcat_1(A)))) # label(fc13_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6466 (all A (l1_grcat_1(A) -> u3_grcat_1(A) = k11_grcat_1(A))) # label(d16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6467 (all A (-v1_xboole_0(A) & v1_classes2(A) -> a_1_1_grcat_1(A) = k31_grcat_1(A))) # label(d39_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6468 (exists A l1_grcat_1(A)) # label(existence_l1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6469 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> (all C ((all D (r2_hidden(D,C) -> 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)))) <-> m5_grcat_1(C,A,B))))))) # label(d25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6470 (all A all B all C (-v3_struct_0(A) & v6_rlvect_1(A) & v5_rlvect_1(B) & v6_rlvect_1(B) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (exists D (m1_subset_1(D,C) & v2_grcat_1(D) & v3_grcat_1(D))))) # label(rc9_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6471 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m3_grcat_1(B,k20_grcat_1(A)) -> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> -((all D (m2_grcat_1(D,A) & v1_rlvect_1(D) -> (all E (m2_grcat_1(E,A) & v1_rlvect_1(E) -> (all F (m2_grcat_1(F,A) & v1_rlvect_1(F) -> -(m1_grcat_1(B,E,F) & m1_grcat_1(C,D,E)))))))) & k22_grcat_1(A,C) = k21_grcat_1(A,B)))))))) # label(t44_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6472 (all A all B all C all D -((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> D != k4_tarski(E,F))))) & r1_tarski(C,k2_zfmisc_1(A,B)) & r2_hidden(D,C))) # label(t2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6473 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m3_grcat_1(C,k20_grcat_1(k19_grcat_1(A))) -> (C = B -> k21_grcat_1(k19_grcat_1(A),C) = k2_cat_1(k28_grcat_1(A),B) & k22_grcat_1(k19_grcat_1(A),C) = k3_cat_1(k28_grcat_1(A),B)))))))) # label(t49_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6474 (all A (l1_grcat_1(A) & v3_grcat_1(A) -> (exists B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & (exists C (v6_rlvect_1(C) & l1_rlvect_1(C) & m1_grcat_1(A,B,C) & v5_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C))) & v6_rlvect_1(B) & v5_rlvect_1(B))))) # label(t24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6475 (all A all B all C all D all E (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & l1_rlvect_1(B) & v4_rlvect_1(C) & v5_rlvect_1(C) & m1_grcat_1(E,A,B) & m1_grcat_1(D,B,C) & l1_rlvect_1(C) & v6_rlvect_1(C) & -v3_struct_0(C) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v4_rlvect_1(A) -> m1_grcat_1(k16_grcat_1(A,B,C,D,E),A,C) & v2_grcat_1(k16_grcat_1(A,B,C,D,E)))) # label(dt_k16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6476 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,k19_grcat_1(A)) -> v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v1_rlvect_1(B) & -v3_struct_0(B))))) # label(t43_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6477 (all A (-v1_xboole_0(A) & v1_classes2(A) -> r2_hidden(k1_tarski(k1_xboole_0),A) & r2_hidden(k4_tarski(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A) & r2_hidden(k2_zfmisc_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),A) & r2_hidden(k7_vectsp_2,A) & r2_hidden(k2_midsp_1,A))) # label(t6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6478 (all A (l1_grcat_1(A) -> u1_grcat_1(A) = k9_grcat_1(A))) # label(d14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6479 (all A (v1_classes2(A) & -v1_xboole_0(A) -> v1_cat_1(k28_grcat_1(A)))) # label(fc10_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6480 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) -> k2_partfun1(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k1_grcat_1(A,B)) = k3_grcat_1(A,B))))) # label(d7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6481 (all A all B (v4_grcat_1(A) & m1_subset_1(B,k20_grcat_1(A)) & -v1_xboole_0(A) -> m2_grcat_1(k21_grcat_1(A,B),A) & v1_rlvect_1(k21_grcat_1(A,B)))) # label(dt_k21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6482 $T # label(dt_k19_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6483 (all A (-v1_xboole_0(A) & v1_classes2(A) -> m3_cat_2(k30_grcat_1(A),k28_grcat_1(A)))) # label(dt_k30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6484 (all A (l1_grcat_1(A) & v3_grcat_1(A) & v2_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) & v2_grcat_1(B) -> (all C (v2_grcat_1(C) & v3_grcat_1(C) & l1_grcat_1(C) -> (k9_grcat_1(C) = k10_grcat_1(B) & k10_grcat_1(A) = k9_grcat_1(B) -> k15_grcat_1(k15_grcat_1(C,B),A) = k15_grcat_1(C,k15_grcat_1(B,A))))))))) # label(t33_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6485 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (exists B m2_grcat_1(B,A)))) # label(existence_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6486 (all 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) -> C = k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k7_grcat_1(A),C) & C = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),C,k7_grcat_1(B)))))))) # label(t12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6487 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u1_cat_1(k28_grcat_1(A))) -> (all C (m2_grcat_1(C,k19_grcat_1(A)) -> (B = C -> k5_cat_1(k28_grcat_1(A),B) = k23_grcat_1(k19_grcat_1(A),C)))))))) # label(t48_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6488 (all A (v1_classes2(A) & -v1_xboole_0(A) -> m1_subset_1(k31_grcat_1(A),k1_zfmisc_1(u1_cat_1(k30_grcat_1(A)))))) # label(dt_k31_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6489 (all A all B all C (r1_grcat_1(A,B) & r1_grcat_1(A,C) -> B = C)) # label(t40_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6490 (all A (v3_grcat_1(A) & l1_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) -> (k10_grcat_1(B) = k9_grcat_1(A) -> (all C (l1_grcat_1(C) & v3_grcat_1(C) & v2_grcat_1(C) -> (C = k15_grcat_1(A,B) <-> (all D (v4_rlvect_1(D) & v5_rlvect_1(D) & l1_rlvect_1(D) & v6_rlvect_1(D) & -v3_struct_0(D) -> (all E (-v3_struct_0(E) & l1_rlvect_1(E) & v6_rlvect_1(E) & v5_rlvect_1(E) & v4_rlvect_1(E) -> (all F (-v3_struct_0(F) & v4_rlvect_1(F) & v6_rlvect_1(F) & l1_rlvect_1(F) & v5_rlvect_1(F) -> (all G (v1_funct_1(G) & v1_funct_2(G,u1_struct_0(E),u1_struct_0(F)) & m2_relset_1(G,u1_struct_0(E),u1_struct_0(F)) -> (all H (v1_funct_2(H,u1_struct_0(D),u1_struct_0(E)) & m2_relset_1(H,u1_struct_0(D),u1_struct_0(E)) & v1_funct_1(H) -> (g1_grcat_1(D,E,H) = g1_grcat_1(u1_grcat_1(B),u2_grcat_1(B),u3_grcat_1(B)) & g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) = g1_grcat_1(E,F,G) -> g1_grcat_1(D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),H,G)) = C))))))))))))))))))) # label(d21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6491 (all A all B all C (-v3_struct_0(B) & -v1_xboole_0(C) & m5_grcat_1(C,A,B) & l1_struct_0(B) & l1_struct_0(A) -> (exists D m6_grcat_1(D,A,B,C)))) # label(existence_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6492 (all A (-v3_struct_0(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(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)) -> (v1_grcat_1(C,A,B) -> m1_grcat_1(g1_grcat_1(A,B,C),A,B) & v2_grcat_1(g1_grcat_1(A,B,C))))))))) # label(t20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6493 (all A (l1_struct_0(A) -> (all B (l1_struct_0(B) -> k17_grcat_1(A,B) = k1_funct_2(u1_struct_0(A),u1_struct_0(B)))))) # label(d26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6494 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (exists B (r1_grcat_1(B,k2_algstr_1) & r2_hidden(B,A))))) # label(t41_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6495 (all A (-v1_xboole_0(A) & v1_classes2(A) -> u1_cat_1(k32_grcat_1(A)) = k31_grcat_1(A))) # label(t53_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6496 $T # label(d3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6497 (all A all B all C (v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & -v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(A) -> (all D (m7_grcat_1(D,A,B,C) -> m1_grcat_1(D,A,B))))) # label(dt_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6498 (all A all B (l1_cat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & v2_cat_1(A) -> -v1_xboole_0(k1_grcat_1(A,B)))) # label(fc2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6499 (all A all B all C all D all E (-v3_struct_0(A) & v4_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v5_rlvect_1(C) & l1_rlvect_1(C) & m1_grcat_1(D,B,C) & m1_grcat_1(E,A,B) & v6_rlvect_1(C) & v4_rlvect_1(C) & -v3_struct_0(C) & v5_rlvect_1(B) & -v3_struct_0(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> k16_grcat_1(A,B,C,D,E) = k15_grcat_1(D,E))) # label(redefinition_k16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6500 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> k13_grcat_1(A) = g1_grcat_1(A,A,k7_grcat_1(A)))) # label(d20_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6501 (all A all B (l1_cat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & v2_cat_1(A) -> v1_funct_1(k2_grcat_1(A,B)) & v1_funct_2(k2_grcat_1(A,B),k1_grcat_1(A,B),B) & m2_relset_1(k2_grcat_1(A,B),k1_grcat_1(A,B),B))) # label(dt_k2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6502 $T # label(d2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6503 (all A (-v3_struct_0(A) & l1_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B))))) # label(t11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6504 (all A (l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) -> (all C (m1_grcat_1(C,A,B) & v2_grcat_1(C) -> (exists D (m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) & C = g1_grcat_1(A,B,D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(D))))))))) # label(t23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6505 (all A (-v3_struct_0(A) & l2_struct_0(A) -> (all B (l2_struct_0(B) & -v3_struct_0(B) -> k8_grcat_1(A,B) = k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)))))) # label(d12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6506 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k20_grcat_1(A),A) & v1_funct_2(B,k20_grcat_1(A),A) -> (k24_grcat_1(A) = B <-> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> k8_funct_2(k20_grcat_1(A),A,B,C) = k21_grcat_1(A,C)))))))) # label(d32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6507 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(A) & v5_rlvect_1(A) -> (exists C m1_grcat_1(C,A,B)))) # label(existence_m1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6508 $T # label(t1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6509 (all A (v1_classes2(A) & -v1_xboole_0(A) -> -v1_xboole_0(k29_grcat_1(A)))) # label(fc12_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6510 $T # label(d4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6511 (all A all B (l1_struct_0(A) & l1_struct_0(B) & -v3_struct_0(B) -> (exists C (m5_grcat_1(C,A,B) & -v1_xboole_0(C))))) # label(rc8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6512 (all A (-v1_xboole_0(A) & v4_grcat_1(A) -> (all B (m1_subset_1(B,A) <-> m2_grcat_1(B,A))))) # label(redefinition_m2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6513 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> A = k1_xboole_0)) # label(t8_grcat_1_AndLHS) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6514 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> k1_xboole_0 = k5_rlvect_1(k2_algstr_1,A))) # label(t8_grcat_1_AndRHS_AndLHS) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6515 (all A (m1_subset_1(A,u1_struct_0(k2_algstr_1)) -> (all B (m1_subset_1(B,u1_struct_0(k2_algstr_1)) -> k1_xboole_0 = k4_rlvect_1(k2_algstr_1,A,B))))) # label(t8_grcat_1_AndRHS_AndRHS_AndRHS) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6516 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) -> (all C (v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & -v3_struct_0(C) -> (all D (m1_grcat_1(D,B,C) -> (all E (m1_grcat_1(E,A,B) -> (all F (v1_funct_1(F) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C)) & m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) -> (all G (m2_relset_1(G,u1_struct_0(A),u1_struct_0(B)) & v1_funct_2(G,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(G) -> (D = g1_grcat_1(B,C,F) & g1_grcat_1(A,B,G) = E -> k16_grcat_1(A,B,C,D,E) = g1_grcat_1(A,C,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),G,F))))))))))))))))) # label(t29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6517 $T # label(t35_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6518 (all A (v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> g1_grcat_1(A,B,k8_grcat_1(A,B)) = k12_grcat_1(A,B))))) # label(d17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6519 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_hidden(k2_algstr_1,k19_grcat_1(A)))) # label(t42_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6520 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(B) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v5_rlvect_1(A) -> (all D (m1_subset_1(D,C) <-> m7_grcat_1(D,A,B,C))))) # label(redefinition_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6521 (all A all B (l1_cat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & -v1_xboole_0(B) & v2_cat_1(A) -> m1_subset_1(k1_grcat_1(A,B),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6522 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k2_grcat_1(A,B) = k2_partfun1(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k1_grcat_1(A,B)))))) # label(d6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6523 (all A all B all C (v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(B) & l1_rlvect_1(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)) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v6_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all D all E all F (g1_grcat_1(A,B,C) = g1_grcat_1(D,E,F) -> D = A & C = F & E = B)))) # label(free_g1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6524 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & -v3_struct_0(B) -> (exists C m4_grcat_1(C,A,B)))) # label(existence_m4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6525 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (l1_rlvect_1(B) & -v3_struct_0(B) -> (all C (l1_rlvect_1(C) & -v3_struct_0(C) -> (all D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) -> (all E (v1_funct_1(E) & m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) -> (v1_grcat_1(E,B,C) & v1_grcat_1(D,A,B) -> v1_grcat_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)))))))))))) # label(t14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.90 6526 (all A (-v3_struct_0(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) -> (all C (-v1_xboole_0(C) & v5_grcat_1(C) -> (m4_grcat_1(C,A,B) <-> (all D (m3_grcat_1(D,C) -> v2_grcat_1(D) & m1_grcat_1(D,A,B)))))))))) # label(d24_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6527 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) & v2_cat_1(A) -> v1_funct_2(k5_grcat_1(A,B),B,k1_grcat_1(A,B)) & m2_relset_1(k5_grcat_1(A,B),B,k1_grcat_1(A,B)) & v1_funct_1(k5_grcat_1(A,B)))) # label(dt_k5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6528 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) -> k1_grcat_1(A,B) = k3_tarski(a_2_0_grcat_1(A,B)))))) # label(d5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6529 (all A ((all B (r2_hidden(B,A) -> l1_grcat_1(B) & v3_grcat_1(B) & v2_grcat_1(B))) <-> v5_grcat_1(A))) # label(d23_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6530 $T # label(dt_l1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6531 (exists A (l1_grcat_1(A) & v2_grcat_1(A) & v3_grcat_1(A))) # label(rc2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6532 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k20_grcat_1(A)) & v4_grcat_1(A) -> v1_rlvect_1(k22_grcat_1(A,B)) & m2_grcat_1(k22_grcat_1(A,B),A))) # label(dt_k22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6533 (all A all B (-v3_struct_0(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) & v4_rlvect_1(A) & -v3_struct_0(A) -> v2_grcat_1(k12_grcat_1(A,B)))) # label(fc4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6534 (all A (-v1_xboole_0(A) & v1_classes2(A) -> v2_cat_1(k28_grcat_1(A)) & v1_cat_1(k28_grcat_1(A)))) # label(fc11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6535 (all A (l1_grcat_1(A) -> (v2_grcat_1(A) -> A = g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A))))) # label(abstractness_v2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6536 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B all C (r2_hidden(B,C) & r2_hidden(C,A) -> r2_hidden(B,A))))) # label(t4_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6537 (all A (v2_grcat_1(A) & l1_grcat_1(A) & v3_grcat_1(A) -> -v1_xboole_0(k1_tarski(A)) & v5_grcat_1(k1_tarski(A)))) # label(t37_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6538 (all A (-v1_xboole_0(A) & v1_classes2(A) -> (all B (m1_subset_1(B,u2_cat_1(k28_grcat_1(A))) -> (all C (m1_subset_1(C,u2_cat_1(k28_grcat_1(A))) -> (r2_hidden(k4_tarski(C,B),k1_relat_1(u5_cat_1(k28_grcat_1(A)))) <-> k3_cat_1(k28_grcat_1(A),B) = k2_cat_1(k28_grcat_1(A),C)))))))) # label(t46_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6539 $T # label(t27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6540 (all A (v1_classes2(A) & -v1_xboole_0(A) -> (all B ((all C (r2_hidden(C,B) <-> (exists D (r1_grcat_1(D,C) & r2_hidden(D,A))))) <-> k19_grcat_1(A) = B)))) # label(d29_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6541 (all A (v4_rlvect_1(A) & v5_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & -v3_struct_0(A) -> k9_grcat_1(k13_grcat_1(A)) = A & (all B (v2_grcat_1(B) & v3_grcat_1(B) & l1_grcat_1(B) -> (k10_grcat_1(B) = A -> k15_grcat_1(k13_grcat_1(A),B) = B))) & (all B (v3_grcat_1(B) & l1_grcat_1(B) & v2_grcat_1(B) -> (A = k9_grcat_1(B) -> B = k15_grcat_1(B,k13_grcat_1(A))))) & k10_grcat_1(k13_grcat_1(A)) = A)) # label(t34_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6542 (all A (-v3_struct_0(A) & l1_rlvect_1(A) -> (all B (l1_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> v1_grcat_1(k8_grcat_1(A,B),A,B))))) # label(t16_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6543 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> v1_funct_1(k27_grcat_1(A)) & m2_relset_1(k27_grcat_1(A),k2_zfmisc_1(k20_grcat_1(A),k20_grcat_1(A)),k20_grcat_1(A)))) # label(dt_k27_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6544 (all A (l1_struct_0(A) -> v1_funct_1(k7_grcat_1(A)) & m2_relset_1(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)))) # label(dt_k7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6545 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> m2_relset_1(k26_grcat_1(A),A,k20_grcat_1(A)) & v1_funct_2(k26_grcat_1(A),A,k20_grcat_1(A)) & v1_funct_1(k26_grcat_1(A)))) # label(dt_k26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6546 $T # label(t36_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6547 (all A (v5_grcat_1(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) <-> m3_grcat_1(B,A))))) # label(redefinition_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6548 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (all B (m3_grcat_1(B,k20_grcat_1(A)) -> (all C (m3_grcat_1(C,k20_grcat_1(A)) -> (k21_grcat_1(A,B) = k22_grcat_1(A,C) -> r2_hidden(k15_grcat_1(B,C),k20_grcat_1(A))))))))) # label(t45_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6549 (all A all B (v2_cat_1(A) & -v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) -> v1_funct_1(k3_grcat_1(A,B)) & v1_funct_2(k3_grcat_1(A,B),k1_grcat_1(A,B),B) & m2_relset_1(k3_grcat_1(A,B),k1_grcat_1(A,B),B))) # label(dt_k3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6550 (all A all B ((exists C exists D exists E exists F ((exists G (-v3_struct_0(G) & v1_rlvect_1(G) & v4_rlvect_1(G) & v5_rlvect_1(G) & C = u1_struct_0(G) & F = u2_struct_0(G) & k7_vectsp_1(G) = E & D = u1_rlvect_1(G) & G = B & l1_rlvect_1(G) & v6_rlvect_1(G))) & k4_mcart_1(C,D,E,F) = A)) <-> r1_grcat_1(A,B))) # label(d28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6551 (all A (v1_classes2(A) & -v1_xboole_0(A) -> r2_hidden(k2_algstr_1,k31_grcat_1(A)))) # label(t54_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6552 (all A all B all C (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & m4_grcat_1(C,A,B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v5_rlvect_1(A) -> (exists D m7_grcat_1(D,A,B,C)))) # label(existence_m7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6553 (all A all B all C (l1_struct_0(A) & -v3_struct_0(B) & m5_grcat_1(C,A,B) & -v1_xboole_0(C) & l1_struct_0(B) -> (all D (m6_grcat_1(D,A,B,C) <-> m1_subset_1(D,C))))) # label(redefinition_m6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6554 (all A (v1_classes2(A) & -v1_xboole_0(A) -> k29_grcat_1(A) = a_1_0_grcat_1(A))) # label(d37_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6555 $T # label(dt_m5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6556 (all A (v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(A) & -v3_struct_0(A) -> (all B (v5_rlvect_1(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & l1_rlvect_1(C) & v6_rlvect_1(C) -> (all D (l1_rlvect_1(D) & v6_rlvect_1(D) & v5_rlvect_1(D) & v4_rlvect_1(D) & -v3_struct_0(D) -> (all E (m1_grcat_1(E,A,B) & v2_grcat_1(E) -> (all F (m1_grcat_1(F,B,C) & v2_grcat_1(F) -> (all G (v2_grcat_1(G) & m1_grcat_1(G,C,D) -> k16_grcat_1(A,C,D,G,k16_grcat_1(A,B,C,F,E)) = k16_grcat_1(A,B,D,k16_grcat_1(B,C,D,G,F),E))))))))))))))) # label(t32_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6557 (all A (-v3_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) & v6_rlvect_1(A) & v5_rlvect_1(A) -> (all B (-v3_struct_0(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) -> (all C (m1_grcat_1(C,A,B) -> (exists D (g1_grcat_1(A,B,D) = g1_grcat_1(u1_grcat_1(C),u2_grcat_1(C),u3_grcat_1(C)) & v1_grcat_1(D,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)) & v1_funct_1(D))))))))) # label(t22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6558 (all A ((all B (r2_hidden(B,A) -> -v3_struct_0(B) & v1_rlvect_1(B) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B))) <-> v4_grcat_1(A))) # label(d22_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6559 (all A (-v1_xboole_0(A) & v1_classes2(A) -> l1_cat_1(k28_grcat_1(A)))) # label(dt_k28_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6560 (all A (l1_grcat_1(A) & v3_grcat_1(A) -> (all B (l1_grcat_1(B) & v3_grcat_1(B) -> -((all C (v4_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v5_rlvect_1(C) & -v3_struct_0(C) -> (all D (v5_rlvect_1(D) & v6_rlvect_1(D) & l1_rlvect_1(D) & v4_rlvect_1(D) & -v3_struct_0(D) -> (all E (v4_rlvect_1(E) & l1_rlvect_1(E) & v6_rlvect_1(E) & v5_rlvect_1(E) & -v3_struct_0(E) -> -(m1_grcat_1(B,C,D) & m1_grcat_1(A,D,E)))))))) & k9_grcat_1(A) = k10_grcat_1(B)))))) # label(t26_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6561 (all A (l1_grcat_1(A) -> m2_relset_1(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))) & v1_funct_2(u3_grcat_1(A),u1_struct_0(u1_grcat_1(A)),u1_struct_0(u2_grcat_1(A))) & v1_funct_1(u3_grcat_1(A)))) # label(dt_u3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6562 (all A (l1_rlvect_1(A) & -v3_struct_0(A) -> v1_grcat_1(k7_grcat_1(A),A,A))) # label(t21_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6563 (all A all B (l1_grcat_1(A) & l1_grcat_1(B) & v3_grcat_1(B) & v3_grcat_1(A) -> v2_grcat_1(k15_grcat_1(A,B)) & l1_grcat_1(k15_grcat_1(A,B)) & v3_grcat_1(k15_grcat_1(A,B)))) # label(dt_k15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6564 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> (exists B (v5_rlvect_1(B) & v1_algstr_1(B) & v4_algstr_1(B) & v5_algstr_1(B) & v6_algstr_1(B) & v3_algstr_1(B) & v2_algstr_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & v1_rlvect_1(B) & -v3_struct_0(B) & m1_subset_1(B,A))))) # label(rc5_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6565 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> (r2_hidden(A,a_1_0_grcat_1(B)) <-> (exists C (C = A & (exists D (-v3_struct_0(D) & v6_rlvect_1(D) & l1_rlvect_1(D) & C = D & v5_rlvect_1(D) & v4_rlvect_1(D) & v3_rlvect_1(D))) & m1_subset_1(C,u1_cat_1(k28_grcat_1(B)))))))) # label(fraenkel_a_1_0_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6566 (all A (l1_grcat_1(A) -> (all B (v4_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v5_rlvect_1(B) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v4_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)) -> (A = g1_grcat_1(B,C,D) -> k10_grcat_1(A) = C & k11_grcat_1(A) = D & B = k9_grcat_1(A)))))))))) # label(t17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6567 (all A (l2_struct_0(A) & -v3_struct_0(A) -> (all B (l1_rlvect_1(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_rlvect_1(B) = k8_funct_2(u1_struct_0(A),u1_struct_0(B),k8_grcat_1(A,B),C))))))) # label(t15_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6568 (all A (l1_grcat_1(A) & v3_grcat_1(A) & v2_grcat_1(A) -> (exists B (-v3_struct_0(B) & v6_rlvect_1(B) & l1_rlvect_1(B) & (exists C (-v3_struct_0(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & (exists D (v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & g1_grcat_1(B,C,D) = A & v1_grcat_1(D,B,C) & m1_grcat_1(A,B,C) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)))) & l1_rlvect_1(C))) & v5_rlvect_1(B) & v4_rlvect_1(B))))) # label(t25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6569 (all A all B (-v1_xboole_0(B) & v1_classes2(B) -> ((exists C (A = C & (exists D (-v3_struct_0(D) & v3_rlvect_1(D) & v1_midsp_2(D) & l1_rlvect_1(D) & D = C & v6_rlvect_1(D) & v5_rlvect_1(D) & v4_rlvect_1(D))) & m1_subset_1(C,u1_cat_1(k30_grcat_1(B))))) <-> r2_hidden(A,a_1_1_grcat_1(B))))) # label(fraenkel_a_1_1_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6570 (all A (v5_grcat_1(A) & -v1_xboole_0(A) -> (exists B m3_grcat_1(B,A)))) # label(existence_m3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6571 (all A (v2_grcat_1(A) & v3_grcat_1(A) & l1_grcat_1(A) -> (all B (v3_grcat_1(B) & l1_grcat_1(B) & v2_grcat_1(B) -> -(k10_grcat_1(A) = k9_grcat_1(B) & (all C (-v3_struct_0(C) & v6_rlvect_1(C) & l1_rlvect_1(C) & v5_rlvect_1(C) & v4_rlvect_1(C) -> (all D (-v3_struct_0(D) & v5_rlvect_1(D) & l1_rlvect_1(D) & v6_rlvect_1(D) & v4_rlvect_1(D) -> (all E (-v3_struct_0(E) & v5_rlvect_1(E) & v6_rlvect_1(E) & l1_rlvect_1(E) & v4_rlvect_1(E) -> (all F (m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) & v1_funct_1(F) -> (all G (v1_funct_1(G) & m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E)) -> -(A = g1_grcat_1(C,D,F) & k15_grcat_1(B,A) = g1_grcat_1(C,E,k7_funct_2(u1_struct_0(C),u1_struct_0(D),u1_struct_0(E),F,G)) & B = g1_grcat_1(D,E,G))))))))))))))))) # label(t30_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6572 (all A (v1_classes2(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) -> (all E (m1_subset_1(E,A) -> m1_subset_1(k3_mcart_1(B,C,D),A) & m1_subset_1(k4_mcart_1(B,C,D,E),A))))))))))) # label(t3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6573 (exists A (-v1_xboole_0(A) & v5_grcat_1(A))) # label(rc6_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6574 (all A all B (l1_struct_0(A) & -v3_struct_0(B) & l1_struct_0(B) -> -v1_xboole_0(k17_grcat_1(A,B)))) # label(fc7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6575 (all A all B (l2_struct_0(B) & -v3_struct_0(B) & l2_struct_0(A) & -v3_struct_0(A) -> v1_funct_1(k8_grcat_1(A,B)) & v1_funct_2(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(k8_grcat_1(A,B),u1_struct_0(A),u1_struct_0(B)))) # label(dt_k8_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6576 (all A (l1_grcat_1(A) -> m2_relset_1(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) & v1_funct_2(k11_grcat_1(A),u1_struct_0(k9_grcat_1(A)),u1_struct_0(k10_grcat_1(A))) & v1_funct_1(k11_grcat_1(A)))) # label(dt_k11_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6577 (all A (v5_grcat_1(A) & -v1_xboole_0(A) -> (exists B (v2_grcat_1(B) & v3_grcat_1(B) & m1_subset_1(B,A))))) # label(rc7_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6578 (all A (l1_grcat_1(A) -> -v3_struct_0(u2_grcat_1(A)) & v4_rlvect_1(u2_grcat_1(A)) & v6_rlvect_1(u2_grcat_1(A)) & l1_rlvect_1(u2_grcat_1(A)) & v5_rlvect_1(u2_grcat_1(A)))) # label(dt_u2_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6579 (all A all B (l1_struct_0(B) & l1_struct_0(A) -> m5_grcat_1(k17_grcat_1(A,B),A,B))) # label(dt_k17_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6580 (all A all B (-v3_struct_0(A) & v4_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) & v5_rlvect_1(B) & l1_rlvect_1(B) & v6_rlvect_1(B) & v4_rlvect_1(B) & -v3_struct_0(B) & v5_rlvect_1(A) -> v2_grcat_1(k14_grcat_1(A,B)) & m1_grcat_1(k14_grcat_1(A,B),A,B))) # label(dt_k14_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6581 (all A (v4_grcat_1(A) & -v1_xboole_0(A) -> m2_relset_1(k25_grcat_1(A),k20_grcat_1(A),A) & v1_funct_2(k25_grcat_1(A),k20_grcat_1(A),A) & v1_funct_1(k25_grcat_1(A)))) # label(dt_k25_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6582 (all A all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_cat_1(A))) & l1_cat_1(A) & v2_cat_1(A) -> v2_cat_1(k6_grcat_1(A,B)) & v1_cat_1(k6_grcat_1(A,B)))) # label(fc3_grcat_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6583 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_pre_topc(C,A) & v1_borsuk_1(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_borsuk_1(k2_tsep_1(A,B,C),A)))))))) # label(t32_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6584 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D ((exists E (r2_tsep_1(A,D,E) & r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t67_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6585 (all A (v1_pre_topc(A) & l1_pre_topc(A) -> k3_pre_topc(A,k2_pre_topc(A)) = A)) # label(t3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6586 $T # label(t50_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6587 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -((all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (-v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(D,A) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & -(-r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E)) & (all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v3_pre_topc(F,A) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F))))) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & v4_pre_topc(E,A)))))) & -r1_tarski(C,B) & -r1_tarski(B,C) & r2_tsep_1(A,B,C)))))))) # label(t60_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6588 (all A all B all C (-v3_struct_0(A) & -v3_struct_0(B) & -v3_struct_0(C) & m1_pre_topc(C,A) & m1_pre_topc(B,A) & l1_pre_topc(A) -> v1_pre_topc(k1_tsep_1(A,B,C)) & m1_pre_topc(k1_tsep_1(A,B,C),A) & -v3_struct_0(k1_tsep_1(A,B,C)))) # label(dt_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6589 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) & (exists E (-v3_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E))))))))))))) # label(t81_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6590 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_pre_topc(C,B) & v1_borsuk_1(C,B) -> m1_pre_topc(C,A) & v1_borsuk_1(C,A))))))) # label(t13_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6591 $T # label(t37_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6592 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & r1_tarski(E,C) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(D,A) & v3_pre_topc(F,A) & v4_pre_topc(E,A) & r1_tarski(D,B))))))) <-> r2_tsep_1(A,B,C))))))))) # label(t61_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6593 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) & v3_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) -> v3_pre_topc(C,A) & v3_pre_topc(B,A)))))))) # label(t42_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6594 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) <-> (exists D ((exists E ((exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(E,A) & v4_pre_topc(F,A) & v3_pre_topc(D,A) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t63_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6595 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v1_borsuk_1(B,A) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & v1_borsuk_1(C,A) -> r4_tsep_1(A,B,C))))))) # label(t87_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6596 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(r2_tsep_1(A,B,C) & -r1_tarski(B,C) & -r1_tarski(C,B) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(D) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(E) -> -(v3_pre_topc(E,A) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & -((all F (-v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(F,A) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = u1_struct_0(A)))) & -r1_tarski(k4_subset_1(u1_struct_0(A),B,C),k4_subset_1(u1_struct_0(A),D,E))) & v3_pre_topc(D,A))))))))))))) # label(t64_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6597 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (A = k1_tsep_1(A,B,C) -> (-((all D (m1_pre_topc(D,A) & v1_tsep_1(D,A) & -v3_struct_0(D) -> (all E (v1_tsep_1(E,A) & m1_pre_topc(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(E,C) & -((all F (-v3_struct_0(F) & m1_pre_topc(F,A) & v1_borsuk_1(F,A) -> -(m1_pre_topc(F,k2_tsep_1(A,B,C)) & k1_tsep_1(A,k1_tsep_1(A,D,E),F) = A))) & k1_tsep_1(A,D,E) != A) & m1_pre_topc(D,B)))))) & -m1_pre_topc(C,B) & -m1_pre_topc(B,C)) <-> r4_tsep_1(A,B,C)) | r1_tsep_1(A,B,C)))))))) # label(t97_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6598 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (u1_struct_0(B) = C -> (v1_borsuk_1(B,A) & m1_pre_topc(B,A) <-> v4_pre_topc(C,A))))))))) # label(t11_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6599 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> -(-r1_tsep_1(A,B,D) & -(k1_tsep_1(A,k2_tsep_1(A,D,B),k2_tsep_1(A,D,C)) = k2_tsep_1(A,D,k1_tsep_1(A,B,C)) & k1_tsep_1(A,k2_tsep_1(A,B,D),k2_tsep_1(A,C,D)) = k2_tsep_1(A,k1_tsep_1(A,B,C),D)) & -r1_tsep_1(A,D,C)))))))))) # label(t35_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6600 (all A (l1_pre_topc(A) & v2_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(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & r1_tarski(D,C) & E = D & v3_pre_topc(C,A) -> (v3_pre_topc(E,B) <-> v3_pre_topc(D,A))))))))))))) # label(t9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6601 $T # label(t26_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6602 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (r1_xboole_0(u1_struct_0(B),u1_struct_0(C)) <-> r1_tsep_1(A,B,C)))))))) # label(d3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6603 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,D),k5_subset_1(u1_struct_0(A),C,D))))))))))) # label(t43_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6604 (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))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,D),k4_subset_1(u1_struct_0(A),C,D))))))))))) # label(t55_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6605 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),k1_tsep_1(A,B,C))))))))) # label(t34_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6606 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> k1_tsep_1(A,k1_tsep_1(A,B,C),D) = k1_tsep_1(A,B,k1_tsep_1(A,C,D)))))))))) # label(t21_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6607 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,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))) -> (E = u1_struct_0(C) & u1_struct_0(B) = D -> r1_connsp_1(A,D,E)))))) <-> r3_tsep_1(A,B,C)))))))) # label(d8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6608 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> ((exists D (-v3_struct_0(D) & v1_tsep_1(D,A) & (exists E (m1_pre_topc(E,A) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(C,E) & m1_pre_topc(B,D) & v1_tsep_1(E,A) & -v3_struct_0(E))) & m1_pre_topc(D,A))) <-> r3_tsep_1(A,B,C)))))))) # label(t83_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6609 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & v1_pre_topc(D) & m1_pre_topc(D,A) -> (k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) = u1_struct_0(D) <-> k1_tsep_1(A,B,C) = D))))))))) # label(d2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6610 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (all E (-v3_struct_0(E) & m1_pre_topc(E,A) -> (m1_pre_topc(E,C) & r4_tsep_1(A,C,B) & m1_pre_topc(D,B) -> r4_tsep_1(A,k1_tsep_1(A,C,D),k1_tsep_1(A,B,E)) & r4_tsep_1(A,k1_tsep_1(A,D,C),k1_tsep_1(A,E,B))))))))))))) # label(t90_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6611 $T # label(t84_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6612 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> -((all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_tsep_1(D,A) -> (all E (m1_pre_topc(E,A) & v1_tsep_1(E,A) & -v3_struct_0(E) -> -(m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C) & -((all F (v1_borsuk_1(F,A) & m1_pre_topc(F,A) & -v3_struct_0(F) -> -(m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F)))) & -m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E))) & m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B)))))) & -m1_pre_topc(C,B) & -m1_pre_topc(B,C)))))))))) # label(t96_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6613 $T # label(t28_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.91 6614 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) <-> (exists D (-v3_struct_0(D) & (exists E (-v3_struct_0(E) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & r1_tsep_1(A,E,B) & r1_tsep_1(A,D,C) & v1_borsuk_1(E,A))) & m1_pre_topc(D,A) & v1_borsuk_1(D,A)))))))))) # label(t80_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6615 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> (r1_xboole_0(B,C) <-> r1_connsp_1(A,B,C))))))))) # label(t41_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6616 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(B) -> -(v3_pre_topc(B,A) & (all C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> u1_struct_0(C) != B))))))) # label(t20_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6617 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (-r1_tsep_1(A,B,C) -> k2_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D)) = k1_tsep_1(A,k2_tsep_1(A,B,C),D) & k2_tsep_1(A,k1_tsep_1(A,D,B),k1_tsep_1(A,D,C)) = k1_tsep_1(A,D,k2_tsep_1(A,B,C))))))))))) # label(t36_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6618 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> -(u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C) & -r1_tarski(B,C) & -r1_tarski(C,B) & (all D (-v1_xboole_0(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))) & -v1_xboole_0(E) -> -(v4_pre_topc(E,A) & r1_tarski(E,C) & -(k4_subset_1(u1_struct_0(A),B,C) != k4_subset_1(u1_struct_0(A),D,E) & (all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(k4_subset_1(u1_struct_0(A),B,C) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v3_pre_topc(F,A))))) & r1_tarski(D,B) & v4_pre_topc(D,A)))))) & r2_tsep_1(A,B,C)))))))) # label(t62_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6619 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (exists B (v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & -v3_struct_0(B) & m1_pre_topc(B,A))))) # label(rc2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6620 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (u1_struct_0(B) = u1_struct_0(C) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))))) # label(t5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6621 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,B,C) <-> (exists D ((exists E ((exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(E,A) & v3_pre_topc(F,A) & v4_pre_topc(D,A) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) & r1_tarski(k5_subset_1(u1_struct_0(A),F,k4_subset_1(u1_struct_0(A),B,C)),k5_subset_1(u1_struct_0(A),B,C)) & r1_tarski(k5_subset_1(u1_struct_0(A),E,k4_subset_1(u1_struct_0(A),B,C)),C) & r1_tarski(k5_subset_1(u1_struct_0(A),D,k4_subset_1(u1_struct_0(A),B,C)),B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t59_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6622 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(k4_subset_1(u1_struct_0(A),B,C),A) & r1_connsp_1(A,B,C) -> v4_pre_topc(C,A) & v4_pre_topc(B,A)))))))) # label(t39_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6623 (all A all B all C (-v3_struct_0(A) & l1_pre_topc(A) & -v3_struct_0(B) & m1_pre_topc(B,A) & -v3_struct_0(C) & m1_pre_topc(C,A) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_pre_topc(k2_tsep_1(A,B,C)) & -v3_struct_0(k2_tsep_1(A,B,C)))) # label(dt_k2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6624 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,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))) -> (D = u1_struct_0(B) & u1_struct_0(C) = E -> r2_tsep_1(A,D,E)))))) <-> r4_tsep_1(A,B,C)))))))) # label(d9_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6625 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> m1_pre_topc(B,k1_tsep_1(A,B,C)))))))) # label(t22_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6626 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (m1_pre_topc(B,C) <-> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k1_tsep_1(A,B,C)))))))) # label(t23_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6627 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(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))) -> (D = C -> (v3_pre_topc(C,A) <-> v3_pre_topc(D,B))))))))))) # label(t17_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6628 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r3_tsep_1(A,B,C) -> r1_tsep_1(A,B,C)))))))) # label(t68_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6629 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> v1_tsep_1(B,C) & m1_pre_topc(B,C)))))))) # label(t19_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6630 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (k1_tsep_1(A,B,C) = A & r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> m1_pre_topc(C,A) & v1_tsep_1(C,A) & m1_pre_topc(B,A) & v1_tsep_1(B,A))))))))) # label(t98_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6631 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v4_pre_topc(B,A) & (all C (v1_pre_topc(C) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) & -v3_struct_0(C) -> B != u1_struct_0(C)))))))) # label(t15_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6632 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> (all B (-v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (exists C (-v3_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & B = u1_struct_0(C))))))) # label(t10_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6633 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(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))) -> (D = C -> (v4_pre_topc(D,B) <-> v4_pre_topc(C,A))))))))))) # label(t12_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6634 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (m1_pre_topc(B,C) -> r4_tsep_1(A,B,C)))))))) # label(t86_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6635 (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))) -> (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_tsep_1(A,C,B) & r1_tarski(E,C) & r1_tarski(D,B) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),C,D),k4_subset_1(u1_struct_0(A),B,E))))))))))))) # label(t56_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6636 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (r1_tarski(u1_struct_0(B),u1_struct_0(C)) -> -v3_struct_0(B) & v1_borsuk_1(B,C) & m1_pre_topc(B,C)))))))) # label(t14_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6637 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(B,A) & m1_pre_topc(C,A) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,C,B)))) # label(symmetry_r4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6638 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> (all D (m1_pre_topc(D,A) & v1_pre_topc(D) & -v3_struct_0(D) -> (k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) = u1_struct_0(D) <-> D = k2_tsep_1(A,B,C))))))))))) # label(d5_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6639 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,D) | r1_connsp_1(A,C,D) -> r1_connsp_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t44_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6640 (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))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,C,D) & r2_tsep_1(A,B,D) -> r2_tsep_1(A,k4_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t58_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6641 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & r1_tarski(C,E) & r1_xboole_0(D,C) & r1_xboole_0(E,B) & v3_pre_topc(D,A) & v3_pre_topc(E,A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))))))))))) # label(t48_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6642 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (A = k1_tsep_1(A,B,C) & r3_tsep_1(A,B,C) -> m1_pre_topc(B,A) & v1_tsep_1(B,A)))))))) # label(t74_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6643 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r4_tsep_1(A,C,D) & r4_tsep_1(A,B,D) -> r4_tsep_1(A,k1_tsep_1(A,B,C),D)) & (r4_tsep_1(A,D,B) & r4_tsep_1(A,D,C) -> r4_tsep_1(A,D,k1_tsep_1(A,B,C))))))))))) # label(t92_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6644 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & m1_pre_topc(D,A) -> (r4_tsep_1(A,B,C) -> r4_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D))))))))))) # label(t89_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6645 $T # label(t27_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6646 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) & m1_pre_topc(C,B) -> g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))))) # label(t6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6647 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & (exists F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(F,A) & v3_pre_topc(E,A) & v3_pre_topc(D,A) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & r1_tarski(E,C) & r1_tarski(D,B) & k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r2_tsep_1(A,B,C))))))))) # label(t65_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6648 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) -> m1_pre_topc(B,C)) & (m1_pre_topc(C,B) -> g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k2_tsep_1(A,B,C)) & (k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) -> m1_pre_topc(C,B)) & (m1_pre_topc(B,C) -> k2_tsep_1(A,B,C) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))))))))) # label(t31_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6649 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(C,A) & v4_pre_topc(B,A) -> (r1_connsp_1(A,B,C) <-> r1_xboole_0(B,C))))))))) # label(t38_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6650 (all A all B all C (-v3_struct_0(A) & l1_pre_topc(A) & m1_pre_topc(B,A) & -v3_struct_0(C) & m1_pre_topc(C,A) & -v3_struct_0(B) -> k1_tsep_1(A,B,C) = k1_tsep_1(A,C,B))) # label(commutativity_k1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6651 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) & -v3_struct_0(B) -> (all C (v1_tsep_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) <-> r1_tsep_1(A,B,C)))))))) # label(t73_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6652 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_tarski(B,C) -> r2_tsep_1(A,B,C)))))))) # label(t52_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6653 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) <-> (exists D (m1_pre_topc(D,A) & (exists E (r4_tsep_1(A,D,E) & m1_pre_topc(C,E) & (r1_tsep_1(A,k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) | r1_tsep_1(A,D,E)) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & -v3_struct_0(E))) & -v3_struct_0(D)))))))))) # label(t99_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6654 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) & r1_xboole_0(B,C) -> r1_xboole_0(B,k6_pre_topc(A,C))))))))) # label(t40_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6655 (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))) -> ((exists D ((exists E (r1_tarski(C,E) & r1_xboole_0(E,B) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_xboole_0(D,C) & r1_tarski(B,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r1_connsp_1(A,B,C)))))))) # label(t46_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6656 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) -> (m1_pre_topc(B,C) <-> r1_tarski(u1_struct_0(B),u1_struct_0(C))))))))) # label(t4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6657 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,C) <-> (exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & (exists E (r1_tarski(C,E) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(E,A) & v4_pre_topc(D,A) & r1_tarski(B,D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))))))))))))) # label(t47_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6658 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r2_tsep_1(A,C,D) & r2_tsep_1(A,B,D) -> r2_tsep_1(A,k5_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t57_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6659 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,k1_tsep_1(A,B,C),D) <-> r3_tsep_1(A,B,D) & r3_tsep_1(A,C,D)))))))))) # label(t79_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6660 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r3_tsep_1(A,B,C) & m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_borsuk_1(k1_tsep_1(A,B,C),A) -> v1_borsuk_1(B,A) & m1_pre_topc(B,A)))))))) # label(t72_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6661 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r4_tsep_1(A,B,C) & r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t85_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6662 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (v1_tsep_1(C,B) & m1_pre_topc(C,B) -> v1_tsep_1(C,A) & m1_pre_topc(C,A))))))) # label(t18_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6663 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(C,A) & v3_pre_topc(B,A) -> r2_tsep_1(A,B,C)))))))) # label(t54_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6664 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),A) & v1_tsep_1(k2_tsep_1(A,B,C),A)))))))) # label(t33_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6665 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))))))) # label(t1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6666 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & v1_borsuk_1(B,A) & -v3_struct_0(B) -> (all C (v1_borsuk_1(C,A) & m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tsep_1(A,B,C) <-> r3_tsep_1(A,B,C)))))))) # label(t70_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6667 $T # label(d6_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6668 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) & v1_tsep_1(C,A) -> v1_tsep_1(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A))))))) # label(t25_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6669 $T # label(t69_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6670 (all A (v2_pre_topc(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))) -> (u1_struct_0(B) = C -> (v1_tsep_1(B,A) & m1_pre_topc(B,A) <-> v3_pre_topc(C,A))))))))) # label(t16_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6671 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) -> (all E (m1_pre_topc(E,A) -> (m1_pre_topc(D,B) & m1_pre_topc(E,C) & r3_tsep_1(A,B,C) -> r3_tsep_1(A,D,E)))))))))))) # label(t77_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6672 (all A all B all C (l1_pre_topc(A) & m1_pre_topc(C,A) & m1_pre_topc(B,A) -> (r1_tsep_1(A,B,C) -> r1_tsep_1(A,C,B)))) # label(symmetry_r1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6673 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> ((exists D ((exists E (r1_tsep_1(A,E,B) & r1_tsep_1(A,D,C) & m1_pre_topc(C,E) & m1_pre_topc(B,D) & m1_pre_topc(E,A) & v1_tsep_1(E,A) & -v3_struct_0(E))) & m1_pre_topc(D,A) & v1_tsep_1(D,A) & -v3_struct_0(D))) <-> r3_tsep_1(A,B,C)))))))) # label(t82_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6674 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (v1_tsep_1(k1_tsep_1(A,B,C),A) & m1_pre_topc(k1_tsep_1(A,B,C),A) & r3_tsep_1(A,B,C) -> v1_tsep_1(B,A) & m1_pre_topc(B,A)))))))) # label(t75_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6675 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (v4_pre_topc(B,A) & v4_pre_topc(C,A) -> r2_tsep_1(A,B,C)))))))) # label(t53_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6676 (all A (l1_pre_topc(A) -> m1_pre_topc(A,A))) # label(t2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6677 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & v1_tsep_1(B,A) -> (all C (m1_pre_topc(C,A) & v1_tsep_1(C,A) -> r4_tsep_1(A,B,C))))))) # label(t88_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6678 (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))) -> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (r1_connsp_1(A,B,D) & r1_connsp_1(A,C,D) <-> r1_connsp_1(A,k4_subset_1(u1_struct_0(A),B,C),D)))))))))) # label(t45_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6679 (all A all B all C (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & l1_pre_topc(A) -> (r2_tsep_1(A,B,C) -> r2_tsep_1(A,C,B)))) # label(symmetry_r2_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6680 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) & v1_borsuk_1(B,A) -> (all C (m1_pre_topc(C,A) & v1_borsuk_1(C,A) & -v3_struct_0(C) -> m1_pre_topc(k1_tsep_1(A,B,C),A) & v1_borsuk_1(k1_tsep_1(A,B,C),A))))))) # label(t24_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6681 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,B) -> m1_pre_topc(C,A))))))) # label(t7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6682 (all A (l1_pre_topc(A) & v2_pre_topc(A) -> (exists B (v1_tsep_1(B,A) & v2_pre_topc(B) & v1_pre_topc(B) & m1_pre_topc(B,A))))) # label(rc1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6683 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,C,D) -> r3_tsep_1(A,k2_tsep_1(A,C,B),k2_tsep_1(A,D,B)) & r3_tsep_1(A,k2_tsep_1(A,B,C),k2_tsep_1(A,B,D)) | r1_tsep_1(A,D,B) | r1_tsep_1(A,C,B)))))))))) # label(t76_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6684 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (k1_tsep_1(A,B,C) = A & r3_tsep_1(A,B,C) -> m1_pre_topc(B,A) & v1_borsuk_1(B,A)))))))) # label(t71_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6685 (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))) -> ((exists D ((exists E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(B,D) & v3_pre_topc(E,A) & v3_pre_topc(D,A) & r1_xboole_0(k5_subset_1(u1_struct_0(A),D,E),k4_subset_1(u1_struct_0(A),B,C)) & r1_tarski(C,E))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))))) <-> r1_connsp_1(A,B,C)))))))) # label(t49_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6686 (all A (l1_pre_topc(A) & v2_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(A))) -> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) -> (r1_tarski(C,u1_struct_0(B)) & E = D & r1_tarski(D,C) & v4_pre_topc(C,A) -> (v4_pre_topc(D,A) <-> v4_pre_topc(E,B))))))))))))) # label(t8_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6687 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (-r1_tsep_1(A,C,D) -> (r4_tsep_1(A,D,B) & r4_tsep_1(A,C,B) -> r4_tsep_1(A,k2_tsep_1(A,C,D),B)) & (r4_tsep_1(A,B,D) & r4_tsep_1(A,B,C) -> r4_tsep_1(A,B,k2_tsep_1(A,C,D)))))))))))) # label(t91_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6688 $T # label(d4_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6689 (all A (l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) -> (v1_tsep_1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (C = u1_struct_0(B) -> v3_pre_topc(C,A))))))))) # label(d1_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6690 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (k1_tsep_1(A,B,C) = A -> (-((all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) -> (all E (-v3_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) -> -(-((all F (m1_pre_topc(F,A) & v1_tsep_1(F,A) & -v3_struct_0(F) -> -(A = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(F,k2_tsep_1(A,B,C))))) & A != k1_tsep_1(A,D,E)) & m1_pre_topc(E,C) & m1_pre_topc(D,B)))))) & -m1_pre_topc(C,B) & -m1_pre_topc(B,C)) <-> r4_tsep_1(A,B,C)) | r1_tsep_1(A,B,C)))))))) # label(t94_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6691 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (r3_tsep_1(A,B,D) -> r1_tsep_1(A,B,C) | r3_tsep_1(A,k2_tsep_1(A,B,C),D)))))))))) # label(t78_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6692 (all A (v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r1_xboole_0(B,C) & r2_tsep_1(A,B,C) <-> r1_connsp_1(A,B,C)))))))) # label(t51_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6693 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (all C (m1_subset_1(C,k1_zfmisc_1(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))) -> -(v3_pre_topc(D,A) & v3_pre_topc(E,A) & r1_tarski(E,C) & -((all F (m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & -v1_xboole_0(F) -> -(k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),D,E),F) = k4_subset_1(u1_struct_0(A),B,C) & r1_tarski(F,k5_subset_1(u1_struct_0(A),B,C)) & v4_pre_topc(F,A)))) & k4_subset_1(u1_struct_0(A),D,E) != k4_subset_1(u1_struct_0(A),B,C)) & r1_tarski(D,B)))))) & -r1_tarski(C,B) & -r1_tarski(B,C) & r2_tsep_1(A,B,C) & u1_struct_0(A) = k4_subset_1(u1_struct_0(A),B,C)))))))) # label(t66_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6694 (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))) -> (r2_tsep_1(A,B,C) <-> r1_connsp_1(A,k6_subset_1(u1_struct_0(A),B,C),k6_subset_1(u1_struct_0(A),C,B))))))))) # label(d7_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.92 6695 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (-v3_struct_0(C) & m1_pre_topc(C,A) -> (all D (m1_pre_topc(D,A) & -v3_struct_0(D) -> (-r1_tsep_1(A,B,C) -> k2_tsep_1(A,B,C) = k2_tsep_1(A,C,B)) & (-r1_tsep_1(A,B,k2_tsep_1(A,C,D)) & -r1_tsep_1(A,C,D) | -r1_tsep_1(A,B,C) & -r1_tsep_1(A,k2_tsep_1(A,B,C),D) -> k2_tsep_1(A,B,k2_tsep_1(A,C,D)) = k2_tsep_1(A,k2_tsep_1(A,B,C),D)))))))))) # label(t29_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6696 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> m1_pre_topc(k2_tsep_1(A,B,C),C) & m1_pre_topc(k2_tsep_1(A,B,C),B)))))))) # label(t30_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6697 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (-v3_struct_0(B) & m1_pre_topc(B,A) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (-r1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> -(-m1_pre_topc(B,C) & -m1_pre_topc(C,B) & (all D (-v3_struct_0(D) & m1_pre_topc(D,A) & v1_borsuk_1(D,A) -> (all E (-v3_struct_0(E) & m1_pre_topc(E,A) & v1_borsuk_1(E,A) -> -(m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,B,C)),C) & -(-m1_pre_topc(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E)) & (all F (-v3_struct_0(F) & v1_tsep_1(F,A) & m1_pre_topc(F,A) -> -(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)))))) & m1_pre_topc(k2_tsep_1(A,D,k1_tsep_1(A,B,C)),B))))))))))))))) # label(t93_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6698 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_pre_topc(B,A) & -v3_struct_0(B) -> (all C (m1_pre_topc(C,A) & -v3_struct_0(C) -> (r1_tsep_1(A,B,C) & A = k1_tsep_1(A,B,C) -> (r4_tsep_1(A,B,C) <-> m1_pre_topc(B,A) & m1_pre_topc(C,A) & v1_borsuk_1(C,A) & v1_borsuk_1(B,A))))))))) # label(t95_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6699 (all A all B all C (m1_pre_topc(B,A) & m1_pre_topc(C,A) & l1_pre_topc(A) -> (r3_tsep_1(A,B,C) -> r3_tsep_1(A,C,B)))) # label(symmetry_r3_tsep_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6700 (all A all B (v10_lattices(B) & l3_lattices(B) & v17_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r3_lattice3(B,C,A) <-> r4_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B))))))) # label(t24_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6701 (exists A (v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v6_lattice3(A) & v5_lattice3(A) & v4_lattice3(A) & v10_lattices(A) & v9_lattices(A) & v8_lattices(A) & v3_lattices(A) & -v3_struct_0(A) & l3_lattices(A))) # label(rc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6702 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> v2_lattice3(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)))) # label(t11_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6703 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(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))))) <-> v5_lattice3(A)))) # label(t33_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6704 r1_tarski(f2_s2_lattice3,k1_relat_1(f4_s2_lattice3)) -> a_0_2_lattice3 = k9_relat_1(f4_s2_lattice3,a_0_1_lattice3) # label(s2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6705 (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]. 183.74/184.93 6706 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)))) # label(d2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6707 (all A (l1_orders_2(A) -> l1_orders_2(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)))) # label(dt_k7_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6708 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_lattice3(A))) -> k5_lattice3(A,B) = B)))) # label(d4_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6709 (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]. 183.74/184.93 6710 (all A all B all C (v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & v2_lattice3(A) -> k12_lattice3(A,B,C) = k11_lattice3(A,B,C))) # label(redefinition_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6711 (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)) -> B = k16_lattice3(A,a_2_4_lattice3(A,B)) & B = k15_lattice3(A,a_2_3_lattice3(A,B)))))) # label(t45_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6712 (all A all B (v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & v5_lattice3(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k15_lattice3(B,a_3_7_lattice3(A,B,C)) = k4_lattices(B,C,k15_lattice3(B,A)) & k15_lattice3(B,a_3_8_lattice3(A,B,C)) = k4_lattices(B,k15_lattice3(B,A),C))))) # label(t54_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6713 (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)) -> (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]. 183.74/184.93 6714 (all A (l3_lattices(A) & -v3_struct_0(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) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r4_lattice3(A,F,B) -> r1_lattices(A,C,F)))) & (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)))) & r4_lattice3(A,E,a_3_0_lattice3(A,B,D)) -> r1_lattices(A,k2_lattices(A,D,C),E))))))))))) # label(d19_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6715 (all A (-v1_xboole_0(A) -> (all B (v1_funct_1(B) & v1_funct_2(B,k1_zfmisc_1(A),A) & m2_relset_1(B,k1_zfmisc_1(A),A) -> -((all C (m1_subset_1(C,A) -> C = k8_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)))) & (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 (-v3_struct_0(C) & v3_lattices(C) & v4_lattice3(C) & l3_lattices(C) & v10_lattices(C) -> -(u1_struct_0(C) = A & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> k15_lattice3(C,D) = k1_funct_1(B,D))))))))))) # label(t56_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6716 (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 (m1_subset_1(C,u1_struct_0(A)) -> k3_lattices(A,B,C) = k15_lattice3(A,k2_struct_0(A,B,C)) & k16_lattice3(A,k2_struct_0(A,B,C)) = k4_lattices(A,B,C))))))) # label(t44_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6717 (all A all B (-v3_struct_0(B) & l3_lattices(B) & v10_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]. 183.74/184.93 6718 (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)) -> (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]. 183.74/184.93 6719 (all A all B all C all D (l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_lattice3(B,C,D)) <-> (exists E (A = k1_lattices(B,D,E) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6720 (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)) -> B = k16_lattice3(A,k1_struct_0(A,B)) & B = k15_lattice3(A,k1_struct_0(A,B)))))) # label(t43_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6721 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> v4_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & -v3_struct_0(k3_lattice3(A)))) # label(fc4_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6722 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,B,D)))) <-> r3_lattice3(A,B,C))))))) # label(d16_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6723 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) -> v8_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)) & v4_relat_2(k2_lattice3(A)) & v1_relat_2(k2_lattice3(A)))) # label(dt_k2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6724 (all A (l1_orders_2(A) & -v3_struct_0(A) -> v1_orders_2(k7_lattice3(A)) & -v3_struct_0(k7_lattice3(A)))) # label(fc6_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6725 (all A all B (-v3_struct_0(A) & l3_lattices(A) -> m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)))) # label(dt_k15_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6726 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> B = k8_lattice3(A,B))))) # label(d6_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6727 (all A (-v3_struct_0(A) & l1_orders_2(A) -> (v3_lattice3(A) -> v1_lattice3(A) & v2_lattice3(A)))) # label(t12_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6728 (all A all B all C all D (v10_lattices(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) & v4_lattice3(B) & -v3_struct_0(B) -> ((exists E (r2_hidden(E,C) & A = k3_lattices(B,D,E) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_5_lattice3(B,C,D))))) # label(fraenkel_a_3_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6729 (all A all B (l3_lattices(A) & m1_subset_1(B,u1_struct_0(A)) & v10_lattices(A) & -v3_struct_0(A) -> m1_subset_1(k4_lattice3(A,B),u1_struct_0(k3_lattice3(A))))) # label(dt_k4_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6730 (all A all B all C all D (v4_lattice3(C) & v6_lattice3(C) & l3_lattices(C) & m1_subset_1(D,u1_struct_0(C)) & v10_lattices(C) & -v3_struct_0(C) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & A = k3_lattices(C,D,E) & r2_hidden(E,B))) <-> r2_hidden(A,a_3_9_lattice3(B,C,D))))) # label(fraenkel_a_3_9_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6731 (all A all B all C (-v3_struct_0(C) & v10_lattices(C) & v17_lattices(C) & l3_lattices(C) -> ((exists D (m1_subset_1(D,u1_struct_0(C)) & k7_lattices(C,D) = A & r2_hidden(D,B))) <-> r2_hidden(A,a_2_0_lattice3(B,C))))) # label(fraenkel_a_2_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6732 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k8_lattice3(A,B),u1_struct_0(k7_lattice3(A))))) # label(dt_k8_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6733 (all A all B all C all D (-v3_struct_0(C) & v4_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) & v6_lattice3(C) & v10_lattices(C) -> ((exists E (r2_hidden(E,B) & A = k3_lattices(C,E,D) & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_10_lattice3(B,C,D))))) # label(fraenkel_a_3_10_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6734 (all A all B all C (l3_lattices(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & r3_lattice3(B,D,C) & D = A)) <-> r2_hidden(A,a_2_1_lattice3(B,C))))) # label(fraenkel_a_2_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6735 (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]. 183.74/184.93 6736 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> v10_lattices(A) & v13_lattices(A) & k5_lattices(A) = k15_lattice3(A,k1_xboole_0) & l3_lattices(A) & -v3_struct_0(A))) # label(t50_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6737 (all A (l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) & -v3_struct_0(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]. 183.74/184.93 6738 (all A (l1_orders_2(A) -> g1_orders_2(u1_struct_0(A),k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))) = k7_lattice3(A))) # label(d5_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6739 (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]. 183.74/184.93 6740 (all A (v10_lattices(A) & l3_lattices(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B all C ((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,C) & r3_lattices(A,D,E))))))) -> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)))))) # label(t48_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6741 (all A (v4_orders_2(A) & l1_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)) -> (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]. 183.74/184.93 6742 (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 (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))))))))))) # label(d11_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6743 (all A (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_orders_2(A) -> v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)))) # label(fc5_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6744 (all A all B all C all D (-v3_struct_0(C) & v10_lattices(C) & v4_lattice3(C) & v5_lattice3(C) & m1_subset_1(D,u1_struct_0(C)) & l3_lattices(C) -> ((exists E (m1_subset_1(E,u1_struct_0(C)) & r2_hidden(E,B) & A = k4_lattices(C,E,D))) <-> r2_hidden(A,a_3_8_lattice3(B,C,D))))) # label(fraenkel_a_3_8_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6745 (all A ((exists B (p1_s1_lattice3(B) & f1_s1_lattice3 = A & m1_subset_1(B,f2_s1_lattice3))) <-> r2_hidden(A,a_0_0_lattice3))) # label(fraenkel_a_0_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6746 (all A all B all C (v4_orders_2(A) & v2_lattice3(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l1_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]. 183.74/184.93 6747 (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]. 183.74/184.93 6748 (all A all B (-v3_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & v6_lattice3(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> k16_lattice3(B,a_3_10_lattice3(A,B,C)) = k3_lattices(B,k16_lattice3(B,A),C) & k3_lattices(B,C,k16_lattice3(B,A)) = k16_lattice3(B,a_3_9_lattice3(A,B,C)))))) # label(t55_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6749 (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]. 183.74/184.93 6750 (all A (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & v4_lattice3(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]. 183.74/184.93 6751 (all A (l1_orders_2(A) -> -v3_struct_0(k14_lattice3(A)) & v3_lattices(k14_lattice3(A)) & l3_lattices(k14_lattice3(A)) & v10_lattices(k14_lattice3(A)))) # label(dt_k14_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6752 (all A all B all C (-v3_struct_0(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & v10_lattices(B) -> ((exists D (A = D & r3_lattices(B,C,D) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_4_lattice3(B,C))))) # label(fraenkel_a_2_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6753 (all A all B (l3_lattices(B) & v3_lattices(B) -> (k1_lattice3(A) = B <-> u1_struct_0(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)) -> k5_subset_1(A,C,D) = k1_binop_1(u1_lattices(B),C,D) & k1_binop_1(u2_lattices(B),C,D) = k4_subset_1(A,C,D)))))))) # label(d1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6754 (all A (v3_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v1_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) -> (exists B (-v3_struct_0(B) & v10_lattices(B) & k3_lattice3(B) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) & l3_lattices(B) & v3_lattices(B))))) # label(t19_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6755 (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]. 183.74/184.93 6756 (all A all B all C all D (v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) -> (r2_hidden(A,a_3_4_lattice3(B,C,D)) <-> (exists E (k3_lattices(B,C,E) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_4_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6757 (all A (-v3_struct_0(A) & l3_lattices(A) -> ((all B exists C ((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) & m1_subset_1(C,u1_struct_0(A)))) <-> v4_lattice3(A)))) # label(d18_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6758 (all A all B (v1_relat_2(B) & v4_relat_2(B) & m1_relset_1(B,A,A) & v1_partfun1(B,A,A) & v8_relat_2(B) -> v1_partfun1(k6_lattice3(A,B),A,A) & m2_relset_1(k6_lattice3(A,B),A,A) & v8_relat_2(k6_lattice3(A,B)) & v4_relat_2(k6_lattice3(A,B)) & v1_relat_2(k6_lattice3(A,B)))) # label(dt_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6759 (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)) -> (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]. 183.74/184.93 6760 (all A v5_lattice3(k1_lattice3(A))) # label(t26_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6761 (exists A (v1_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v3_lattice3(A) & v2_lattice3(A) & v3_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6762 (all A all B all C all D (-v3_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) -> ((exists E (E = A & r3_lattices(B,k4_lattices(B,C,E),D) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_6_lattice3(B,C,D))))) # label(fraenkel_a_3_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6763 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B all C (m1_subset_1(C,u1_struct_0(A)) -> (k15_lattice3(A,B) = C <-> (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]. 183.74/184.93 6764 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & -v3_struct_0(A) -> (v3_filter_0(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> v5_lattice3(A)))) # label(t53_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6765 (all A all B (v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v1_relat_2(B) -> B = k6_lattice3(A,k6_lattice3(A,B)))) # label(involutiveness_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6766 (all A (-v3_struct_0(A) & v4_lattice3(A) & l3_lattices(A) & v10_lattices(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]. 183.74/184.93 6767 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C ((all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(D,C) -> r1_lattices(A,D,B)))) <-> r4_lattice3(A,B,C))))))) # label(d17_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6768 (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]. 183.74/184.93 6769 (all A (l1_orders_2(A) -> (all B (m1_subset_1(B,u1_struct_0(k7_lattice3(A))) -> B = k9_lattice3(A,B))))) # label(d7_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6770 (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]. 183.74/184.93 6771 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) & v10_lattices(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]. 183.74/184.93 6772 $T # label(t39_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6773 (all A (l1_orders_2(A) -> (v2_lattice3(A) -> -v3_struct_0(A)))) # label(cc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6774 (all A (l1_orders_2(A) -> (v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v2_lattice3(A) & v1_lattice3(A) & v2_orders_2(A) -> (all B (-v3_struct_0(B) & v3_lattices(B) & v10_lattices(B) & l3_lattices(B) -> (g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) <-> k14_lattice3(A) = B)))))) # label(d15_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6775 (all A (-v3_struct_0(A) & v3_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & v4_orders_2(A) & v2_orders_2(A) -> -v3_struct_0(k14_lattice3(A)) & v5_lattices(k14_lattice3(A)) & v6_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)) & v4_lattices(k14_lattice3(A)) & v3_lattices(k14_lattice3(A)))) # label(fc7_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6776 (all A (l1_orders_2(A) -> (v1_lattice3(A) <-> v2_lattice3(k7_lattice3(A))))) # label(t10_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6777 (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(k10_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k10_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6778 (all A (v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A)))) # label(dt_k1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6779 (all A all B all C all D (m1_subset_1(C,u1_struct_0(B)) & l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & A = k4_lattices(B,C,E))) <-> r2_hidden(A,a_3_2_lattice3(B,C,D))))) # label(fraenkel_a_3_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6780 (all A all B all C all D (v4_lattice3(B) & m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists E (k4_lattices(B,D,E) = A & 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]. 183.74/184.93 6781 (all A all B all C (v1_lattice3(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & l1_orders_2(A) & v4_orders_2(A) -> k10_lattice3(A,B,C) = k13_lattice3(A,B,C))) # label(redefinition_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6782 (all A (v10_lattices(A) & l3_lattices(A) & -v3_struct_0(A) -> v1_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & l1_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)))) # label(dt_k3_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6783 (all A all B all C (-v3_struct_0(B) & v4_lattice3(B) & l3_lattices(B) & v10_lattices(B) -> ((exists D (D = A & (exists E (r3_lattices(B,D,E) & r2_hidden(E,C) & m1_subset_1(E,u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B)))) <-> r2_hidden(A,a_2_5_lattice3(B,C))))) # label(fraenkel_a_2_5_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6784 (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)) -> k10_lattice3(A,C,B) = k10_lattice3(A,B,C))))))) # label(t13_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6785 (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)) -> (r4_lattice3(A,B,k2_struct_0(A,C,D)) <-> r3_lattices(A,k3_lattices(A,C,D),B)))))))))) # label(t22_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6786 (all A v4_lattice3(k1_lattice3(A))) # label(t25_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6787 (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 ((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) & r1_orders_2(A,B,D) & m1_subset_1(D,u1_struct_0(A)))) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k10_lattice3(A,B,C) = D <-> 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)))))))))))) # label(d13_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6788 (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)) -> (l3_lattices(A) & v3_filter_0(A) & v10_lattices(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]. 183.74/184.93 6789 (all A (v3_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v12_lattices(k1_lattice3(A)) & v13_lattices(k1_lattice3(A)) & v16_lattices(k1_lattice3(A)) & v17_lattices(k1_lattice3(A)) & v15_lattices(k1_lattice3(A)) & v14_lattices(k1_lattice3(A)) & v11_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc3_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6790 (all A all B (l1_orders_2(A) & m1_subset_1(B,u1_struct_0(k7_lattice3(A))) -> m1_subset_1(k9_lattice3(A,B),u1_struct_0(A)))) # label(dt_k9_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6791 (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_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]. 183.74/184.93 6792 (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]. 183.74/184.93 6793 (all A (v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_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)) -> k12_lattice3(A,B,k13_lattice3(A,B,C)) = B)))))) # label(t18_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6794 (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,B,C) = k11_lattice3(A,C,B))))))) # label(t15_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6795 (all A ((exists B (p1_s2_lattice3(B) & A = f3_s2_lattice3(B) & m1_subset_1(B,f1_s2_lattice3))) <-> r2_hidden(A,a_0_1_lattice3))) # label(fraenkel_a_0_1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6796 (all A all B all C (-v3_struct_0(B) & v4_lattice3(B) & l3_lattices(B) & v10_lattices(B) -> ((exists D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(D,C) & k15_lattice3(B,D) = A)) <-> r2_hidden(A,a_2_7_lattice3(B,C))))) # label(fraenkel_a_2_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6797 (all A (v3_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & -v3_struct_0(k1_lattice3(A)))) # label(fc2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6798 (all A (-v3_struct_0(A) & l3_lattices(A) & v4_lattice3(A) & v10_lattices(A) -> (all B all C (r1_tarski(B,C) -> r3_lattices(A,k15_lattice3(A,B),k15_lattice3(A,C)) & r3_lattices(A,k16_lattice3(A,C),k16_lattice3(A,B)))))) # label(t46_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6799 (all A all B all C (l1_orders_2(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,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]. 183.74/184.93 6800 (all 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)) -> (r2_hidden(D,B) -> r1_orders_2(A,C,D)))) <-> r1_lattice3(A,B,C)))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6801 (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) & r4_lattice3(A,B,C) -> k15_lattice3(A,C) = B)))))) # label(t41_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6802 (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) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & A = D & 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]. 183.74/184.93 6803 (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)) -> (all C (B = k16_lattice3(A,C) <-> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattice3(A,D,C) -> r3_lattices(A,D,B)))) & r3_lattice3(A,B,C))))))) # label(t34_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.93 6804 (all A (l3_lattices(A) & -v3_struct_0(A) -> (v6_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)) -> ((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,E,a_3_1_lattice3(A,B,D)) & (all F (m1_subset_1(F,u1_struct_0(A)) -> (r3_lattice3(A,F,B) -> r1_lattices(A,F,C)))) & r3_lattice3(A,C,B) -> r1_lattices(A,E,k1_lattices(A,D,C)))))))))))) # label(d20_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6805 (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,C) & r1_orders_2(A,E,B) -> 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)) -> (D = k11_lattice3(A,B,C) <-> 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)))) & r1_orders_2(A,D,B)))))))))))) # label(d14_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6806 (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_tarski(B,C) <-> r1_lattices(k1_lattice3(A),B,C)))))) # label(t2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6807 (all A (v4_lattice3(A) & l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (k16_lattice3(A,a_2_6_lattice3(A,B)) = k16_lattice3(A,B) & k15_lattice3(A,a_2_5_lattice3(A,B)) = k15_lattice3(A,B))))) # label(t47_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6808 (all A all B (-v3_struct_0(A) & l3_lattices(A) -> m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)))) # label(dt_k16_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6809 (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)) -> k13_lattice3(A,k12_lattice3(A,B,C),C) = C)))))) # label(t17_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6810 (all A all B all C (l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_2_6_lattice3(B,C)) <-> (exists D ((exists E (r2_hidden(E,C) & r3_lattices(B,E,D) & m1_subset_1(E,u1_struct_0(B)))) & A = D & m1_subset_1(D,u1_struct_0(B))))))) # label(fraenkel_a_2_6_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6811 (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) & v1_lattice3(A) & v4_orders_2(A) -> k13_lattice3(A,C,B) = k13_lattice3(A,B,C))) # label(commutativity_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6812 (all A all B all C (v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) -> m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)))) # label(dt_k13_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6813 (all A all B (v17_lattices(B) & l3_lattices(B) & v10_lattices(B) & -v3_struct_0(B) -> (all C (m1_subset_1(C,u1_struct_0(B)) -> (r4_lattice3(B,C,A) <-> r3_lattice3(B,k7_lattices(B,C),a_2_0_lattice3(A,B))))))) # label(t23_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6814 (all A all B (-v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,u1_struct_0(k3_lattice3(A))) -> m1_subset_1(k5_lattice3(A,B),u1_struct_0(A)))) # label(dt_k5_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6815 (all A (k1_xboole_0 = k5_lattices(k1_lattice3(A)) & v13_lattices(k1_lattice3(A)))) # label(t3_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6816 (all A all B all C all D (m1_subset_1(D,u1_struct_0(B)) & l3_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_0_lattice3(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & k2_lattices(B,D,E) = A & r2_hidden(E,C)))))) # label(fraenkel_a_3_0_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6817 (all A (-v3_struct_0(A) & l3_lattices(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_lattice3(A,B) = B)))) # label(d3_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6818 (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]. 183.74/184.94 6819 (all A (v14_lattices(k1_lattice3(A)) & k6_lattices(k1_lattice3(A)) = A)) # label(t4_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6820 (all A v6_lattice3(k1_lattice3(A))) # label(t27_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6821 (all A (-v3_struct_0(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)))) # label(fc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6822 (all A all B all C all D (-v3_struct_0(C) & v5_lattice3(C) & l3_lattices(C) & m1_subset_1(D,u1_struct_0(C)) & v4_lattice3(C) & v10_lattices(C) -> ((exists E (r2_hidden(E,B) & k4_lattices(C,D,E) = A & m1_subset_1(E,u1_struct_0(C)))) <-> r2_hidden(A,a_3_7_lattice3(B,C,D))))) # label(fraenkel_a_3_7_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6823 (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]. 183.74/184.94 6824 (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) <-> r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C))))))))) # label(t7_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6825 (all A all B all C (l3_lattices(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists D (r4_lattice3(B,D,C) & D = A & 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]. 183.74/184.94 6826 (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]. 183.74/184.94 6827 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B k15_lattice3(A,a_2_1_lattice3(A,B)) = k16_lattice3(A,B)))) # label(d22_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6828 (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]. 183.74/184.94 6829 (all A ((exists B (m1_subset_1(B,f1_s2_lattice3) & k1_funct_1(f4_s2_lattice3,f3_s2_lattice3(B)) = A & p1_s2_lattice3(B))) <-> r2_hidden(A,a_0_2_lattice3))) # label(fraenkel_a_0_2_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6830 (all A (l1_orders_2(A) -> (v1_lattice3(A) -> -v3_struct_0(A)))) # label(cc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6831 (all A all B (v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v8_relat_2(B) & v4_relat_2(B) & v1_relat_2(B) -> k6_lattice3(A,B) = k4_relat_1(B))) # label(redefinition_k6_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6832 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) -> -v3_struct_0(A) & v14_lattices(A) & l3_lattices(A) & k15_lattice3(A,u1_struct_0(A)) = k6_lattices(A) & v10_lattices(A))) # label(t51_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6833 (exists A (v1_orders_2(A) & v3_orders_2(A) & v3_lattice3(A) & v4_orders_2(A) & v2_orders_2(A) & -v3_struct_0(A) & l1_orders_2(A))) # label(rc1_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6834 (all A all B all C (v2_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) -> k12_lattice3(A,C,B) = k12_lattice3(A,B,C))) # label(commutativity_k12_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6835 (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 (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) & m1_subset_1(D,u1_struct_0(A)))))))) <-> v1_lattice3(A)))) # label(d10_lattice3) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6836 (all A all B (v10_lattices(B) & l3_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]. 183.74/184.94 6837 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) -> (all B (m2_finseq_1(B,k5_numbers) -> (B = k3_unialg_1(A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> (all D (m2_relset_1(D,k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) & v1_unialg_1(D,u1_struct_0(A)) & v1_funct_1(D) & -v1_xboole_0(D) -> (D = k1_funct_1(u1_unialg_1(A),C) -> k1_funct_1(B,C) = k2_unialg_1(u1_struct_0(A),D))))))) & k3_finseq_1(u1_unialg_1(A)) = k3_finseq_1(B)))))) # label(d11_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6838 (all A (l1_unialg_1(A) & v7_unialg_1(A) -> v1_funct_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v5_unialg_1(u1_unialg_1(A),u1_struct_0(A)) & v1_relat_1(u1_unialg_1(A)))) # label(fc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6839 (all A (l1_unialg_1(A) & v6_unialg_1(A) -> v1_finseq_1(u1_unialg_1(A)) & v4_unialg_1(u1_unialg_1(A),u1_struct_0(A)) & v1_funct_1(u1_unialg_1(A)) & v1_relat_1(u1_unialg_1(A)))) # label(fc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6840 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (v4_unialg_1(B,A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_1(D) & m2_relset_1(D,k13_finseq_1(A),A) -> (D = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)) -> v1_unialg_1(D,A))))))))) # label(d4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6841 (all A all B (-v1_xboole_0(A) & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> v3_unialg_1(g1_unialg_1(A,B)) & -v3_struct_0(g1_unialg_1(A,B)))) # label(fc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6842 (all A (l1_unialg_1(A) -> (v8_unialg_1(A) <-> v2_relat_1(u1_unialg_1(A)) & k1_xboole_0 != u1_unialg_1(A)))) # label(d9_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6843 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> v3_unialg_1(g1_unialg_1(A,B)) & l1_unialg_1(g1_unialg_1(A,B)))) # label(dt_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6844 (all A all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> ((all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (v1_funct_1(D) & m2_relset_1(D,k13_finseq_1(A),A) -> (D = k1_funct_1(B,C) & r2_hidden(C,k4_finseq_1(B)) -> v2_unialg_1(D,A)))))) <-> v5_unialg_1(B,A)))) # label(d5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6845 $T # label(d3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6846 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> (v2_unialg_1(B,A) <-> (all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (r2_hidden(C,k1_relat_1(B)) & k3_finseq_1(C) = k3_finseq_1(D) -> r2_hidden(D,k1_relat_1(B)))))))))) # label(d2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6847 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> (all C (m1_subset_1(C,k4_partfun1(k13_finseq_1(A),A)) -> (C = k2_funcop_1(k1_tarski(k6_finseq_1(A)),B) -> v4_unialg_1(k1_unialg_1(A,C),A) & v5_unialg_1(k1_unialg_1(A,C),A) & v2_relat_1(k1_unialg_1(A,C))))))))) # label(t4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6848 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> -(k1_relat_1(B) = k1_xboole_0 & -v1_xboole_0(B)) & -(k1_xboole_0 != k1_relat_1(B) & v1_xboole_0(B)))) # label(t1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6849 (all A all B (-v1_xboole_0(B) & v1_unialg_1(B,A) & m1_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) & -v1_xboole_0(A) -> m2_subset_1(k2_unialg_1(A,B),k1_numbers,k5_numbers))) # label(dt_k2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6850 (exists A (v6_unialg_1(A) & v7_unialg_1(A) & v8_unialg_1(A) & v3_unialg_1(A) & -v3_struct_0(A) & l1_unialg_1(A))) # label(rc5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6851 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> v1_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & v2_unialg_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),A) & m2_relset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k13_finseq_1(A),A) & v1_funct_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)) & -v1_xboole_0(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B)))))) # label(t2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6852 (all A (l1_unialg_1(A) & v8_unialg_1(A) -> v1_relat_1(u1_unialg_1(A)) & v2_relat_1(u1_unialg_1(A)) & v1_finseq_1(u1_unialg_1(A)) & v1_funct_1(u1_unialg_1(A)) & -v1_xboole_0(u1_unialg_1(A)))) # label(fc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6853 $T # label(d6_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6854 (all A all B (m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)) -> (all C all D (g1_unialg_1(A,B) = g1_unialg_1(C,D) -> A = C & D = B)))) # label(free_g1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6855 (all A all B (m2_relset_1(B,k13_finseq_1(A),A) & v1_funct_1(B) -> (v1_unialg_1(B,A) <-> (all C (m2_finseq_1(C,A) -> (all D (m2_finseq_1(D,A) -> (r2_hidden(C,k1_relat_1(B)) & r2_hidden(D,k1_relat_1(B)) -> k3_finseq_1(C) = k3_finseq_1(D))))))))) # label(d1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6856 (all A (-v3_struct_0(A) & v6_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) -> m2_finseq_1(k3_unialg_1(A),k5_numbers))) # label(dt_k3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6857 (all A all B (-v1_xboole_0(A) & m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) -> k1_unialg_1(A,B) = k5_finseq_1(B))) # label(redefinition_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6858 (all A (-v1_xboole_0(A) -> (all B (m1_subset_1(B,A) -> m1_subset_1(k2_funcop_1(k1_tarski(k6_finseq_1(A)),B),k4_partfun1(k13_finseq_1(A),A)))))) # label(t3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6859 (all A (v8_unialg_1(A) & l1_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (m2_subset_1(B,k1_numbers,k5_numbers) -> (r2_hidden(B,k4_finseq_1(u1_unialg_1(A))) -> m2_relset_1(k1_funct_1(u1_unialg_1(A),B),k13_finseq_1(u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(k1_funct_1(u1_unialg_1(A),B))))))) # label(t5_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6860 (all A (l1_unialg_1(A) -> (v3_unialg_1(A) -> g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) = A))) # label(abstractness_v3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6861 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) & v1_funct_1(B) & m2_relset_1(B,k13_finseq_1(A),A) & v1_unialg_1(B,A) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (k2_unialg_1(A,B) = C <-> (all D (m2_finseq_1(D,A) -> (r2_hidden(D,k1_relat_1(B)) -> k3_finseq_1(D) = C)))))))))) # label(d10_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6862 (all A (-v1_xboole_0(A) -> (exists B (m1_relset_1(B,k13_finseq_1(A),A) & v1_relat_1(B) & v1_unialg_1(B,A) & v2_unialg_1(B,A) & v1_funct_1(B) & -v1_xboole_0(B))))) # label(rc1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6863 (exists A (v3_unialg_1(A) & -v3_struct_0(A) & l1_unialg_1(A))) # label(rc3_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6864 (all A (-v1_xboole_0(A) -> (exists B (v4_unialg_1(B,A) & v5_unialg_1(B,A) & v1_finseq_1(B) & v1_funct_1(B) & v2_relat_1(B) & v1_relat_1(B) & m1_finseq_1(B,k4_partfun1(k13_finseq_1(A),A)))))) # label(rc4_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6865 (all A (l1_unialg_1(A) -> (v6_unialg_1(A) <-> v4_unialg_1(u1_unialg_1(A),u1_struct_0(A))))) # label(d7_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6866 (all A (l1_unialg_1(A) -> (v7_unialg_1(A) <-> v5_unialg_1(u1_unialg_1(A),u1_struct_0(A))))) # label(d8_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6867 (all A (l1_unialg_1(A) -> l1_struct_0(A))) # label(dt_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6868 (exists A (v3_unialg_1(A) & l1_unialg_1(A))) # label(rc2_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6869 (all A (l1_unialg_1(A) -> m2_finseq_1(u1_unialg_1(A),k4_partfun1(k13_finseq_1(u1_struct_0(A)),u1_struct_0(A))))) # label(dt_u1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6870 (exists A l1_unialg_1(A)) # label(existence_l1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6871 (all A all B (m1_subset_1(B,k4_partfun1(k13_finseq_1(A),A)) & -v1_xboole_0(A) -> m2_finseq_1(k1_unialg_1(A,B),k4_partfun1(k13_finseq_1(A),A)))) # label(dt_k1_unialg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6872 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_finseq_1(C,k2_zfmisc_1(A,B)) -> k16_mcart_1(C) = k2_pralg_1(A,B,C))) # label(redefinition_k2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6873 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k4_finseq_2(D,B) = k4_finseq_2(C,A) -> D = C))))))))) # label(t1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6874 (all A (-v1_xboole_0(A) -> (all B (v1_pralg_1(B) & m1_pboole(B,A) & v3_pralg_1(B) -> k25_pralg_1(A,B) = g1_unialg_1(k4_card_3(k12_pralg_1(A,B)),k24_pralg_1(A,B)))))) # label(d24_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6875 (all A (-v3_struct_0(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> (all B (v6_unialg_1(B) & v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> v8_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & l1_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v7_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v6_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & v3_unialg_1(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))) & -v3_struct_0(g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B)))))))) # label(t2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6876 (all A exists B (v1_funct_1(B) & v2_pralg_1(B) & v1_relat_1(B) & m1_pboole(B,A))) # label(rc4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6877 (all A (-v1_xboole_0(A) -> (exists B (m1_pboole(B,A) & v1_relat_1(B) & v3_pralg_1(B) & v2_pralg_1(B) & v1_pralg_1(B) & v1_funct_1(B))))) # label(rc5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6878 (all A (l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v7_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v6_unialg_1(B) -> (r1_unialg_2(A,B) -> (all C (m2_unialg_2(C,u1_struct_0(A),k1_unialg_2(A)) -> (all D (m2_unialg_2(D,u1_struct_0(B),k1_unialg_2(B)) -> (all E (m2_unialg_2(E,u1_struct_0(k5_pralg_1(A,B)),k1_unialg_2(k5_pralg_1(A,B))) -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (k1_funct_1(u1_unialg_1(B),F) = D & k1_funct_1(u1_unialg_1(k5_pralg_1(A,B)),F) = E & r2_hidden(F,k4_finseq_1(u1_unialg_1(A))) & C = k1_funct_1(u1_unialg_1(A),F) -> k2_unialg_1(u1_struct_0(B),D) = k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E) & E = k3_pralg_1(u1_struct_0(A),u1_struct_0(B),C,D) & k2_unialg_1(u1_struct_0(A),C) = k2_unialg_1(u1_struct_0(k5_pralg_1(A,B)),E))))))))))))))) # label(t6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6879 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (m1_pralg_1(C,A,B) & v4_pralg_1(C) -> (all D (-v1_xboole_0(D) & v1_funct_1(D) & v1_unialg_1(D,k4_card_3(B)) & m2_relset_1(D,k3_finseq_2(k4_card_3(B)),k4_card_3(B)) & v2_unialg_1(D,k4_card_3(B)) -> (k4_finseq_2(k20_pralg_1(A,B,C),k4_card_3(B)) = k1_relat_1(D) & (all E (m2_finseq_2(E,k4_card_3(B),k3_finseq_2(k4_card_3(B))) -> (r2_hidden(E,k1_relat_1(D)) -> (k1_xboole_0 = k4_finseq_1(E) -> k16_pralg_1(A,C,k21_pralg_1(A,B)) = k1_funct_1(D,E)) & (k4_finseq_1(E) != k1_xboole_0 -> (all F (-v1_xboole_0(F) -> (all G (m1_pboole(G,k2_zfmisc_1(A,F)) -> (G = k18_pralg_1(k4_finseq_1(E),A,k17_pralg_1(A,B,E)) & k4_finseq_1(E) = F -> k1_funct_1(D,E) = k16_pralg_1(A,C,k19_pralg_1(A,F,G))))))))))) <-> k22_pralg_1(A,B,C) = D))))))))) # label(d21_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6880 (all A all B all C all D (m1_pboole(B,A) & m1_pralg_1(C,A,B) & m1_subset_1(D,A) & v2_relat_1(B) & -v1_xboole_0(A) -> -v1_xboole_0(k14_pralg_1(A,B,C,D)) & m2_relset_1(k14_pralg_1(A,B,C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) & v2_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D)) & v1_unialg_1(k14_pralg_1(A,B,C,D),k1_funct_1(B,D)) & v1_funct_1(k14_pralg_1(A,B,C,D)))) # label(dt_k14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6881 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v2_unialg_1(C,A) & m2_relset_1(C,k3_finseq_2(A),A) & v1_unialg_1(C,A) & v1_funct_1(C) & -v1_xboole_0(C) -> (all D (m2_relset_1(D,k3_finseq_2(B),B) & v2_unialg_1(D,B) & v1_unialg_1(D,B) & v1_funct_1(D) & -v1_xboole_0(D) -> (k2_unialg_1(B,D) = k2_unialg_1(A,C) -> (all E (-v1_xboole_0(E) & v1_funct_1(E) & m2_relset_1(E,k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v2_unialg_1(E,k2_zfmisc_1(A,B)) & v1_unialg_1(E,k2_zfmisc_1(A,B)) -> (k4_finseq_2(k2_unialg_1(A,C),k2_zfmisc_1(A,B)) = k1_relat_1(E) & (all F (m2_finseq_1(F,k2_zfmisc_1(A,B)) -> (r2_hidden(F,k1_relat_1(E)) -> k4_tarski(k1_funct_1(C,k1_pralg_1(A,B,F)),k1_funct_1(D,k2_pralg_1(A,B,F))) = k1_funct_1(E,F)))) <-> E = k3_pralg_1(A,B,C,D))))))))))))) # label(d3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6882 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_finseq_1(C,k2_zfmisc_1(A,B)) -> k15_mcart_1(C) = k1_pralg_1(A,B,C))) # label(redefinition_k1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6883 (all A (v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (v6_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) & -v3_struct_0(B) -> (r1_unialg_2(A,B) -> k5_pralg_1(A,B) = g1_unialg_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_pralg_1(A,B))))))) # label(d5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6884 (all A (-v3_struct_0(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> (all B (-v3_struct_0(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) & v6_unialg_1(B) -> (r1_unialg_2(A,B) -> (all C (m2_finseq_1(C,k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) -> (k3_finseq_1(u1_unialg_1(A)) = k3_finseq_1(C) & (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> (all E (v2_unialg_1(E,u1_struct_0(A)) & m2_relset_1(E,k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)) & v1_unialg_1(E,u1_struct_0(A)) & v1_funct_1(E) & -v1_xboole_0(E) -> (all F (v2_unialg_1(F,u1_struct_0(B)) & m2_relset_1(F,k3_finseq_2(u1_struct_0(B)),u1_struct_0(B)) & v1_unialg_1(F,u1_struct_0(B)) & v1_funct_1(F) & -v1_xboole_0(F) -> (k1_funct_1(u1_unialg_1(B),D) = F & k1_funct_1(u1_unialg_1(A),D) = E -> k3_pralg_1(u1_struct_0(A),u1_struct_0(B),E,F) = k1_funct_1(C,D))))))))) <-> k4_pralg_1(A,B) = C)))))))) # label(d4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6885 (all A (m1_finseq_1(A,k5_numbers) & -v1_xboole_0(A) -> v3_unialg_1(k9_pralg_1(A)) & v6_unialg_1(k9_pralg_1(A)) & v7_unialg_1(k9_pralg_1(A)) & l1_unialg_1(k9_pralg_1(A)) & v8_unialg_1(k9_pralg_1(A)) & -v3_struct_0(k9_pralg_1(A)))) # label(dt_k9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6886 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> m1_pboole(k18_pralg_1(A,B,C),k2_zfmisc_1(B,A)))) # label(dt_k18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6887 (all A (-v1_xboole_0(A) -> (exists B (-v1_xboole_0(B) & v1_relat_1(B) & v1_finseq_1(B) & v1_funct_1(B) & m1_finseq_1(B,A))))) # label(rc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6888 (all A (v1_relat_1(A) & v1_funct_1(A) & v1_pralg_1(A) -> v1_funct_1(A) & v2_pralg_1(A) & v1_relat_1(A))) # label(cc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6889 (all A all B all C (v2_relat_1(B) & m1_finseq_1(C,k4_card_3(B)) & m1_pboole(B,A) & -v1_xboole_0(A) -> k4_funct_5(C) = k17_pralg_1(A,B,C))) # label(redefinition_k17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6890 (all A all B (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) -> -v1_xboole_0(k4_card_3(B)) & v1_fraenkel(k4_card_3(B)))) # label(fc3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6891 (all A (m2_finseq_1(A,k5_numbers) -> v4_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0)) & v2_relat_1(k8_pralg_1(A)) & v5_unialg_1(k8_pralg_1(A),k1_tarski(k1_xboole_0)))) # label(t10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6892 (all A all B (v1_relat_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(A) & v1_funct_1(A) -> v1_funct_1(k15_pralg_1(A,B)) & v1_relat_1(k15_pralg_1(A,B)))) # label(dt_k15_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6893 (all A all B all C (m1_pboole(C,k2_zfmisc_1(A,B)) -> k2_funct_4(C) = k18_pralg_1(A,B,C))) # label(redefinition_k18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6894 (all A all B (v2_relat_1(B) & m1_pboole(B,A) & -v1_xboole_0(A) -> (exists C (m1_pralg_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v4_pralg_1(C) & v1_funcop_1(C))))) # label(rc6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6895 (all A all B (m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (C = k21_pralg_1(A,B) <-> (all D (r2_hidden(D,A) -> k1_subset_1(k1_funct_1(B,D)) = k1_funct_1(C,D)))))))) # label(d20_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6896 (all A all B all C all D (-v1_xboole_0(D) & m1_relset_1(D,k3_finseq_2(B),B) & v2_unialg_1(D,B) & v1_unialg_1(D,B) & v1_funct_1(D) & m1_relset_1(C,k3_finseq_2(A),A) & v2_unialg_1(C,A) & v1_unialg_1(C,A) & v1_funct_1(C) & -v1_xboole_0(C) & -v1_xboole_0(B) & -v1_xboole_0(A) -> -v1_xboole_0(k3_pralg_1(A,B,C,D)) & v1_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B)) & v2_unialg_1(k3_pralg_1(A,B,C,D),k2_zfmisc_1(A,B)) & m2_relset_1(k3_pralg_1(A,B,C,D),k3_finseq_2(k2_zfmisc_1(A,B)),k2_zfmisc_1(A,B)) & v1_funct_1(k3_pralg_1(A,B,C,D)))) # label(dt_k3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6897 (all A all B (-v3_struct_0(A) & v7_unialg_1(A) & v8_unialg_1(A) & l1_unialg_1(A) & -v3_struct_0(B) & l1_unialg_1(B) & v8_unialg_1(B) & v7_unialg_1(B) & v6_unialg_1(B) & v6_unialg_1(A) -> m2_finseq_1(k4_pralg_1(A,B),k4_partfun1(k13_finseq_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))))) # label(dt_k4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6898 (all A all B all C all D (-v1_xboole_0(A) & m1_pboole(B,A) & m1_pralg_1(C,A,B) & m1_subset_1(D,A) & v2_relat_1(B) -> k1_funct_1(C,D) = k14_pralg_1(A,B,C,D))) # label(redefinition_k14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6899 (all A all B (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) -> (exists C m1_pralg_1(C,A,B)))) # label(existence_m1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6900 (all A all B all C (m1_pboole(C,A) & m1_pboole(B,A) & v1_funcop_1(B) -> k16_pralg_1(A,B,C) = k15_pralg_1(B,C))) # label(redefinition_k16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6901 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v3_pralg_1(B) & v1_pralg_1(B) -> (all C (m2_finseq_1(C,k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B)))) -> (k24_pralg_1(A,B) = C <-> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (r2_hidden(D,k4_finseq_1(C)) -> k1_funct_1(C,D) = k22_pralg_1(A,k12_pralg_1(A,B),k23_pralg_1(A,B,D))))) & k3_finseq_1(k13_pralg_1(A,B)) = k3_finseq_1(C)))))))) # label(d23_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.94 6902 (all A all B all C (-v1_xboole_0(A) & v1_pralg_1(B) & v4_ordinal2(C) & m1_pboole(B,A) & v3_pralg_1(B) -> m1_pralg_1(k23_pralg_1(A,B,C),A,k12_pralg_1(A,B)) & v4_pralg_1(k23_pralg_1(A,B,C)))) # label(dt_k23_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6903 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> k9_funcop_1(k2_zfmisc_1(A,B),B,A,k6_pralg_1(A,B)) = k2_zfmisc_1(B,A))))) # label(t3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6904 (all A (v4_ordinal2(A) -> v1_funct_1(k7_pralg_1(A)) & m2_relset_1(k7_pralg_1(A),k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)))) # label(dt_k7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6905 (exists A (v1_relat_1(A) & v1_funct_1(A) & v1_pralg_1(A))) # label(rc3_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6906 (all A all B (-v1_xboole_0(A) & v1_pralg_1(B) & m1_pboole(B,A) & v3_pralg_1(B) -> -v3_struct_0(k25_pralg_1(A,B)) & v6_unialg_1(k25_pralg_1(A,B)) & v7_unialg_1(k25_pralg_1(A,B)) & v8_unialg_1(k25_pralg_1(A,B)) & l1_unialg_1(k25_pralg_1(A,B)) & v3_unialg_1(k25_pralg_1(A,B)))) # label(dt_k25_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6907 (all A all B all C (v1_pralg_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> v8_unialg_1(k11_pralg_1(A,B,C)) & l1_unialg_1(k11_pralg_1(A,B,C)) & v7_unialg_1(k11_pralg_1(A,B,C)) & v6_unialg_1(k11_pralg_1(A,B,C)) & -v3_struct_0(k11_pralg_1(A,B,C)))) # label(dt_k11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6908 (all A all B all C (v1_pralg_1(B) & m1_subset_1(C,A) & m1_pboole(B,A) & -v1_xboole_0(A) -> k1_funct_1(B,C) = k11_pralg_1(A,B,C))) # label(redefinition_k11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6909 (all A (m2_finseq_1(A,k5_numbers) & -v1_xboole_0(A) -> g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)) = k9_pralg_1(A))) # label(d9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6910 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_pboole(B,A) & v2_pralg_1(B) -> k10_pralg_1(A,B,C) = k1_funct_1(B,C))) # label(redefinition_k10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6911 (all A all B (m1_pboole(B,A) & v1_pralg_1(B) & -v1_xboole_0(A) -> v1_funct_1(k12_pralg_1(A,B)) & -v3_relat_1(k12_pralg_1(A,B)) & v2_relat_1(k12_pralg_1(A,B)) & v1_relat_1(k12_pralg_1(A,B)))) # label(fc2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6912 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v2_pralg_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> l1_struct_0(k1_funct_1(A,B))))))) # label(d11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6913 (all A (-v1_xboole_0(A) -> (all B (v2_relat_1(B) & m1_pboole(B,A) -> (all C (v4_pralg_1(C) & m1_pralg_1(C,A,B) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> ((all E (m1_subset_1(E,A) -> D = k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)))) <-> D = k20_pralg_1(A,B,C)))))))))) # label(d19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6914 (all A all B (-v1_xboole_0(B) & -v1_xboole_0(A) -> m2_relset_1(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & v1_funct_2(k6_pralg_1(A,B),k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & v1_funct_1(k6_pralg_1(A,B)))) # label(dt_k6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6915 (all A all B all C (m1_finseq_1(C,k2_zfmisc_1(A,B)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m2_finseq_1(k1_pralg_1(A,B,C),A))) # label(dt_k1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6916 (all A all B all C (m1_pboole(B,A) & v4_pralg_1(C) & m1_pralg_1(C,A,B) & v2_relat_1(B) & -v1_xboole_0(A) -> -v1_xboole_0(k22_pralg_1(A,B,C)) & v1_funct_1(k22_pralg_1(A,B,C)) & v1_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B)) & m2_relset_1(k22_pralg_1(A,B,C),k3_finseq_2(k4_card_3(B)),k4_card_3(B)) & v2_unialg_1(k22_pralg_1(A,B,C),k4_card_3(B)))) # label(dt_k22_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6917 (all A (m2_finseq_1(A,k5_numbers) -> (all B (m2_finseq_1(B,k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))) -> (B = k8_pralg_1(A) <-> (all C (m2_subset_1(C,k1_numbers,k5_numbers) -> (r2_hidden(C,k4_finseq_1(B)) -> (all D (m2_subset_1(D,k1_numbers,k5_numbers) -> (k1_funct_1(A,C) = D -> k1_funct_1(B,C) = k7_pralg_1(D))))))) & k3_finseq_1(A) = k3_finseq_1(B)))))) # label(d8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6918 (all A all B all C (-v1_xboole_0(B) & m1_pboole(C,k2_zfmisc_1(A,B)) -> k3_funct_5(C) = k19_pralg_1(A,B,C))) # label(redefinition_k19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6919 (all A all B all C (-v1_xboole_0(A) & m1_subset_1(C,A) & m1_pboole(B,A) & v2_pralg_1(B) -> l1_struct_0(k10_pralg_1(A,B,C)))) # label(dt_k10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6920 (all A all B (v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) & -v1_xboole_0(A) -> m2_finseq_1(k24_pralg_1(A,B),k4_partfun1(k13_finseq_1(k4_card_3(k12_pralg_1(A,B))),k4_card_3(k12_pralg_1(A,B)))))) # label(dt_k24_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6921 (all A all B (-v3_struct_0(A) & v7_unialg_1(A) & -v3_struct_0(B) & l1_unialg_1(B) & v8_unialg_1(B) & v7_unialg_1(B) & v6_unialg_1(B) & l1_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) -> v6_unialg_1(k5_pralg_1(A,B)) & v7_unialg_1(k5_pralg_1(A,B)) & v8_unialg_1(k5_pralg_1(A,B)) & l1_unialg_1(k5_pralg_1(A,B)) & v3_unialg_1(k5_pralg_1(A,B)) & -v3_struct_0(k5_pralg_1(A,B)))) # label(dt_k5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6922 (all A (-v1_xboole_0(A) -> (all B (v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) -> (all C (v4_ordinal2(C) -> (r2_hidden(C,k4_finseq_1(k13_pralg_1(A,B))) -> (all D (m1_pralg_1(D,A,k12_pralg_1(A,B)) & v4_pralg_1(D) -> (k23_pralg_1(A,B,C) = D <-> (all E (m1_subset_1(E,A) -> (all F (m2_unialg_2(F,u1_struct_0(k11_pralg_1(A,B,E)),k1_unialg_2(k11_pralg_1(A,B,E))) -> (k1_funct_1(u1_unialg_1(k11_pralg_1(A,B,E)),C) = F -> F = k14_pralg_1(A,k12_pralg_1(A,B),D,E)))))))))))))))) # label(d22_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6923 (all A (-v1_xboole_0(A) -> (all B (v3_pralg_1(B) & m1_pboole(B,A) & v1_pralg_1(B) -> (all C (m2_finseq_1(C,k5_numbers) -> (k13_pralg_1(A,B) = C <-> (all D (m1_subset_1(D,A) -> k3_unialg_1(k11_pralg_1(A,B,D)) = C))))))))) # label(d14_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6924 (all A all B (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) -> (all C (m1_pralg_1(C,A,B) -> v1_funcop_1(C) & m1_pboole(C,A))))) # label(dt_m1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6925 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,k2_zfmisc_1(A,B)) -> (all D (m2_finseq_1(D,A) -> ((all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k1_funct_1(D,E) = k1_mcart_1(k1_funct_1(C,E))))) & k3_finseq_1(D) = k3_finseq_1(C) <-> D = k1_pralg_1(A,B,C)))))))))) # label(d1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6926 (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)) -> (all D (v6_unialg_1(D) & v7_unialg_1(D) & l1_unialg_1(D) & v8_unialg_1(D) & -v3_struct_0(D) -> (all E (v6_unialg_1(E) & v8_unialg_1(E) & l1_unialg_1(E) & v7_unialg_1(E) & -v3_struct_0(E) -> (k1_funct_1(A,B) = D & E = k1_funct_1(A,C) -> k3_unialg_1(D) = k3_unialg_1(E)))))))) <-> v3_pralg_1(A)))) # label(d12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6927 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (m1_pralg_1(C,A,B) -> (v4_pralg_1(C) <-> (all D (m1_subset_1(D,A) -> (all E (m1_subset_1(E,A) -> k2_unialg_1(k1_funct_1(B,E),k14_pralg_1(A,B,C,E)) = k2_unialg_1(k1_funct_1(B,D),k14_pralg_1(A,B,C,D))))))))))))) # label(t12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6928 (all A all B all C (v1_funcop_1(B) & m1_pboole(B,A) & m1_pboole(C,A) -> m1_pboole(k16_pralg_1(A,B,C),A))) # label(dt_k16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6929 (all A all B (m1_pboole(B,A) -> m1_pboole(k21_pralg_1(A,B),A))) # label(dt_k21_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6930 (all A all B all C (-v1_xboole_0(A) & -v1_xboole_0(B) & m1_finseq_1(C,k2_zfmisc_1(A,B)) -> m2_finseq_1(k2_pralg_1(A,B,C),B))) # label(dt_k2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6931 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & m2_relset_1(C,k2_zfmisc_1(A,B),k2_zfmisc_1(B,A)) & v1_funct_1(C) -> ((all D (m1_subset_1(D,k2_zfmisc_1(A,B)) -> k8_funct_2(k2_zfmisc_1(A,B),k2_zfmisc_1(B,A),C,D) = k1_domain_1(B,A,k3_domain_1(A,B,D),k2_domain_1(A,B,D)))) <-> k6_pralg_1(A,B) = C))))))) # label(d6_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6932 (all A (v4_ordinal2(A) -> A = k2_unialg_1(k1_tarski(k1_xboole_0),k7_pralg_1(A)))) # label(t9_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6933 (all A (v7_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v6_unialg_1(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v6_unialg_1(B) & v7_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) -> (all C (v8_unialg_1(C) & l1_unialg_1(C) & v7_unialg_1(C) & v6_unialg_1(C) & -v3_struct_0(C) -> (all D (-v3_struct_0(D) & l1_unialg_1(D) & v8_unialg_1(D) & v7_unialg_1(D) & v6_unialg_1(D) -> (m3_unialg_2(A,B) & m3_unialg_2(C,D) & r1_unialg_2(B,D) -> m3_unialg_2(k5_pralg_1(A,C),k5_pralg_1(B,D))))))))))) # label(t8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6934 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_finseq_1(C,k2_zfmisc_1(A,B)) -> (all D (m2_finseq_1(D,B) -> (k3_finseq_1(D) = k3_finseq_1(C) & (all E (m2_subset_1(E,k1_numbers,k5_numbers) -> (r2_hidden(E,k4_finseq_1(D)) -> k2_mcart_1(k1_funct_1(C,E)) = k1_funct_1(D,E)))) <-> D = k2_pralg_1(A,B,C)))))))))) # label(d2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6935 (all A all B all C (m1_finseq_1(C,k4_card_3(B)) & m1_pboole(B,A) & v2_relat_1(B) & -v1_xboole_0(A) -> m1_pboole(k17_pralg_1(A,B,C),k2_zfmisc_1(k4_finseq_1(C),A)))) # label(dt_k17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6936 (all A all B (-v1_xboole_0(A) & m1_pboole(B,A) & v3_pralg_1(B) & v1_pralg_1(B) -> m2_finseq_1(k13_pralg_1(A,B),k5_numbers))) # label(dt_k13_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6937 (all A (m1_finseq_1(A,k5_numbers) -> m2_finseq_1(k8_pralg_1(A),k4_partfun1(k13_finseq_1(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))))) # label(dt_k8_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6938 (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)) -> (all D (v1_funct_1(D) & v1_relat_1(D) -> (all E (v1_relat_1(E) & v1_funct_1(E) -> (E = k1_funct_1(A,C) & k1_funct_1(A,B) = D -> (all F (m2_subset_1(F,k1_numbers,k5_numbers) -> (all G (m2_subset_1(G,k1_numbers,k5_numbers) -> (all H (-v1_xboole_0(H) -> (all I (-v1_xboole_0(I) -> (k4_finseq_2(F,H) = k1_relat_1(D) & k1_relat_1(E) = k4_finseq_2(G,I) -> (all J (v1_unialg_1(J,H) & v2_unialg_1(J,H) & m2_relset_1(J,k3_finseq_2(H),H) & v1_funct_1(J) & -v1_xboole_0(J) -> (all K (-v1_xboole_0(K) & v1_funct_1(K) & v2_unialg_1(K,I) & m2_relset_1(K,k3_finseq_2(I),I) & v1_unialg_1(K,I) -> (E = K & J = D -> k2_unialg_1(H,J) = k2_unialg_1(I,K)))))))))))))))))))))) <-> v4_pralg_1(A)))) # label(d16_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6939 (all A (m2_finseq_1(A,k5_numbers) -> (k1_xboole_0 != A -> -v3_struct_0(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v7_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v8_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & l1_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v6_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A))) & v3_unialg_1(g1_unialg_1(k1_tarski(k1_xboole_0),k8_pralg_1(A)))))) # label(t11_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6940 (all A (v1_relat_1(A) & v1_funcop_1(A) & v1_funct_1(A) -> (all B (v1_funct_1(B) & v1_relat_1(B) -> (all C (v1_funct_1(C) & v1_relat_1(C) -> (C = k15_pralg_1(A,B) <-> k1_relat_1(C) = k1_relat_1(A) & (all D (r2_hidden(D,k1_relat_1(A)) -> k1_funct_1(k1_funct_1(A,D),k1_funct_1(B,D)) = k1_funct_1(C,D)))))))))) # label(d17_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6941 (all A (-v3_struct_0(A) & v6_unialg_1(A) & l1_unialg_1(A) & v8_unialg_1(A) & v7_unialg_1(A) -> (all B (-v3_struct_0(B) & v6_unialg_1(B) & l1_unialg_1(B) & v8_unialg_1(B) & v7_unialg_1(B) -> (r1_unialg_2(A,B) -> v1_funct_2(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A))) & m2_relset_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k5_pralg_1(A,B)),u1_struct_0(k5_pralg_1(B,A))) & v1_funct_1(k6_pralg_1(u1_struct_0(A),u1_struct_0(B)))))))) # label(t5_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6942 (all A all B all C (-v1_xboole_0(B) & m1_pboole(C,k2_zfmisc_1(A,B)) -> m1_pboole(k19_pralg_1(A,B,C),A))) # label(dt_k19_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6943 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> v2_funct_1(k6_pralg_1(A,B)))))) # label(t4_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6944 (all A (v4_ordinal2(A) -> v1_relat_1(k7_pralg_1(A)) & v1_funct_1(k7_pralg_1(A)) & v1_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0)) & v2_unialg_1(k7_pralg_1(A),k1_tarski(k1_xboole_0)) & -v1_xboole_0(k7_pralg_1(A)))) # label(fc1_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6945 (all A (-v1_xboole_0(A) -> (exists B (v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(B) & -v1_xboole_0(B) & m1_subset_1(B,k3_finseq_2(A)))))) # label(rc2_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6946 (all A (v4_ordinal2(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)) -> (k1_tarski(k1_xboole_0) = k2_relat_1(B) & k1_relat_1(B) = k1_tarski(k2_finseq_2(A,k1_xboole_0)) <-> B = k7_pralg_1(A)))))) # label(d7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6947 (all A all B all C (-v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & v4_pralg_1(C) & m1_pralg_1(C,A,B) -> m2_subset_1(k20_pralg_1(A,B,C),k1_numbers,k5_numbers))) # label(dt_k20_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6948 (all A all B (m1_pboole(B,A) & v2_pralg_1(B) -> m1_pboole(k12_pralg_1(A,B),A))) # label(dt_k12_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6949 (all A (-v1_xboole_0(A) -> (all B (m1_pboole(B,A) & v2_relat_1(B) -> (all C (v1_funcop_1(C) & m1_pboole(C,A) -> ((all D (m1_subset_1(D,A) -> -v1_xboole_0(k1_funct_1(C,D)) & v2_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D)) & m2_relset_1(k1_funct_1(C,D),k3_finseq_2(k1_funct_1(B,D)),k1_funct_1(B,D)) & v1_unialg_1(k1_funct_1(C,D),k1_funct_1(B,D)) & v1_funct_1(k1_funct_1(C,D)))) <-> m1_pralg_1(C,A,B)))))))) # label(d15_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6950 (all A (-v3_struct_0(A) & v8_unialg_1(A) & l1_unialg_1(A) & v7_unialg_1(A) & v6_unialg_1(A) -> (all B (-v3_struct_0(B) & v6_unialg_1(B) & v8_unialg_1(B) & l1_unialg_1(B) & v7_unialg_1(B) -> (r1_unialg_2(A,B) -> r1_unialg_2(k5_pralg_1(A,B),A)))))) # label(t7_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6951 (all A all B (m1_pboole(B,A) & v2_pralg_1(B) -> (all C (m1_pboole(C,A) -> ((all D -((all E (l1_struct_0(E) -> -(k1_funct_1(B,D) = E & u1_struct_0(E) = k1_funct_1(C,D)))) & r2_hidden(D,A))) <-> C = k12_pralg_1(A,B)))))) # label(d13_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6952 (all A (v1_funct_1(A) & v1_relat_1(A) -> (v1_pralg_1(A) <-> (all B (r2_hidden(B,k1_relat_1(A)) -> v6_unialg_1(k1_funct_1(A,B)) & v7_unialg_1(k1_funct_1(A,B)) & v8_unialg_1(k1_funct_1(A,B)) & l1_unialg_1(k1_funct_1(A,B)) & -v3_struct_0(k1_funct_1(A,B))))))) # label(d10_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6953 (all A all B (v1_funcop_1(B) & m1_pboole(B,A) -> (all C (m1_pboole(C,A) -> (all D (m1_pboole(D,A) -> (k16_pralg_1(A,B,C) = D <-> (all E (r2_hidden(E,A) -> (all F (v1_relat_1(F) & v1_funct_1(F) -> (F = k1_funct_1(B,E) -> k1_funct_1(D,E) = k1_funct_1(F,k1_funct_1(C,E)))))))))))))) # label(d18_pralg_1) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6954 (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(k3_t_0topsp(A)))) -> (v3_pre_topc(B,k3_t_0topsp(A)) <-> r2_hidden(k3_tarski(B),u1_pre_topc(A))))))) # label(t6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.74/184.95 6955 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B))))) # label(t8_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6956 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_funct_1(k4_t_0topsp(A)) & v1_funct_2(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))) & v5_pre_topc(k4_t_0topsp(A),A,k3_t_0topsp(A)) & m2_relset_1(k4_t_0topsp(A),u1_struct_0(A),u1_struct_0(k3_t_0topsp(A))))) # label(dt_k4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6957 (all A (v2_pre_topc(A) & l1_pre_topc(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)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) <-> r2_hidden(k8_borsuk_1(A,A,C,B),k1_t_0topsp(A))))))))) # label(t9_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6958 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (v1_funct_2(C,A,B) & m2_relset_1(C,A,B) & v1_funct_1(C) -> (all D (m1_subset_1(D,k1_zfmisc_1(A)) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,A) -> (k8_funct_2(A,B,C,F) = k8_funct_2(A,B,C,E) & r2_hidden(E,D) -> r2_hidden(F,D)))))) -> k3_funct_2(A,B,C,k2_funct_2(A,B,C,D)) = D))))))))) # label(t2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6959 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),D) = k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),C) & r2_hidden(C,B) -> r2_hidden(D,B))))))))))) # label(t10_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6960 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> v3_relat_2(k1_t_0topsp(A)) & v1_partfun1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k1_t_0topsp(A),u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(k1_t_0topsp(A)))) # label(dt_k1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6961 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> -v3_struct_0(k3_t_0topsp(A)) & l1_pre_topc(k3_t_0topsp(A)) & v2_t_0topsp(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(t13_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6962 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (v2_pre_topc(B) & l1_pre_topc(B) & v2_t_0topsp(B) & -v3_struct_0(B) -> (all C (v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(C) -> (exists D (v5_pre_topc(D,k3_t_0topsp(A),B) & m2_relset_1(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)) & k4_borsuk_1(A,k3_t_0topsp(A),B,k4_t_0topsp(A),D) = C & v1_funct_2(D,u1_struct_0(k3_t_0topsp(A)),u1_struct_0(B)) & v1_funct_1(D))))))))) # label(t17_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6963 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_t_0topsp(B) & v2_pre_topc(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)) & v5_pre_topc(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> k4_pre_topc(A,B,C,k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),D)) = k1_struct_0(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)))))))))) # label(t16_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6964 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(B,A) -> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> (r2_hidden(C,k2_t_0topsp(A)) -> r1_xboole_0(C,B) | r1_tarski(C,B))))))))) # label(t11_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6965 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> r2_hidden(B,k8_funct_2(u1_struct_0(A),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(A),B)))))) # label(t3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6966 (all A (l1_pre_topc(A) & -v3_struct_0(A) -> (all B (v3_relat_2(B) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v8_relat_2(B) -> (k1_t_0topsp(A) = B <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r2_hidden(k4_tarski(C,D),B) <-> (all E (m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(E,A) -> (r2_hidden(D,E) <-> r2_hidden(C,E))))))))))))))) # label(d3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6967 (all A all B (v2_pre_topc(B) & l1_pre_topc(B) & -v3_struct_0(B) -> ((exists C (m1_subset_1(C,k1_zfmisc_1(k2_t_0topsp(B))) & r2_hidden(k3_tarski(C),u1_pre_topc(B)) & C = A)) <-> r2_hidden(A,a_1_0_t_0topsp(B))))) # label(fraenkel_a_1_0_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6968 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> v1_t_0topsp(k4_t_0topsp(A),A,k3_t_0topsp(A)))) # label(t12_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6969 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> -v1_xboole_0(k2_t_0topsp(A)) & m1_eqrel_1(k2_t_0topsp(A),u1_struct_0(A)))) # label(dt_k2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6970 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> k4_t_0topsp(A) = k17_borsuk_1(A,k2_t_0topsp(A)))) # label(d6_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6971 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> (all B (m1_subset_1(B,u1_struct_0(k3_t_0topsp(A))) <-> (exists C (k6_eqrel_1(u1_struct_0(A),k1_t_0topsp(A),C) = B & m1_subset_1(C,u1_struct_0(A)))))))) # label(t7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6972 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(B) -> ((exists C (v1_funct_1(C) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_tops_2(C,A,B) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)))) <-> r1_t_0topsp(A,B)))))) # label(d1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6973 (all A (-v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) -> r1_tarski(k2_relat_1(k4_t_0topsp(A)),u1_struct_0(k3_t_0topsp(A))) & k1_relat_1(k4_t_0topsp(A)) = u1_struct_0(A))) # label(t4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6974 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> l1_pre_topc(k3_t_0topsp(A)) & v2_pre_topc(k3_t_0topsp(A)))) # label(dt_k3_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6975 (all A (l1_pre_topc(A) -> (all B (l1_pre_topc(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)) -> (v1_t_0topsp(C,A,B) <-> (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) -> (v3_pre_topc(D,A) -> v3_pre_topc(k4_pre_topc(A,B,C,D),B))))))))))) # label(d2_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6976 (all A (l1_pre_topc(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))) -> -(v3_pre_topc(D,A) & (r2_hidden(C,D) & -r2_hidden(B,D) | -r2_hidden(C,D) & r2_hidden(B,D))))) & B != C))))) <-> v2_t_0topsp(A)))) # label(d7_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6977 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> k2_t_0topsp(A) = u1_struct_0(k3_t_0topsp(A)) & a_1_0_t_0topsp(A) = u1_pre_topc(k3_t_0topsp(A)))) # label(t5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6978 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> v2_pre_topc(k3_t_0topsp(A)) & -v3_struct_0(k3_t_0topsp(A)))) # label(fc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6979 (all A (-v3_struct_0(A) & l1_pre_topc(A) & v2_pre_topc(A) -> k3_t_0topsp(A) = k16_borsuk_1(A,k2_t_0topsp(A)))) # label(d5_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6980 (all A (-v3_struct_0(A) & l1_pre_topc(A) -> k8_eqrel_1(u1_struct_0(A),k1_t_0topsp(A)) = k2_t_0topsp(A))) # label(d4_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6981 (exists A (l1_pre_topc(A) & v2_pre_topc(A) & v2_t_0topsp(A) & -v3_struct_0(A))) # label(rc1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6982 (all A (v2_pre_topc(A) & l1_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l1_pre_topc(B) & v2_pre_topc(B) -> ((exists C (m2_relset_1(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & r1_rfinseq(k4_t_0topsp(A),k7_funct_2(u1_struct_0(B),u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A)),k4_t_0topsp(B),C)) & v3_tops_2(C,k3_t_0topsp(B),k3_t_0topsp(A)) & v1_funct_2(C,u1_struct_0(k3_t_0topsp(B)),u1_struct_0(k3_t_0topsp(A))) & v1_funct_1(C))) -> r1_t_0topsp(A,B)))))) # label(t14_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6983 (all A (-v1_xboole_0(A) -> (all B (-v1_xboole_0(B) -> (all C (m2_relset_1(C,A,B) -> (all D (m2_relset_1(D,A,B) -> ((all E (m1_subset_1(E,A) -> (all F (m1_subset_1(F,B) -> (r2_hidden(k4_tarski(E,F),C) <-> r2_hidden(k4_tarski(E,F),D)))))) -> D = C))))))))) # label(t1_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6984 (all A (l1_pre_topc(A) & v2_pre_topc(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & v2_t_0topsp(B) & l1_pre_topc(B) & v2_pre_topc(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)) & v5_pre_topc(C,A,B) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (all E (m1_subset_1(E,u1_struct_0(A)) -> (r2_hidden(k8_borsuk_1(A,A,D,E),k1_t_0topsp(A)) -> 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,D)))))))))))) # label(t15_t_0topsp) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6985 (all A all B all C all D all E (v1_funct_1(B) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & 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_2(B,k2_zfmisc_1(A,A),A) -> (all F all G all H all I all J (g2_quantal1(A,B,C,D,E) = g2_quantal1(F,G,H,I,J) -> J = E & D = I & H = C & B = G & F = A)))) # label(free_g2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6986 (all A (l3_quantal1(A) -> u1_quantal1(A) = k3_quantal1(A))) # label(d21_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6987 (all A (l3_quantal1(A) -> m1_subset_1(k3_quantal1(A),u1_struct_0(A)))) # label(dt_k3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6988 (exists A (l1_quantal1(A) & -v3_struct_0(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v7_group_1(A) & v8_quantal1(A) & v7_quantal1(A) & v6_quantal1(A) & v5_quantal1(A) & v4_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) & v6_lattices(A) & v5_lattices(A) & v4_lattices(A))) # label(rc6_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6989 (exists A (v4_quantal1(A) & v5_quantal1(A) & v6_quantal1(A) & -v3_struct_0(A) & l1_group_1(A))) # label(rc5_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6990 (all A all B all C all D (l3_lattices(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_5_quantal1(B,C,D)) <-> (exists E (r2_hidden(E,D) & k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E) = A & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_5_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6991 (all A all B (-v3_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) & l3_quantal1(A) -> m1_subset_1(k5_quantal1(A,B),u1_struct_0(A)))) # label(dt_k5_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6992 (all A (-v3_struct_0(A) & l1_group_1(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_group_1(A,B,C))) & m1_subset_1(B,u1_struct_0(A)))) <-> v4_quantal1(A)))) # label(d2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6993 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k1_quantal1(A,B,k3_quantal1(A)) = k5_quantal1(A,B))))) # label(d23_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6994 (exists A (l2_quantal1(A) & v4_lattices(A) & v5_lattices(A) & v9_lattices(A) & v4_lattice3(A) & v10_lattices(A) & v8_lattices(A) & v7_lattices(A) & v6_lattices(A) & -v3_struct_0(A))) # label(rc7_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6995 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v2_group_1(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k9_quantal1(A,B,C) = k5_quantal1(A,k4_monoid_0(A,k5_quantal1(A,B),k5_quantal1(A,C))))))))) # label(d27_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6996 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_lattice3(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (v18_quantal1(B,A) -> r3_lattices(A,C,k1_quantal1(A,k1_quantal1(A,C,B),B)) & r3_lattices(A,C,k2_quantal1(A,k2_quantal1(A,C,B),B))))))))) # label(t16_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6997 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> ((all C (v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) -> (exists D (r2_hidden(D,B) & r1_lattices(A,k15_lattice3(A,C),D) & m1_subset_1(D,u1_struct_0(A)))))) <-> v1_quantal1(B,A)))))) # label(d1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6998 (all A (v2_group_1(A) & l2_quantal1(A) & -v3_struct_0(A) -> (v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_group_1(A) & -v3_struct_0(A) -> v4_lattice3(A) & v4_group_1(A) & v10_quantal1(A) & l2_quantal1(A) & v9_quantal1(A) & v6_quantal1(A) & v4_quantal1(A) & v2_group_1(A) & v10_lattices(A) & -v3_struct_0(A)))) # label(t7_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 6999 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k9_quantal1(A,k3_quantal1(A),B) = B & B = k9_quantal1(A,B,k3_quantal1(A)))))) # label(t33_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 7000 (all A (l1_group_1(A) -> (v5_quantal1(A) & v4_quantal1(A) & -v3_struct_0(A) -> -v3_struct_0(A) & v6_quantal1(A)))) # label(cc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 7001 (exists A (l2_quantal1(A) & -v3_struct_0(A))) # label(rc4_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 7002 (all A (v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_lattice3(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_monoid_0(A,k3_lattices(A,B,C),D) = k3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) & k3_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C)) = k4_monoid_0(A,D,k3_lattices(A,B,C)))))))))) # label(t6_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 7003 (all A all B all C all D (v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_3_quantal1(B,C,D)) <-> (exists E exists F (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & r2_hidden(F,D) & A = k4_monoid_0(B,E,F) & m1_subset_1(F,u1_struct_0(B))))))) # label(fraenkel_a_3_3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 7004 (exists A (l1_quantal1(A) & v2_quantal1(A))) # label(rc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 7005 (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_quantal1(A) -> m1_subset_1(k2_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.95 7006 (all A all B (m1_subset_1(B,u1_struct_0(f1_s3_quantal1)) -> ((exists C (A = f2_s3_quantal1(B,C) & r2_hidden(C,f4_s3_quantal1) & m1_subset_1(C,u1_struct_0(f1_s3_quantal1)))) <-> r2_hidden(A,a_1_0_quantal1(B))))) # label(fraenkel_a_1_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7007 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k5_quantal1(A,k3_lattices(A,B,C)) = k4_lattices(A,k5_quantal1(A,B),k5_quantal1(A,C)) & k3_lattices(A,k5_quantal1(A,B),k5_quantal1(A,C)) = k5_quantal1(A,k4_lattices(A,B,C)))))))) # label(t26_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7008 (all A all B all C all D all E all F (v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & m1_subset_1(F,A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> l3_quantal1(g3_quantal1(A,B,C,D,E,F)) & v19_quantal1(g3_quantal1(A,B,C,D,E,F)))) # label(dt_g3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7009 (all A (l2_quantal1(A) -> (v3_quantal1(A) -> A = g2_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A),u1_vectsp_1(A))))) # label(abstractness_v3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7010 (all A (l3_quantal1(A) -> l2_quantal1(A))) # label(dt_l3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7011 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> (r3_lattices(A,k4_monoid_0(A,B,C),D) <-> r3_lattices(A,C,k2_quantal1(A,B,D))))))))))) # label(t11_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7012 (all A (l1_quantal1(A) -> (v2_quantal1(A) -> g1_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A)) = A))) # label(abstractness_v2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7013 (all A all B all C all D (v7_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v20_quantal1(B) & v8_quantal1(B) & v4_group_1(B) & v2_group_1(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_8_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,D) & k4_monoid_0(B,C,E) = A))))) # label(fraenkel_a_3_8_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7014 (all A (v1_relat_1(A) & v1_funct_1(A) -> (v11_quantal1(A) <-> k5_relat_1(A,A) = A))) # label(d9_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7015 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) -> -(v1_quantal1(B,A) & v1_xboole_0(B)))))) # label(t3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7016 (all A (-v3_struct_0(A) & v10_lattices(A) & v2_group_1(A) & v4_group_1(A) & v7_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v4_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)) -> k9_quantal1(A,k9_quantal1(A,B,C),D) = k9_quantal1(A,B,k9_quantal1(A,C,D)))))))))) # label(t31_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7017 (all A (l3_lattices(A) & v10_lattices(A) & -v3_struct_0(A) -> (exists B (v12_quantal1(B,A) & v13_quantal1(B,A) & v14_quantal1(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) & v1_funct_1(B) & v1_relat_1(B) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)))))) # label(rc9_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7018 (all A (-v3_struct_0(A) & v4_lattice3(A) & v4_group_1(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(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,k4_monoid_0(A,C,D),B) -> r3_lattices(A,k4_monoid_0(A,D,C),B)))))) <-> v18_quantal1(B,A)))))) # label(t15_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7019 (all A (v4_lattice3(A) & v2_group_1(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v20_quantal1(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k5_quantal1(A,k5_quantal1(A,B)) = B)))) # label(t22_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7020 (all A (l3_quantal1(A) & -v3_struct_0(A) -> m1_subset_1(k4_quantal1(A),u1_struct_0(A)))) # label(dt_k4_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7021 (all A (l1_group_1(A) & -v3_struct_0(A) -> (v4_quantal1(A) & v5_quantal1(A) <-> v6_quantal1(A)))) # label(d4_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7022 (all A all B (l3_quantal1(A) & v1_funct_1(B) & m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & -v3_struct_0(A) -> v1_funct_2(k8_quantal1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(k8_quantal1(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_1(k8_quantal1(A,B)))) # label(dt_k8_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7023 (all A (l3_quantal1(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) -> k7_quantal1(A,B) = k2_monoid_0(u1_struct_0(A),B,k6_quantal1(A)))))) # label(d25_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7024 (all A (m1_subset_1(A,f1_s2_quantal1) -> -p1_s2_quantal1(A))) -> a_0_3_quantal1 = k1_xboole_0 # label(s2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7025 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (all B (v1_funct_1(B) & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) -> k8_quantal1(A,B) = k7_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A),B,k6_quantal1(A)))))) # label(d26_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7026 (all A all B all C all D (-v3_struct_0(B) & v7_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v8_quantal1(B) & v4_group_1(B) & v2_group_1(B) & v4_lattice3(B) & v10_lattices(B) -> (r2_hidden(A,a_3_10_quantal1(B,C,D)) <-> (exists E (k4_monoid_0(B,E,C) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_10_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7027 (exists A (-v3_struct_0(A) & v4_lattices(A) & v7_lattices(A) & v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v7_group_1(A) & v5_quantal1(A) & v7_quantal1(A) & v10_quantal1(A) & v9_quantal1(A) & v8_quantal1(A) & v6_quantal1(A) & v4_quantal1(A) & v4_group_1(A) & v9_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A) & l2_quantal1(A))) # label(rc8_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7028 (all A all B all C (-v3_struct_0(A) & l1_quantal1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) -> m1_subset_1(k1_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7029 (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_quantal1(B) -> (r2_hidden(A,a_3_7_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & r1_lattices(B,k4_monoid_0(B,C,E),D) & A = E))))) # label(fraenkel_a_3_7_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7030 (all A (l3_quantal1(A) & -v3_struct_0(A) -> k4_quantal1(A) = k1_quantal1(A,k3_quantal1(A),k3_quantal1(A)))) # label(d22_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7031 (all A all B all C all D (-v3_struct_0(B) & v4_group_1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v8_quantal1(B) & v7_quantal1(B) & v2_group_1(B) & v4_lattice3(B) & v10_lattices(B) -> (r2_hidden(A,a_3_9_quantal1(B,C,D)) <-> (exists E (r2_hidden(E,D) & A = k9_quantal1(B,C,E) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_9_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7032 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,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 (m1_subset_1(D,u1_struct_0(A)) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k1_quantal1(A,k1_quantal1(A,D,B),B))) -> v14_quantal1(C,A)))))))) # label(t14_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7033 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (v10_quantal1(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_quantal1(C,A) & v1_quantal1(B,A) -> k15_lattice3(A,a_3_2_quantal1(A,B,C)) = k4_monoid_0(A,k15_lattice3(A,B),k15_lattice3(A,C)))))))))) # label(d8_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7034 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (v7_quantal1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C k15_lattice3(A,a_3_0_quantal1(A,B,C)) = k4_monoid_0(A,B,k15_lattice3(A,C)))))))) # label(d5_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7035 (all A (l1_quantal1(A) & -v3_struct_0(A) -> (v8_quantal1(A) <-> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C k15_lattice3(A,a_3_1_quantal1(A,B,C)) = k4_monoid_0(A,k15_lattice3(A,C),B))))))) # label(d6_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7036 (all A (-v3_struct_0(A) & l1_quantal1(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)) -> (v16_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(A)) -> r1_lattices(A,k4_monoid_0(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k4_monoid_0(A,C,D)))))))))))) # label(d14_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7037 (all A (-v3_struct_0(A) & l3_quantal1(A) -> v1_funct_1(k6_quantal1(A)) & v1_funct_2(k6_quantal1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k6_quantal1(A),u1_struct_0(A),u1_struct_0(A)))) # label(dt_k6_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7038 (all A (l3_quantal1(A) -> m1_subset_1(u1_quantal1(A),u1_struct_0(A)))) # label(dt_u1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7039 (all A (r2_hidden(A,a_0_4_quantal1) <-> (exists B (m1_subset_1(B,u1_struct_0(f1_s3_quantal1)) & k15_lattice3(f1_s3_quantal1,a_1_0_quantal1(B)) = A & r2_hidden(B,f3_s3_quantal1))))) # label(fraenkel_a_0_4_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7040 (all A (-v3_struct_0(A) & l3_lattices(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)) -> (v14_quantal1(B,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,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)))))))))))) # label(d12_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7041 (all A (l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v4_lattice3(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)) -> (v17_quantal1(B,A) -> k1_quantal1(A,C,D) = k1_quantal1(A,k4_monoid_0(A,C,k2_quantal1(A,D,B)),B) & k2_quantal1(A,k4_monoid_0(A,k1_quantal1(A,D,B),C),B) = k2_quantal1(A,C,D)))))))))) # label(t20_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7042 (all A (-v3_struct_0(A) & l3_lattices(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 (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C)))) <-> v12_quantal1(B,A)))))) # label(d10_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7043 (all A (-v3_struct_0(A) & v4_lattice3(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(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,B,C) & r3_lattices(A,D,E) -> r3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,E))))))))))))) # label(t9_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7044 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) & v4_lattice3(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)) -> (v18_quantal1(B,A) -> r3_lattices(A,k4_monoid_0(A,k1_quantal1(A,k1_quantal1(A,C,B),B),k1_quantal1(A,k1_quantal1(A,D,B),B)),k1_quantal1(A,k1_quantal1(A,k4_monoid_0(A,C,D),B),B))))))))))) # label(t18_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7045 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v17_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> k1_quantal1(A,k2_quantal1(A,C,B),B) = C & C = k2_quantal1(A,k1_quantal1(A,C,B),B)))))))) # label(d17_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7046 (exists A l2_quantal1(A)) # label(existence_l2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7047 (all A (r2_hidden(A,a_0_2_quantal1) <-> (exists B (p1_s1_quantal1(B) & f3_s1_quantal1(f4_s1_quantal1(B)) = A & m1_subset_1(B,f1_s1_quantal1))))) # label(fraenkel_a_0_2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7048 (all A (l1_group_1(A) & -v3_struct_0(A) -> ((exists B ((all C (m1_subset_1(C,u1_struct_0(A)) -> B = k1_group_1(A,C,B))) & m1_subset_1(B,u1_struct_0(A)))) <-> v5_quantal1(A)))) # label(d3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7049 (all A all B all C all D all E all F (-v1_xboole_0(A) & m1_relset_1(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(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_subset_1(F,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> v19_quantal1(g3_quantal1(A,B,C,D,E,F)) & -v3_struct_0(g3_quantal1(A,B,C,D,E,F)))) # label(fc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7050 (all A (l2_quantal1(A) -> l1_vectsp_1(A) & l1_quantal1(A))) # label(dt_l2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7051 (exists A (l1_quantal1(A) & -v3_struct_0(A))) # label(rc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7052 (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_quantal1(B) -> (r2_hidden(A,a_3_6_quantal1(B,C,D)) <-> (exists E (A = E & r1_lattices(B,k4_monoid_0(B,E,C),D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_6_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7053 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v8_quantal1(A) & l1_quantal1(A) & v7_quantal1(A) -> (all B all C k4_monoid_0(A,k15_lattice3(A,B),k15_lattice3(A,C)) = k15_lattice3(A,a_3_3_quantal1(A,B,C))))) # label(t5_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7054 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (v18_quantal1(u1_quantal1(A),A) <-> v20_quantal1(A)))) # label(d19_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7055 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l1_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (v17_quantal1(B,A) -> v2_group_1(A) & k3_binop_1(u1_struct_0(A),u1_group_1(A)) = k2_quantal1(A,B,B) & k1_quantal1(A,B,B) = k3_binop_1(u1_struct_0(A),u1_group_1(A))))))) # label(t19_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7056 (all A (-v3_struct_0(A) & l3_quantal1(A) -> (v21_quantal1(A) <-> v17_quantal1(u1_quantal1(A),A)))) # label(d20_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7057 (all A (v4_lattice3(A) & v7_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v10_lattices(A) & -v3_struct_0(A) -> (all B k5_quantal1(A,k16_lattice3(A,B)) = k15_lattice3(A,a_2_0_quantal1(A,B))))) # label(t25_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7058 (all A all B all C all D (-v3_struct_0(B) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v1_funct_1(C) & l3_lattices(B) -> (r2_hidden(A,a_3_4_quantal1(B,C,D)) <-> (exists E (m1_subset_1(E,u1_struct_0(B)) & A = k8_funct_2(u1_struct_0(B),u1_struct_0(B),C,E) & r2_hidden(E,D)))))) # label(fraenkel_a_3_4_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7059 (all A ((exists B (m1_subset_1(B,f1_s1_quantal1) & f4_s1_quantal1(B) = A & p1_s1_quantal1(B))) <-> r2_hidden(A,a_0_1_quantal1))) # label(fraenkel_a_0_1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7060 (all A all B (v1_funct_1(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)) & l3_quantal1(A) & -v3_struct_0(A) -> v1_funct_2(k7_quantal1(A,B),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_quantal1(A,B),u1_struct_0(A),u1_struct_0(A)) & v1_funct_1(k7_quantal1(A,B)))) # label(dt_k7_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7061 (all A all B all C all D all E all F (v1_funct_1(B) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_subset_1(F,A) & m1_subset_1(E,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_2(B,k2_zfmisc_1(A,A),A) -> (all G all H all I all J all K all L (g3_quantal1(G,H,I,J,K,L) = g3_quantal1(A,B,C,D,E,F) -> C = I & D = J & E = K & F = L & H = B & A = G)))) # label(free_g3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7062 (all A (-v3_struct_0(A) & v4_lattice3(A) & v8_quantal1(A) & l1_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v10_lattices(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)) -> -(v14_quantal1(B,A) & v15_quantal1(B,A) & (all C (-v3_struct_0(C) & v10_lattices(C) & v4_lattice3(C) & l3_lattices(C) -> -(k2_relat_1(B) = u1_struct_0(C) & (all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) -> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,D)) = k15_lattice3(C,D)))))) & v11_quantal1(B)))))) # label(t34_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7063 (all A (l3_lattices(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)) -> (v15_quantal1(B,A) <-> (all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,C)),k15_lattice3(A,a_3_4_quantal1(A,B,C)))))))))) # label(d13_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7064 (exists A (l2_quantal1(A) & v3_quantal1(A))) # label(rc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7065 (all A all B all C (v4_lattice3(B) & v7_quantal1(B) & l3_quantal1(B) & v21_quantal1(B) & v20_quantal1(B) & v8_quantal1(B) & v4_group_1(B) & v2_group_1(B) & v10_lattices(B) & -v3_struct_0(B) -> ((exists D (m1_subset_1(D,u1_struct_0(B)) & A = k5_quantal1(B,D) & r2_hidden(D,C))) <-> r2_hidden(A,a_2_0_quantal1(B,C))))) # label(fraenkel_a_2_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7066 (all A (v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_lattice3(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)) -> (v18_quantal1(B,A) -> k2_quantal1(A,k2_quantal1(A,k2_quantal1(A,C,B),B),B) = k2_quantal1(A,C,B) & k1_quantal1(A,k1_quantal1(A,k1_quantal1(A,C,B),B),B) = k1_quantal1(A,C,B)))))))) # label(t17_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7067 (all A (v10_lattices(A) & v4_lattice3(A) & l3_lattices(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) -> (v14_quantal1(B,A) -> ((all C (m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) -> k15_lattice3(A,a_3_5_quantal1(A,B,C)) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k15_lattice3(A,C)))) <-> v15_quantal1(B,A))))))) # label(t10_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7068 (all A all B all C all D (l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) -> (r2_hidden(A,a_3_1_quantal1(B,C,D)) <-> (exists E (k4_monoid_0(B,E,C) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7069 (exists A l1_quantal1(A)) # label(existence_l1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7070 (all A (-v3_struct_0(A) & l3_lattices(A) -> (all B (-v3_struct_0(B) & l3_lattices(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)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> (all D (m1_subset_1(D,u1_struct_0(B)) -> (all E (C = D -> (r4_lattice3(A,C,E) -> r4_lattice3(B,D,E)) & (r4_lattice3(B,D,E) -> r4_lattice3(A,C,E)) & (r3_lattice3(B,D,E) -> r3_lattice3(A,C,E)) & (r3_lattice3(A,C,E) -> r3_lattice3(B,D,E))))))))))))) # label(t2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7071 (all A (-v3_struct_0(A) & v4_lattice3(A) & v20_quantal1(A) & v21_quantal1(A) & l3_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v2_group_1(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) -> r3_lattices(A,k5_quantal1(A,C),k5_quantal1(A,B))))))))) # label(t23_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7072 (all A (r2_hidden(A,a_0_0_quantal1) <-> (exists B (m1_subset_1(B,f2_s1_quantal1) & r2_hidden(B,a_0_1_quantal1) & A = f3_s1_quantal1(B))))) # label(fraenkel_a_0_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7073 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v2_group_1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> k4_monoid_0(A,k4_quantal1(A),B) = B & k4_monoid_0(A,B,k4_quantal1(A)) = B)))) # label(t32_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7074 (all A all B all C all D (-v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) -> v2_quantal1(g1_quantal1(A,B,C,D)) & -v3_struct_0(g1_quantal1(A,B,C,D)))) # label(fc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7075 (all A (l1_quantal1(A) -> l1_group_1(A) & l3_lattices(A))) # label(dt_l1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7076 (all A (l3_quantal1(A) & -v3_struct_0(A) -> (g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = k1_lattice3(k1_xboole_0) -> v20_quantal1(A) & v21_quantal1(A)))) # label(t21_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.82/184.96 7077 (all A all B all C all D (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_1(B) -> (all E all F all G all H (g1_quantal1(A,B,C,D) = g1_quantal1(E,F,G,H) -> B = F & D = H & C = G & A = E)))) # label(free_g1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7078 (all A ((exists B (p1_s2_quantal1(B) & f2_s2_quantal1(B) = A & m1_subset_1(B,f1_s2_quantal1))) <-> r2_hidden(A,a_0_3_quantal1))) # label(fraenkel_a_0_3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7079 (all A (l1_group_1(A) -> (-v3_struct_0(A) & v6_quantal1(A) -> -v3_struct_0(A) & v4_quantal1(A) & v5_quantal1(A)))) # label(cc1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7080 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (k1_lattice3(k1_xboole_0) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) -> v6_quantal1(A) & v7_quantal1(A) & v8_quantal1(A) & v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v7_group_1(A) & v4_group_1(A)))) # label(t4_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7081 (all A (-v3_struct_0(A) & l3_lattices(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) -> (v13_quantal1(B,A) <-> (all C (m1_subset_1(C,u1_struct_0(A)) -> r1_lattices(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),C)))))))) # label(d11_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7082 (all A all B all C all D (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_1(D) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_relset_1(D,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) -> l1_quantal1(g1_quantal1(A,B,C,D)) & v2_quantal1(g1_quantal1(A,B,C,D)))) # label(dt_g1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7083 (all A (l3_quantal1(A) -> (v19_quantal1(A) -> A = g3_quantal1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_group_1(A),u1_vectsp_1(A),u1_quantal1(A))))) # label(abstractness_v19_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7084 (all A (-v3_struct_0(A) & v4_lattice3(A) & v4_group_1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v2_group_1(A) & v10_lattices(A) -> (all B k5_quantal1(A,k15_lattice3(A,B)) = k16_lattice3(A,a_2_0_quantal1(A,B))))) # label(t24_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7085 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (m1_subset_1(C,u1_struct_0(A)) -> k2_quantal1(A,B,C) = k15_lattice3(A,a_3_7_quantal1(A,B,C)))))))) # label(d16_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7086 (all A (l1_quantal1(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)) -> k15_lattice3(A,a_3_6_quantal1(A,B,C)) = k1_quantal1(A,B,C))))))) # label(d15_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7087 (all A all B all C (v10_lattices(A) & v4_lattice3(A) & v2_group_1(A) & v21_quantal1(A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(B,u1_struct_0(A)) & l3_quantal1(A) & v20_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & -v3_struct_0(A) -> m1_subset_1(k9_quantal1(A,B,C),u1_struct_0(A)))) # label(dt_k9_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7088 (exists A l3_quantal1(A)) # label(existence_l3_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7089 (exists A (v19_quantal1(A) & l3_quantal1(A))) # label(rc10_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7090 (exists A (l3_quantal1(A) & -v3_struct_0(A) & v4_lattices(A) & v7_lattices(A) & v9_lattices(A) & v2_group_1(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & v10_quantal1(A) & v20_quantal1(A) & v21_quantal1(A) & v19_quantal1(A) & v9_quantal1(A) & v7_group_1(A) & v4_lattice3(A) & v10_lattices(A) & v8_lattices(A) & v6_lattices(A) & v5_lattices(A))) # label(rc12_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7091 (all A (-v3_struct_0(A) & v4_lattice3(A) & v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(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,k4_monoid_0(A,B,C),D) <-> r3_lattices(A,B,k1_quantal1(A,C,D))))))))))) # label(t12_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7092 (all A (v10_lattices(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v4_lattice3(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,k9_quantal1(A,B,D),k9_quantal1(A,C,E))))))))))))) # label(t30_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7093 (exists A (-v3_struct_0(A) & l3_quantal1(A))) # label(rc11_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7094 (all A (l3_lattices(A) & -v3_struct_0(A) -> (all B (-v3_struct_0(B) & l3_lattices(B) -> (g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(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 & D = F -> k2_lattices(B,E,F) = k2_lattices(A,C,D) & (r1_lattices(A,C,D) -> r1_lattices(B,E,F)) & (r1_lattices(B,E,F) -> r1_lattices(A,C,D)) & k1_lattices(B,E,F) = k1_lattices(A,C,D))))))))))))))) # label(t1_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7095 (all A ((exists B exists C (m1_subset_1(B,u1_struct_0(f1_s3_quantal1)) & A = f2_s3_quantal1(B,C) & r2_hidden(C,f4_s3_quantal1) & r2_hidden(B,f3_s3_quantal1) & m1_subset_1(C,u1_struct_0(f1_s3_quantal1)))) <-> r2_hidden(A,a_0_5_quantal1))) # label(fraenkel_a_0_5_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7096 (all A (v10_lattices(A) & v7_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v2_group_1(A) & v4_lattice3(A) & -v3_struct_0(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k15_lattice3(A,a_3_8_quantal1(A,B,C)) = k4_monoid_0(A,B,k15_lattice3(A,C)) & k16_lattice3(A,a_3_9_quantal1(A,B,C)) = k9_quantal1(A,B,k16_lattice3(A,C)))))))) # label(t27_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7097 (all A (-v3_struct_0(A) & v10_lattices(A) & v8_quantal1(A) & l1_quantal1(A) & v7_quantal1(A) & v4_group_1(A) & v4_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)) -> (r3_lattices(A,B,C) -> r3_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) & r3_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C))))))))))) # label(t8_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7098 (all A all B all C all D (m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & l1_quantal1(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_2_quantal1(B,C,D)) <-> (exists E exists F (m1_subset_1(F,u1_struct_0(B)) & A = k4_monoid_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_2_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7099 (all A all B all C all D (v4_group_1(B) & v7_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & v21_quantal1(B) & v20_quantal1(B) & v8_quantal1(B) & v2_group_1(B) & v4_lattice3(B) & v10_lattices(B) & -v3_struct_0(B) -> (r2_hidden(A,a_3_11_quantal1(B,C,D)) <-> (exists E (A = k9_quantal1(B,E,C) & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B))))))) # label(fraenkel_a_3_11_quantal1) # label(axiom) # label(non_clause). [assumption]. 183.84/184.96 7100 (all A all B all C all D all E (-v1_xboole_0(A) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & v1_funct_1(B) -> -v3_struct_0(g2_quantal1(A,B,C,D,E)) & v3_quantal1(g2_quantal1(A,B,C,D,E)))) # label(fc2_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7101 (all A (l2_quantal1(A) -> (-v3_struct_0(A) & v10_lattices(A) & v7_quantal1(A) & v8_quantal1(A) & v4_lattice3(A) -> v5_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v4_lattice3(A) & v10_quantal1(A) & v9_quantal1(A) & v10_lattices(A) & v6_lattices(A) & v4_lattices(A) & -v3_struct_0(A)))) # label(cc3_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7102 (all A (-v3_struct_0(A) & l1_quantal1(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k2_quantal1(A,C,B) = k1_quantal1(A,C,B))) <-> v18_quantal1(B,A)))))) # label(d18_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7103 (all A all B all C all D all E (v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) & v1_funct_1(D) & m1_relset_1(D,k2_zfmisc_1(A,A),A) & m1_subset_1(E,A) & v1_funct_2(D,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) -> l2_quantal1(g2_quantal1(A,B,C,D,E)) & v3_quantal1(g2_quantal1(A,B,C,D,E)))) # label(dt_g2_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7104 (all A all B all C all D (l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & -v3_struct_0(B) -> ((exists E (k4_monoid_0(B,C,E) = A & r2_hidden(E,D) & m1_subset_1(E,u1_struct_0(B)))) <-> r2_hidden(A,a_3_0_quantal1(B,C,D))))) # label(fraenkel_a_3_0_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7105 (all A (-v3_struct_0(A) & v10_lattices(A) & v4_group_1(A) & v7_quantal1(A) & v8_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v20_quantal1(A) & v2_group_1(A) & v4_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)) -> k4_lattices(A,k9_quantal1(A,C,B),k9_quantal1(A,D,B)) = k9_quantal1(A,k4_lattices(A,C,D),B) & k9_quantal1(A,B,k4_lattices(A,C,D)) = k4_lattices(A,k9_quantal1(A,B,C),k9_quantal1(A,B,D)))))))))) # label(t29_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7106 (all A (l1_quantal1(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_monoid_0(A,k1_lattices(A,B,C),D) = k1_lattices(A,k4_monoid_0(A,B,D),k4_monoid_0(A,C,D)) & k1_lattices(A,k4_monoid_0(A,D,B),k4_monoid_0(A,D,C)) = k4_monoid_0(A,D,k1_lattices(A,B,C)))))))) <-> v9_quantal1(A)))) # label(d7_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7107 (all A (-v3_struct_0(A) & v4_group_1(A) & v7_quantal1(A) & v20_quantal1(A) & l3_quantal1(A) & v21_quantal1(A) & v8_quantal1(A) & v2_group_1(A) & v4_lattice3(A) & v10_lattices(A) -> (all B (m1_subset_1(B,u1_struct_0(A)) -> (all C (k16_lattice3(A,a_3_11_quantal1(A,B,C)) = k9_quantal1(A,k16_lattice3(A,C),B) & k15_lattice3(A,a_3_10_quantal1(A,B,C)) = k4_monoid_0(A,k15_lattice3(A,C),B))))))) # label(t28_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7108 (all A (l3_quantal1(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)) -> ((all C (m1_subset_1(C,u1_struct_0(A)) -> k5_quantal1(A,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C))) <-> B = k6_quantal1(A)))))) # label(d24_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7109 (all A (v7_quantal1(A) & l1_quantal1(A) & v8_quantal1(A) & v4_group_1(A) & v4_lattice3(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,C,D) -> r3_lattices(A,k1_quantal1(A,D,B),k1_quantal1(A,C,B)) & r3_lattices(A,k2_quantal1(A,D,B),k2_quantal1(A,C,B))))))))))) # label(t13_quantal1) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7110 (all A (m1_subset_1(A,f1_s1_cat_5) -> (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (all E (m1_subset_1(E,f2_s1_cat_5) -> (p1_s1_cat_5(B,C,E) & p1_s1_cat_5(A,B,D) -> r2_hidden(f3_s1_cat_5(E,D),f2_s1_cat_5) & p1_s1_cat_5(A,C,f3_s1_cat_5(E,D))))))))))))) & (all A (m1_subset_1(A,f1_s1_cat_5) -> (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f1_s1_cat_5) -> (all E (m1_subset_1(E,f2_s1_cat_5) -> (all F (m1_subset_1(F,f2_s1_cat_5) -> (all G (m1_subset_1(G,f2_s1_cat_5) -> (p1_s1_cat_5(A,B,E) & p1_s1_cat_5(C,D,G) & p1_s1_cat_5(B,C,F) -> f3_s1_cat_5(G,f3_s1_cat_5(F,E)) = f3_s1_cat_5(f3_s1_cat_5(G,F),E)))))))))))))))) & (all A (m1_subset_1(A,f1_s1_cat_5) -> (exists B (m1_subset_1(B,f2_s1_cat_5) & (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (p1_s1_cat_5(A,C,D) -> f3_s1_cat_5(D,B) = D) & (p1_s1_cat_5(C,A,D) -> f3_s1_cat_5(B,D) = D))))) & p1_s1_cat_5(A,A,B))))) -> (exists A (v1_cat_1(A) & v2_cat_1(A) & (all B (m1_subset_1(B,f1_s1_cat_5) -> (all C (m1_subset_1(C,f1_s1_cat_5) -> (all D (m1_subset_1(D,f2_s1_cat_5) -> (p1_s1_cat_5(B,C,D) -> m1_subset_1(k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,B,C),D),u2_cat_1(A))))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (all D (m1_subset_1(D,f1_s1_cat_5) -> (all E (m1_subset_1(E,f1_s1_cat_5) -> (all F (m1_subset_1(F,f1_s1_cat_5) -> (all G (m1_subset_1(G,f2_s1_cat_5) -> (all H (m1_subset_1(H,f2_s1_cat_5) -> (k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,E),G) = B & k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,E,F),H) = C -> k4_tarski(k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,D,F),f3_s1_cat_5(H,G)) = k4_cat_1(A,B,C)))))))))))))))) & (all B (m1_subset_1(B,u2_cat_1(A)) -> (exists C ((exists D ((exists E (p1_s1_cat_5(C,D,E) & k1_domain_1(k2_zfmisc_1(f1_s1_cat_5,f1_s1_cat_5),f2_s1_cat_5,k1_domain_1(f1_s1_cat_5,f1_s1_cat_5,C,D),E) = B & m1_subset_1(E,f2_s1_cat_5))) & m1_subset_1(D,f1_s1_cat_5))) & m1_subset_1(C,f1_s1_cat_5))))) & u1_cat_1(A) = f1_s1_cat_5 & l1_cat_1(A) & v1_cat_5(A))) # label(s1_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7111 (all A all B (m1_subset_1(B,u1_cat_1(A)) & l1_cat_1(A) & v2_cat_1(A) -> -v1_xboole_0(k12_cat_5(A,B)))) # label(fc1_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7112 (all A all B (v2_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) & v3_cat_5(A) -> k9_cat_5(A,B) = k18_mcart_1(B))) # label(redefinition_k9_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7113 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m2_cat_1(C,A,B) -> m2_cat_1(C,A,k7_cat_5(A,B,C)))))))) # label(t8_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7114 (all A all B all C all D (-v1_xboole_0(C) & m1_subset_1(D,k2_zfmisc_1(k2_zfmisc_1(A,B),C)) & -v1_xboole_0(B) & -v1_xboole_0(A) -> m1_subset_1(k1_cat_5(A,B,C,D),A))) # label(dt_k1_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7115 (exists A (v2_cat_5(A) & -v1_xboole_0(A))) # label(rc2_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7116 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & m1_subset_1(B,u1_cat_1(A)) -> k17_mcart_1(C) = k17_cat_5(A,B,C))) # label(redefinition_k17_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7117 (all A (v2_cat_5(A) & -v1_xboole_0(A) -> (all B (m1_subset_1(B,A) <-> m1_cat_5(B,A))))) # label(redefinition_m1_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7118 (all A all B (v1_cat_5(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k4_cat_5(A,B),u1_cat_1(A)))) # label(dt_k4_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7119 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & v3_cat_5(A) -> k2_mcart_1(B) = k11_cat_5(A,B))) # label(redefinition_k11_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7120 (all A all B all C (l1_cat_1(A) & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) & m1_subset_1(B,u1_cat_1(A)) & v2_cat_1(A) -> m1_subset_1(k19_cat_5(A,B,C),u2_cat_1(A)))) # label(dt_k19_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.64/189.81 7121 (all A (-v1_xboole_0(A) -> ((all B (m1_subset_1(B,A) -> l1_cat_1(B) & v2_cat_1(B))) <-> v2_cat_5(A)))) # label(d5_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7122 (all A (v2_cat_1(A) & v3_cat_5(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> v3_cat_5(B))))) # label(cc2_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7123 (all A (-v1_xboole_0(A) & v2_cat_5(A) -> (all B (-v1_xboole_0(B) -> -((all C (m1_cat_5(C,A) -> (all D (m1_cat_5(D,A) -> (all E (m1_cat_5(E,A) -> (all F (m2_cat_1(F,C,D) -> (all G (m2_cat_1(G,D,E) -> (r2_hidden(G,B) & r2_hidden(F,B) -> r2_hidden(k14_cat_1(C,D,E,F,G),B)))))))))))) & (all C (v1_cat_1(C) & v2_cat_1(C) & v3_cat_5(C) & l1_cat_1(C) -> -((all D (m1_cat_5(D,A) -> (all E (m1_cat_5(E,A) -> (all F (m2_cat_1(F,D,E) -> (r2_hidden(F,B) <-> m1_subset_1(k1_domain_1(k2_zfmisc_1(A,A),k1_zfmisc_1(k2_zfmisc_1(u2_cat_1(D),u2_cat_1(E))),k1_domain_1(A,A,D,E),F),u2_cat_1(C))))))))) & A = u1_cat_1(C)))) & (all C (m1_cat_5(C,A) -> r2_hidden(k15_cat_1(C),B)))))))) # label(t17_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7124 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (v1_cat_1(C) & l1_cat_1(C) & v1_cat_5(C) & v2_cat_1(C) -> (k14_cat_5(A,B) = C <-> (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> (all F (m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B)) -> (all G (m2_subset_1(G,u2_cat_1(A),k12_cat_5(A,B)) -> (all H (m2_subset_1(H,u2_cat_1(A),k12_cat_5(A,B)) -> (all I (m1_subset_1(I,u2_cat_1(A)) -> (all J (m1_subset_1(J,u2_cat_1(A)) -> (E = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,G,H),J) & k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,G),I) = D -> k4_cat_1(C,D,E) = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,H),k4_cat_1(A,I,J))))))))))))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (exists E ((exists F ((exists G (m1_subset_1(G,u2_cat_1(A)) & k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,E,F),G) = D & E = k4_cat_1(A,G,F) & k2_cat_1(A,F) = k3_cat_1(A,G))) & m2_subset_1(F,u2_cat_1(A),k12_cat_5(A,B)))) & m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B)))))) & (all D (m2_subset_1(D,u2_cat_1(A),k12_cat_5(A,B)) -> (all E (m2_subset_1(E,u2_cat_1(A),k12_cat_5(A,B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k4_cat_1(A,F,E) = D & k3_cat_1(A,F) = k2_cat_1(A,E) -> m1_subset_1(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,D,E),F),u2_cat_1(C))))))))) & k12_cat_5(A,B) = u1_cat_1(C)))))))) # label(d11_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7125 (exists A (v1_cat_5(A) & v3_cat_5(A) & v2_cat_1(A) & v1_cat_1(A) & l1_cat_1(A))) # label(rc3_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7126 (all A (l1_cat_1(A) -> (all B (l1_cat_1(B) -> (v2_cat_1(A) & g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) -> v2_cat_1(B)))))) # label(t1_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7127 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A)) & v3_cat_5(A) -> v3_cat_5(B)))))) # label(t10_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7128 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) & l1_cat_1(A) & v2_cat_1(A) -> m2_subset_1(k18_cat_5(A,B,C),u2_cat_1(A),k12_cat_5(A,B)))) # label(dt_k18_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7129 (all A all B all C (m1_subset_1(B,u1_cat_1(A)) & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) & l1_cat_1(A) & v2_cat_1(A) -> k2_mcart_1(C) = k19_cat_5(A,B,C))) # label(redefinition_k19_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7130 (all A all B (v1_cat_5(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> k18_mcart_1(B) = k5_cat_5(A,B))) # label(redefinition_k5_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7131 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_funct_2(u2_cat_1(A),u1_cat_1(A),u4_cat_1(A),k6_domain_1(u1_cat_1(A),B)) = k12_cat_5(A,B))))) # label(d9_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7132 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (r2_hidden(C,k12_cat_5(A,B)) <-> B = k3_cat_1(A,C)))))))) # label(t23_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7133 (all A (v4_cat_5(A) & l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> (all B (v3_cat_5(B) & l1_cat_1(B) & v4_cat_5(B) & v2_cat_1(B) -> (u1_cat_1(B) = u1_cat_1(A) -> g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))))))) # label(t19_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7134 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m3_cat_2(B,A) -> (m3_cat_2(A,B) -> g1_cat_1(u1_cat_1(B),u2_cat_1(B),u3_cat_1(B),u4_cat_1(B),u5_cat_1(B),u6_cat_1(B)) = g1_cat_1(u1_cat_1(A),u2_cat_1(A),u3_cat_1(A),u4_cat_1(A),u5_cat_1(A),u6_cat_1(A))))))) # label(t3_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7135 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> k3_funct_2(u2_cat_1(A),u1_cat_1(A),u3_cat_1(A),k6_domain_1(u1_cat_1(A),B)) = k13_cat_5(A,B))))) # label(d10_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7136 (all A all B (v2_cat_1(A) & v3_cat_5(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> l1_cat_1(k9_cat_5(A,B)) & v2_cat_1(k9_cat_5(A,B)))) # label(dt_k9_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7137 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (m3_cat_2(C,B) -> (all D (m2_cat_1(D,A,C) -> (all E (m2_cat_1(E,A,B) -> (D = E -> k7_cat_5(A,C,D) = k7_cat_5(A,B,E)))))))))))) # label(t9_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7138 (all A (v2_cat_5(A) <-> (all B (r2_hidden(B,A) -> v2_cat_1(B) & l1_cat_1(B))))) # label(d4_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7139 (all A (v2_cat_1(A) & l1_cat_1(A) & v3_cat_5(A) -> (all B (l1_cat_1(B) & v4_cat_5(B) & v3_cat_5(B) & v2_cat_1(B) -> (r1_tarski(u1_cat_1(A),u1_cat_1(B)) -> m3_cat_2(A,B)))))) # label(t21_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7140 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(k14_cat_5(A,B))) -> k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,k17_cat_5(A,B,C),k18_cat_5(A,B,C)),k16_cat_5(A,B,C)) = C & k17_cat_5(A,B,C) = k4_cat_1(A,k16_cat_5(A,B,C),k18_cat_5(A,B,C)) & k2_cat_1(k14_cat_5(A,B),C) = k17_cat_5(A,B,C) & k3_cat_1(k14_cat_5(A,B),C) = k18_cat_5(A,B,C) & k3_cat_1(A,k16_cat_5(A,B,C)) = k2_cat_1(A,k18_cat_5(A,B,C)))))))) # label(t29_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7141 (all A all B (v1_cat_5(A) & l1_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) -> m1_subset_1(k5_cat_5(A,B),u1_cat_1(A)))) # label(dt_k5_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7142 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> m1_subset_1(k12_cat_5(A,B),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k12_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7143 (all A all B all C (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(C,u2_cat_1(k15_cat_5(A,B))) & m1_subset_1(B,u1_cat_1(A)) -> m2_subset_1(k20_cat_5(A,B,C),u2_cat_1(A),k13_cat_5(A,B)))) # label(dt_k20_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7144 (all A (l1_cat_1(k10_cat_5(A)) & v2_cat_1(k10_cat_5(A)))) # label(dt_k10_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7145 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u2_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k3_cat_1(A,B) = k2_cat_1(A,C) -> k1_partfun1(u2_cat_1(k14_cat_5(A,k2_cat_1(A,B))),u2_cat_1(k14_cat_5(A,k3_cat_1(A,B))),u2_cat_1(k14_cat_5(A,k2_cat_1(A,C))),u2_cat_1(k14_cat_5(A,k3_cat_1(A,C))),k22_cat_5(A,B),k22_cat_5(A,C)) = k22_cat_5(A,k4_cat_1(A,B,C))))))))) # label(t33_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.83 7146 (all A (v3_cat_5(A) & l1_cat_1(A) & v2_cat_1(A) -> ((all B (v2_cat_1(B) & l1_cat_1(B) -> (all C (v2_cat_1(C) & l1_cat_1(C) -> (m1_subset_1(C,u1_cat_1(A)) & m1_subset_1(B,u1_cat_1(A)) -> (all D (m2_cat_1(D,B,C) -> m1_subset_1(k4_tarski(k4_tarski(B,C),D),u2_cat_1(A))))))))) <-> v4_cat_5(A)))) # label(d8_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7147 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> v2_cat_1(k14_cat_5(A,B)) & l1_cat_1(k14_cat_5(A,B)) & v1_cat_5(k14_cat_5(A,B)) & v1_cat_1(k14_cat_5(A,B)))) # label(dt_k14_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7148 (all A (v2_cat_5(A) & -v1_xboole_0(A) -> (exists B (v2_cat_1(B) & l1_cat_1(B) & A = u1_cat_1(B) & v4_cat_5(B) & v3_cat_5(B) & v1_cat_1(B))))) # label(t20_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7149 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (m1_subset_1(C,u2_cat_1(A)) -> (k2_cat_1(A,C) = B <-> r2_hidden(C,k13_cat_5(A,B))))))))) # label(t24_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7150 (all A (l1_cat_1(A) & v3_cat_5(A) & v2_cat_1(A) -> (all B (l1_cat_1(B) & v3_cat_5(B) & v2_cat_1(B) -> (r1_tarski(u2_cat_1(A),u2_cat_1(B)) -> m3_cat_2(A,B)))))) # label(t15_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7151 (all A (l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> (all C (v1_cat_5(C) & l1_cat_1(C) & v2_cat_1(C) & v1_cat_1(C) -> (C = k15_cat_5(A,B) <-> k13_cat_5(A,B) = u1_cat_1(C) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (all E (m1_subset_1(E,u2_cat_1(C)) -> (all F (m2_subset_1(F,u2_cat_1(A),k13_cat_5(A,B)) -> (all G (m2_subset_1(G,u2_cat_1(A),k13_cat_5(A,B)) -> (all H (m2_subset_1(H,u2_cat_1(A),k13_cat_5(A,B)) -> (all I (m1_subset_1(I,u2_cat_1(A)) -> (all J (m1_subset_1(J,u2_cat_1(A)) -> (E = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,G,H),J) & D = k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,G),I) -> k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,F,H),k4_cat_1(A,I,J)) = k4_cat_1(C,D,E)))))))))))))))) & (all D (m1_subset_1(D,u2_cat_1(C)) -> (exists E (m2_subset_1(E,u2_cat_1(A),k13_cat_5(A,B)) & (exists F (m2_subset_1(F,u2_cat_1(A),k13_cat_5(A,B)) & (exists G (k3_cat_1(A,E) = k2_cat_1(A,G) & k4_cat_1(A,E,G) = F & k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,E,F),G) = D & m1_subset_1(G,u2_cat_1(A)))))))))) & (all D (m2_subset_1(D,u2_cat_1(A),k13_cat_5(A,B)) -> (all E (m2_subset_1(E,u2_cat_1(A),k13_cat_5(A,B)) -> (all F (m1_subset_1(F,u2_cat_1(A)) -> (k2_cat_1(A,F) = k3_cat_1(A,D) & k4_cat_1(A,D,F) = E -> m1_subset_1(k13_cat_2(k11_cat_2(A,A),A,k13_cat_2(A,A,D,E),F),u2_cat_1(C)))))))))))))))) # label(d12_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7152 (all A all B (v2_cat_1(A) & m1_subset_1(B,u2_cat_1(A)) & l1_cat_1(A) -> m2_cat_1(k23_cat_5(A,B),k15_cat_5(A,k3_cat_1(A,B)),k15_cat_5(A,k2_cat_1(A,B))))) # label(dt_k23_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7153 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (m3_cat_2(B,A) -> (all C (m3_cat_2(C,A) -> (-r2_subset_1(u1_cat_1(B),u1_cat_1(C)) -> m3_cat_2(k6_cat_5(B,C),C) & m3_cat_2(k6_cat_5(B,C),B)))))))) # label(t6_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7154 (exists A (l1_cat_1(A) & v2_cat_1(A) & v1_cat_5(A) & v1_cat_1(A))) # label(rc1_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7155 (all A (v2_cat_1(A) & l1_cat_1(A) -> (all B (l1_cat_1(B) & v2_cat_1(B) -> (all C (m3_cat_2(C,B) -> (all D (m2_cat_1(D,A,B) -> (r1_tarski(k2_relat_1(D),u2_cat_1(C)) -> m2_cat_1(D,A,C)))))))))) # label(t7_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7156 (all A all B (v2_cat_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_cat_1(A)) -> m1_subset_1(k13_cat_5(A,B),k1_zfmisc_1(u2_cat_1(A))))) # label(dt_k13_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7157 (all A (v2_cat_1(A) & v3_cat_5(A) & l1_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> v2_cat_1(B) & l1_cat_1(B))))) # label(t12_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7158 (all A (v3_cat_5(A) & l1_cat_1(A) & v2_cat_1(A) -> (all B (m1_subset_1(B,u1_cat_1(A)) -> B = k10_cat_5(B))))) # label(t16_cat_5) # label(axiom) # label(non_clause). [assumption]. 188.69/189.85 7159 (all ACputime limit exceeded (core dumped) 300.09/301.23 EOF